Attribution Models in Marketing

Attribution Models

A Business and Statistical Case


A desire to understand the causal effect of campaigns on KPIs

Advertising and marketing costs represent a huge and ever more growing part of the budget of companies. Studies have found out this share is as high as 10% and increases with the size of companies (CMO study by American Marketing Association and Duke University, 2017). Measuring precisely the impact of a specific marketing campaign on the sales of a company is a critical step towards an efficient allocation of this budget. Would the return be higher for an euro spent on a Facebook ad, or should we better spend it on a TV spot? How much should I spend on Twitter ads given the volume of sales this channel is responsible for?

Attribution Models have lately received great attention in Marketing departments to answer these issues. The transition from offline to online marketing methods has indeed permitted the collection of multiple individual data throughout the whole customer journey, and  allowed for the development of user-centric attribution models. In short, Attribution Models use the information provided by Tracking technologies such as Google Analytics or Webtrekk to understand customer journeys from the first click on a Facebook ad to the final purchase and adequately ponderate the different marketing campaigns encountered depending on their responsibility in the final conversion.

Issues on Causal Effects

A key question then becomes: how to declare a channel is responsible for a purchase? In other words, how can we isolate the causal effect or incremental value of a campaign ?

          1. A/B-Tests

One method to estimate the pure impact of a campaign is the design of randomized experiments, wherein a control and treated groups are compared.  A/B tests belong to this broad category of randomized methods. Provided the groups are a priori similar in every aspect except for the treatment received, all subsequent differences may be attributed solely to the treatment. This method is typically used in medical studies to assess the effect of a drug to cure a disease.

Main practical issues regarding Randomized Methods are:

  • Assuring that control and treated groups are really similar before treatment. Uually a random assignment (i.e assuring that on a relevant set of observable variables groups are similar) is realized;
  • Potential spillover-effects, i.e the possibility that the treatment has an impact on the non-treated group as well (Stable unit treatment Value Assumption, or SUTVA in Rubin’s framework);
  • The costs of conducting such an experiment, and especially the costs linked to the deliberate assignment of individuals to a group with potentially lower results;
  • The number of such experiments to design if multiple treatments have to be measured;
  • Difficulties taking into account the interaction effects between campaigns or the effect of spending levels. Indeed, usually A/B tests are led by cutting off temporarily one campaign entirely and measuring the subsequent impact on KPI’s compared to the situation where this campaign is maintained;
  • The dynamical reproduction of experiments if we assume that treatment effects may change over time.

In the marketing context, multiple campaigns must be tested in a dynamical way, and treatment effect is likely to be heterogeneous among customers, leading to practical issues in the lauching of A/B tests to approximate the incremental value of all campaigns. However, sites with a lot of traffic and conversions can highly benefit from A/B testing as it provides a scientific and straightforward way to approximate a causal impact. Leading companies such as Uber, Netflix or Airbnb rely on internal tools for A/B testing automation, which allow them to basically test any decision they are about to make.



Experiment!: Website conversion rate optimization with A/B and multivariate testing, Colin McFarland, ©2013 | New Riders  

A/B testing: the most powerful way to turn clicks into customers. Dan Siroker, Pete Koomen; Wiley, 2013.



        2. Attribution models

Attribution Models do not demand to create an experimental setting. They take into account existing data and derive insights from the variability of customer journeys. One key difficulty is then to differentiate correlation and causality in the links observed between the exposition to campaigns and purchases. Indeed, selection effects may bias results as exposure to campaigns is usually dependant on user-characteristics and thus may not be necessarily independant from the customer’s baseline conversion probabilities. For example, customers purchasing from a discount price comparison website may be intrinsically different from customers buying from FB ad and this a priori difference may alone explain post-exposure differences in purchasing bahaviours. This intrinsic weakness must be remembered when interpreting Attribution Models results.

                          2.1 General Issues

The main issues regarding the implementation of Attribution Models are linked to

  • Causality and fallacious reasonning, as most models do not take into account the aforementionned selection biases.
  • Their difficult evaluation. Indeed, in almost all attribution models (except for those based on classification, where the accuracy of the model can be computed), the additionnal value brought by the use of a given attribution models cannot be evaluated using existing historical data. This additionnal value can only be approximated by analysing how the implementation of the conclusions of the attribution model have impacted a given KPI.
  • Tracking issues, leading to an uncorrect reconstruction of customer journeys
    • Cross-device journeys: cross-device issue arises from the use of different devices throughout the customer journeys, making it difficult to link datapoints. For example, if a customer searches for a product on his computer but later orders it on his mobile, the AM would then mistakenly consider it an order without prior campaign exposure. Though difficult to measure perfectly, the proportion of cross-device orders can approximate 20-30%.
    • Cookies destruction makes it difficult to track the customer his the whole journey. Both regulations and consumers’ rising concerns about data privacy issues mitigate the reliability and use of cookies.1 – From 2002 on, the EU has enacted directives concerning privacy regulation and the extended use of cookies for commercial targeting purposes, which have highly impacted marketing strategies, such as the ‘Privacy and Electronic Communications Directive’ (2002/58/EC). A research was conducted and found out that the adoption of this ‘Privacy Directive’ had led to 64% decrease in advertising methods compared to the rest of the world (Goldfarb et Tucker (2011)). The effect was stronger for generalized sites (Yahoo) than for specialized sites.2 – Users have grown more and more conscious of data privacy issues and have adopted protective measures concerning data privacy, such as automatic destruction of cookies after a session is ended, or simply giving away less personnal information (Goldfarb et Tucker (2012) ) .Valuable user information may be lost, though tracking technologies evolution have permitted to maintain tracking by other means. This issue may be particularly important in countries highly concerned with data privacy issues such as Germany.
    • Offline/Online bridge: an Attribution Model should take into account all campaigns to draw valuable insights. However, the exposure to offline campaigns (TV, newspapers) are difficult to track at the user level. One idea to tackle this issue would be to estimate the proportion of conversions led by offline campaigns through AB testing and deduce this proportion from the credit assigned to the online campaigns accounted for in the Attribution Model.
    • Touch point information available: clicks are easy to follow but irrelevant to take into account the influence of purely visual campaigns such as display ads or video.

                          2.2 Today’s main practices

Two main families of Attribution Models exist:

  • Rule-Based Attribution Models, which have been used for in the last decade but from which companies are gradualy switching.

Attribution depends on the individual journeys that have led to a purchase and is solely based on the rank of the campaign in the journey. Some models focus on a single touch points (First Click, Last Click) while others account for multi-touch journeys (Bathtube, Linear). It can be calculated at the customer level and thus doesn’t require large amounts of data points. We can distinguish two sub-groups of rule-based Attribution Models:

  • One Touch Attribution Models attribute all credit to a single touch point. The First-Click model attributes all credit for a converion to the first touch point of the customer journey; last touch attributes all credit to the last campaign.
  • Multi-touch Rule-Based Attribution Models incorporate information on the whole customer journey are thus an improvement compared to one touch models. To this family belong Linear model where credit is split equally between all channels, Bathtube model where 40% of credit is given to first and last clicks and the remaining 20% is distributed equally between the middle channels, or time-decay models where credit assigned to a click diminishes as the time between the click and the order increases..

The main advantages of rule-based models is their simplicity and cost effectiveness. The main problems are:

– They are a priori known and can thus lead to optimization strategies from competitors
– They do not take into account aggregate intelligence on customer journeys and actual incremental values.
– They tend to bias (depending on the model chosen) channels that are over-represented at the beggining or end of the funnel, according to theoretical assumptions that have no observationnal back-ups.

  • Data-Driven Attribution Models

These models take into account the weaknesses of rule-based models and make a relevant use of available data. Being data-driven, following attribution models cannot be computed using single user level data. On the contrary values are calculated through data aggregation and thus require a certain volume of customer journey information.



        3. Data-Driven Attribution Models in practice

                          3.1 Issues

Several issues arise in the computation of campaigns individual impact on a given KPI within a data-driven model.

  • Selection biases: Exposure to certain types of advertisement is usually highly correlated to non-observable variables which are in turn correlated to consumption practices. Differences in the behaviour of users exposed to different campaigns may thus only be driven by core differences in conversion probabilities between groups whether than by the campaign effect.
  • Complementarity: it may be that campaigns A and B only have an effect when combined, so that measuring their individual impact would lead to misleading conclusions. The model could then try to assess the effect of combinations of campaigns on top of the effect of individual campaigns. As the number of possible non-ordered combinations of k campaigns is 2k, it becomes clear that inclusing all possible combinations would however be time-consuming.
  • Order-sensitivity: The effect of a campaign A may depend on the place where it appears in the customer journey, meaning the rank of a campaign and not merely its presence could be accounted for in the model.
  • Relative Order-sensitivity: it may be that campaigns A and B only have an effect when one is exposed to campaign A before campaign B. If so, it could be useful to assess the effect of given combinations of campaigns as well. And this for all campaigns, leading to tremendous numbers of possible combinations.
  • All previous phenomenon may be present, increasing even more the potential complexity of a comprehensive Attribution Model. The number of all possible ordered combination of k campaigns is indeed :


                          3.2 Main models

                                  A) Logistic Regression and Classification models

If non converting journeys are available, Attribition Model can be shaped as a simple classification issue. Campaign types or campaigns combination and volume of campaign types can be included in the model along with customer or time variables. As we are interested in inference (on campaigns effect) whether than prediction, a parametric model should be used, such as Logistic Regression. Non paramatric models such as Random Forests or Neural Networks can also be used though the interpretation of campaigns value would be more difficult to derive from the model results.

A common pitfall is the usual issue of spurious correlations on one hand and the correct interpretation of coefficients in business terms.

An advantage if the possibility to evaluate the relevance of the model using common model validation methods to evaluate its predictive power (validation set \ AUC \pseudo R squared).

                                  B) Shapley Value


The Shapley Value is based on a Game Theory framework and is named after its creator, the Nobel Price Laureate Lloyd Shapley. Initially meant to calculate the marginal contribution of players in cooperative games, the model has received much attention in research and industry and has lately been applied to marketing issues. This model is typically used by Google Adords and other ad bidding vendors. Campaigns or marketing channels are in this model seen as compementary players looking forward to increasing a given KPI.
Contrarily to Logistic Regressions, it is a non-parametric model. Contrarily to Markov Chains, all results are built using existing journeys, and not simulated ones.

Channels are considered to enter the game sequentially under a certain joining order. Shapley value try to The Shapley value of channel i is the weighted sum of the marginal values that channel i adds to all possible coalitions that don’t contain channel i.
In other words, the main logic is to analyse the difference of gains when a channel i is added after a coalition Ck of k channels, k<=n. We then sum all the marginal contributions over all possible ordered combination Ck of all campaigns excluding i, with k<=n-1.

Subsets framework

A first an most usual way to compute the Shapley Vaue is to consider that when a channel enters coalition, its additionnal value is the same irrelevant of the order in which previous channels have appeared. In other words, journeys (A>B>C) and (B>A>C) trigger the same gains.
Shapley value is computed as the gains associated to adding a channel i to a subset of channels, weighted by the number of (ordered) sequences that the (unordered) subset represents, summed up on all possible subsets of the total set of campaigns where the channel i is not present.
The Shapley value of the channel 𝑥𝑗 is then:

where |S| is the number of campaigns of a coalition S and the sum extends over all subsets S that do not not contain channel j. 𝜈(𝑆)  is the value of the coalition S and 𝜈(𝑆 ∪ {𝑥𝑗})  the value of the coalition formed by adding 𝑥𝑗 to coalition S. 𝜈(𝑆 ∪ {𝑥𝑗}) − 𝜈(𝑆) is thus the marginal contribution of channel 𝑥𝑗 to the coalition S.

The formula can be rewritten and understood as:

This method is convenient when data on the gains of on all possible permutations of all unordered k subsets of the n campaigns are available. It is also more convenient if the order of campaigns prior to the introduction of a campaign is thought to have no impact.

Ordered sequences

Let us define 𝜈((A>B)) as the value of the sequence A then B. What is we let 𝜈((A>B)) be different from 𝜈((B>A)) ?
This time we would need to sum over all possible permutation of the S campaigns present before  𝑥𝑗 and the N-(S+1) campaigns after 𝑥𝑗. Doing so we will sum over all possible orderings (i.e all permutations of the n campaigns of the grand coalition containing all campaigns) and we can remove the permutation coefficient s!(p-s+1)!.

This method is convenient when the order of channels prior to and after the introduction of another channel is assumed to have an impact. It is also necessary to possess data for all possible permutations of all k subsets of the n campaigns, and not only on all (unordered) k-subsets of the n campaigns, k<=n. In other words, one must know the gains of A, B, C, A>B, B>A, etc. to compute the Shapley Value.

Differences between the two approaches

We simulate an ordered case where the value for each ordered sequence k for k<=3 is known. We compare it to the usual Shapley value calculated based on known gains of unordered subsets of campaigns. So as to compare relevant values, we have built the gains matrix so that the gains of a subset A, B i.e  𝜈({B,A}) is the average of the gains of ordered sequences made up with A and B (assuming the number of journeys where A>B equals the number of journeys where B>A, we have 𝜈({B,A})=0.5( 𝜈((A>B)) + 𝜈((B>A)) ). We let the value of the grand coalition be different depending on the order of campaigns-keeping the constraints that it averages to the value used for the unordered case.

Note: mvA refers to the marginal value of A in a given sequence.
With traditionnal unordered coalitions:

With ordered sequences used to compute the marginal values:


We can see that the two approaches yield very different results. In the unordered case, the Shapley Value campaign C is the highest, culminating at 20, while A and B have the same Shapley Value mvA=mvB=15. In the ordered case, campaign A has the highest Shapley Value and all campaigns have different Shapley Values.

This example illustrates the inherent differences between the set and sequences approach to Shapley values. Real life data is more likely to resemble the ordered case as conversion probabilities may for any given set of campaigns be influenced by the order through which the campaigns appear.


Shapley value has become popular in allocation problems in cooperative games because it is the unique allocation which satisfies different axioms:

  • Efficiency: Shaple Values of all channels add up to the total gains (here, orders) observed.
  • Symmetry: if channels A and B bring the same contribution to any coalition of campaigns, then their Shapley Value i sthe same
  • Null player: if a channel brings no additionnal gains to all coalitions, then its Shapley Value is zero
  • Strong monotony: the Shapley Value of a player increases weakly if all its marginal contributions increase weakly

These properties make the Shapley Value close to what we intuitively define as a fair attribution.


  • The Shapley Value is based on combinatory mathematics, and the number of possible coalitions and ordered sequences becomes huge when the number of campaigns increases.
  • If unordered, the Shapley Value assumes the contribution of campaign A is the same if followed by campaign B or by C.
  • If ordered, the number of combinations for which data must be available and sufficient is huge.
  • Channels rarely present or present in long journeys will be played down.
  • Generally, gains are supposed to grow with the number of players in the game. However, it is plausible that in the marketing context a journey with a high number of channels will not necessarily bring more orders than a journey with less channels involved.


R package: GameTheoryAllocation

Zhao & al, 2018 “Shapley Value Methods for Attribution Modeling in Online Advertising “

                                  B) Markov Chains

Markov Chains are used to model random processes, i.e events that occur in a sequential manner and in such a way that the probability to move to a certain state only depends on the past steps. The number of previous steps that are taken into account to model the transition probability is called the memory parameter of the sequence, and for the model to have a solution must be comprised between 0 and 4. A Markov Chain process is thus defined entirely by its Transition Matrix and its initial vector (i.e the starting point of the process).

Markov Chains are applied in many scientific fields. Typically, they are used in weather forecasting, with the sequence of Sunny and Rainy days following a Markov Process of memory parameter 0, so that for each given day the probability that the next day will be rainy or sunny only depends on the weather of the current day. Other applications can be found in sociology to understand the dynamics of social classes intergenerational reproduction. To get more both mathematical and applied illustration, I recommend the reading of this course.

In the marketing context, Markov Chains are an interesting way to model the conversion funnel. To go from the from the Markov Model to the Attribution logic, we calculate the Removal Effect of each channel, i.e the difference in conversions that happen if the channel is removed. Please read below for an introduction to the methodology.

The first step in a Markov Chains Attribution Model is to build the transition matrix that captures the transition probabilities between the campaigns accross existing customer journeys. This Matrix is to be read as a “From state A to state B” table, from the left to the right. A first difficulty is finding the right memory parameter to use. A large memory parameter would allow to take more into account interraction effects within the conversion funnel but would lead to increased computationnal time, a non-readable transition matrix, and be more sensitive to noisy data. Please note that this transition matrix provides useful information on the conversion funnel and on the relationships between campaigns and can be used as such as an analytical tool. I suggest the clear and easily R code which can be found here or here.

Here is an illustration of a Markov Chain with memory Parameter of 0: the probability to go to a certain campaign B in the next step only depend on the campaign we are currently at:

The associated Transition Matrix is then (with null probabilities left as Blank):

The second step is  to compute the actual responsibility of a channel in total conversions. As mentionned above, the main philosophy to do so is to calculate the Removal Effect of each channel, i.e the changes in the number of conversions when a channel is entirely removed. All customer journeys which went through this channel are settled out to be unsuccessful. This calculation is done by applying the transition matrix with and without the removed channels to an initial vector that contains the number of desired simulations.

Building on our current example, we can then settle an initial vector with the desired number of simulations, e.g 10 000:


It is possible at this stage to add a constraint on the maximum number of times the matrix is applied to the data, i.e on the maximal number of campaigns a simulated journey is allowed to have.


  • The dynamic journey is taken into account, as well as the transition between two states. The funnel is not assumed to be linear.
  • It is possile to build a conversion graph that maps the customer journey provides valuable insights.
  • It is possible to evaluate partly the accuracy of the Attribution Model based on Markov Chains. It is for example possible to see how well the transition matrix help predict the future by analysing the number of correct predictions at any given step over all sequences.


  • It can be somewhat difficult to set the memory parameter. Complementarity effects between channels are not well taken into account if the memory is low, but a parameter too high will lead to over-sensitivity to noise in the data and be difficult to implement if customer journeys tend to have a number of campaigns below this memory parameter.
  • Long journeys with different channels involved will be overweighted, as they will count many times in the Removal Effect.  For example, if there are n-1 channels in the customer journey, this journey will be considered as failure for the n-1 channel-RE. If the volume effects (i.e the impact of the overall number of channels in a journey, irrelevant from their type° are important then results may be biased.


R package: ChannelAttribution




“Mapping the Customer Journey: A Graph-Based Framework for Online Attribution Modeling”; Anderl, Eva and Becker, Ingo and Wangenheim, Florian V. and Schumann, Jan Hendrik, 2014. Available at SSRN: or

“Media Exposure through the Funnel: A Model of Multi-Stage Attribution”, Abhishek & al, 2012

“Multichannel Marketing Attribution Using Markov Chains”, Kakalejčík, L., Bucko, J., Resende, P.A.A. and Ferencova, M. Journal of Applied Management and Investments, Vol. 7 No. 1, pp. 49-60.  2018


                          3.3 To go further: Tackling selection biases with Quasi-Experiments

Exposure to certain types of advertisement is usually highly correlated to non-observable variables. Differences in the behaviour of users exposed to different campaigns may thus only be driven by core differences in converison probabilities between groups whether than by the campaign effect. These potential selection effects may bias the results obtained using historical data.

Quasi-Experiments can help correct this selection effect while still using available observationnal data.  These methods recreate the settings on a randomized setting. The goal is to come as close as possible to the ideal of comparing two populations that are identical in all respects except for the advertising exposure. However, populations might still differ with respect to some unobserved characteristics.

Common quasi-experimental methods used for instance in Public Policy Evaluation are:

  • Discontinuity Regressions
  • Matching Methods, such as Exact Matching,  Propensity-score matching or k-nearest neighbourghs.



“Towards a digital Attribution Model: Measuring the impact of display advertising on online consumer behaviour”, Anindya Ghose & al, MIS Quarterly Vol. 40 No. 4, pp. 1-XX, 2016

        4. First Steps towards a Practical Implementation

Identify key points of interests

  • Identify the nature of touchpoints available: is the data based on clicks? If so, is there a way to complement the data with A/B tests to measure the influence of ads without clicks (display, video) ? For example, what happens to sales when display campaign is removed? Analysing this multiplier effect would give the overall responsibility of display on sales, to be deduced from current attribution values given to click-based channels. More interestingly, what is the impact of the removal of display campaign on the occurences of click-based campaigns ? This would give us an idea of the impact of display ads on the exposure to each other campaigns, which would help correct the attribution values more precisely at the campaign level.
  • Define the KPI to track. From a pure Marketing perspective, looking at purchases may be sufficient, but from a financial perspective looking at profits, though a bit more difficult to compute, may drive more interesting results.
  • Define a customer journey. It may seem obvious, but the notion needs to be clarified at first. Would it be defined by a time limit? If so, which one? Does it end when a conversion is observed? For example, if a customer makes 2 purchases, would the campaigns he’s been exposed to before the first order still be accounted for in the second order? If so, with a time decay?
  • Define the research framework: are we interested only in customer journeys which have led to conversions or in all journeys? Keep in mind that successful customer journeys are a non-representative sample of customer journeys. Models built on the analysis of biased samples may be conservative. Take an extreme example: 80% of customers who see campaign A buy the product, VS 1% for campaign B. However, campaign B exposure is great and 100 Million people see it VS only 1M for campaign A. An Attribution Model based on successful journeys will give higher credit to campaign B which is an auguable conclusion. Taking into account costs per campaign (in the case where costs are calculated by clicks) may of course tackle this issue partly, as campaign A could then exhibit higher returns, but a serious fallacious reasonning is at stake here.

Analyse the typical customer journey    

  • Performing a duration analysis on the data may help you improve the definition of the customer journey to be used by your organization. After which days are converison probabilities null? Should we consider the effect of campaigns disappears after x days without orders? For example, if 99% of orders are placed in the 30 days following a first click, it might be interesting to define the customer journey as a 30 days time frame following the first oder.
  • Look at the distribution of the number of campaigns in a typical journey. If you choose to calculate the effect of campaigns interraction in your Attribution Model, it may indeed help you determine the maximum number of campaigns to be included in a combination. Indeed, you may not need to assess the impact of channel combinations with above than 4 different channels if 95% of orders are placed after less then 4 campaigns.
  • Transition matrixes: what if a campaign A systematically leads to a campaign B? What happens if we remove A or B? These insights would give clues to ask precise questions for a latter AB test, for example to find out if there is complementarity between channels A and B – (implying none should be removed) or mere substitution (implying one can be given up).
  • If conversion rates are available: it can be interesting to perform a survival analysis i.e to analyse the likelihood of conversion based on duration since first click. This could help us excluse potential outliers or individuals who have very low conversion probabilities.


Attribution is a complex topic which will probably never be definitively solved. Indeed, a main issue is the difficulty, or even impossibility, to evaluate precisely the accuracy of the attribution model that we’ve built. Attribution Models should be seen as a good yet always improvable approximation of the incremental values of campaigns, and be presented with their intrinsinc limits and biases.

Introduction to ROC Curve

The abbreviation ROC stands for Receiver Operating Characteristic. Its main purpose is to illustrate the diagnostic ability of classifier as the discrimination threshold is varied. It was developed during World War II when Radar operators had to decide if the blip on the screen is an enemy target, a friendly ship or just a noise.  For these purposes they measured the ability of a radar receiver operator to make these important distinctions, which was called the Receiver Operating Characteristic.

Later it was found useful in interpreting medical test results and then in Machine learning classification problems. In order to get an introduction to binary classification and terms like ‘precision’ and ‘recall’ one can look into my earlier blog  here.

True positive rate and false positive rate

Let’s imagine a situation where a fire alarm is installed in a kitchen. The alarm is supposed to emit a sound in case fire smoke is detected in the room. Unfortunately, there is a lot of cooking done in the kitchen and the alarm may trigger the sound too often. Thus, instead of serving a purpose the alarm becomes a nuisance due to a large number of false alarms. In statistical terms these types of errors are called type 1 errors, or false positives.

One way to deal with this problem is to simply decrease sensitivity of the device. We do this by increasing the trigger threshold at the alarm setting. But then, not every alarm should have the same threshold setting. Consider the same type of device but kept in a bedroom. With high threshold, the device might miss smoke from a real short-circuit in the wires which poses a real danger of fire. This kind of failure is called Type 2 error or a false negative. Although the two devices are the same, different types of threshold settings are optimal for different circumstances.

To specify this more formally, let us describe the performance of a binary classifier at a particular threshold by the following parameters:


These parameters take different values at different thresholds. Hence, they define the performance of the classifier at particular threshold. But we want to examine in overall how good a classifier is. Fortunately, there is a way to do that. We plot the True Positive Rate (TPR) and False Positive rate (FPR) at different thresholds and this plot is called ROC curve.

Let’s try to understand this with an example.

A case with a distinct population distribution

Let’s suppose there is a disease which can be identified with deficiency of some parameter (maybe a certain vitamin). The distribution of population with this disease has a mean vitamin concentration sharply distinct from the mean of a healthy population, as shown below.

This is result of dummy data simulating population of 2000 people,the link to the code is given  in the end of this blog.  As the two populations are distinctly separated (there is no  overlap between the two distributions), we can expect that a classifier would have an easy job distinquishing healthy from sick people. We can run a logistic regression classifier with a threshold of .5 and be 100% succesful in detecting the decease.

The confusion matrix may look something like this.

In this ideal case with a threshold  of  .5 we do not make a single wrong classification. The True positive rate and False positive rate are 1 and 0, respectively. But we can shift the threshold. In that case, we will  get different confusion matrices. First we plot threshold vs. TPR.

We see for most values of threshold the TPR is close to 1 which again proves data is easy to classify and the classifier is returning high probabilities  for the most of positives .

Similarly Let’s plot threshold vs. FPR.

For most of the data points FPR is close to zero. This is also good. Now its time to plot the ROC curve using these results (TPR vs FPR).

Let’s try to interpret  the results,  all the points lie on line x=0 and y=1, it means for all the points FPR is zero or TPR is one, making  the curve a square. which means the classifier does perfectly well.

Case with overlapping  population distribution

The above example was about a perfect classifer. However, life is often not so easy. Now let us consider another more realistic situation in which the parameter distribution of the population is not as distinct as in the previous case. Rather, the mean of the parameter with healthy and not healthy datapoints are close and the distributions overlap, as shown in the next figure.

If we set the threshold to 0.5, the confusion matrix may look like this.

Now, any new choice of threshold location will affect both false positives and false negatives. In fact, there is a trade-off. If we shift the threshold with the goal to reduce false negatives, false positives will increase. If we move the threshold to the other direction and reduce false positive, false negatives will increase.

The plots (TPR vs Threshold) , (FPR vs Threshold) are shown below

If we plot the ROC curve from these results, it looks like this:

From the curve we see the classifier does not perform as well as the earlier one.

What else can be infered from this curve? We first need to understand what the diagonal in this plot represent. The diagonal represents ‘Line of no discrimination’, which we obtain if we randomly guess. This is the ROC curve for the worst possible classifier. Therefore, by comparing the obtained ROC curve with the diagonal, we see how much better our classifer is from random guessing.

The further away ROC curve from the diagonal is (the closest it is to the top left corner) , better the classifier is.

Area Under the curve

The overall performance of the classifier is given by the area under the ROC curve and is usually denoted as AUC. Since TPR and FPR lie within the range of 0 to 1, the AUC also assumes values between 0 and 1. The higher the value of AUC, the better is the overall performance of the classifier.

Let’s see this for the two different distributions which we saw earlier.

As we know the classifier had worked perfectly in the first case with points at (0,1) the area under the curve is 1 which is perfect. In the latter case the classifier was not able to perform as good, the ROC curve is between the diagonal and left hand corner. The AUC as we can see is less than 1.

Some other general characteristics

There are still few points that needs to be discussed on a General ROC curve

  • The ROC curve does not provide information about the actual values of thresholds used for the classifier.
  • Performance of different classifiers can be compared using the AUC of different Classifier. The larger the AUC, the better the classifier.
  • The vertical distance of the ROC curve from the no discrimination line gives a measure of ‘INFORMEDNESS’. This is known as Youden’s J satistic. This statistics can take values between 0 and 1.

Youden’s  J statistic is defined for every point on the ROC curve . The point at which Youden’s  J satistics reaches its maximum for a given ROC curve can be used to guide the selection of the threshold to be used for that classifier.

I hope this post does the job of providing an understanding of ROC curves  and AUC. The  Python program for simulating the example given earlier can be found here .

Please feel free to adjust the mean of the distributions and see the changes in the plot.

A common trap when it comes to sampling from a population that intrinsically includes outliers

I will discuss a common fallacy concerning the conclusions drawn from calculating a sample mean and a sample standard deviation and more importantly how to avoid it.

Suppose you draw a random sample x_1, x_2, … x_N of size N and compute the ordinary (arithmetic) sample mean  x_m and a sample standard deviation sd from it.  Now if (and only if) the (true) population mean µ (first moment) and population variance (second moment) obtained from the actual underlying PDF  are finite, the numbers x_m and sd make the usual sense otherwise they are misleading as will be shown by an example.

By the way: The common correlation coefficient will also be undefined (or in practice always point to zero) in the presence of infinite population variances. Hopefully I will create an article discussing this related fallacy in the near future where a suitable generalization to Lévy-stable variables will be proposed.

 Drawing a random sample from a heavy tailed distribution and discussing certain measures

As an example suppose you have a one dimensional random walker whose step length is distributed by a symmetric standard Cauchy distribution (Lorentz-profile) with heavy tails, i.e. an alpha-stable distribution with alpha being equal to one. The PDF of an individual independent step is given by p(x) = \frac{\pi^{-1}}{(1 + x^2)} , thus neither the first nor the second moment exist whereby the first exists and vanishes at least in the sense of a principal value due to symmetry.

Still let us generate N = 3000 (pseudo) standard Cauchy random numbers in R* to analyze the behavior of their sample mean and standard deviation sd as a function of the reduced sample size n \leq N.

*The R-code is shown at the end of the article.

Here are the piecewise sample mean (in blue) and standard deviation (in red) for the mentioned Cauchy sampling. We see that both the sample mean and sd include jumps and do not converge.

Especially the mean deviates relatively largely from zero even after 3000 observations. The sample sd has no target due to the population variance being infinite.

If the data is new and no prior distribution is known, computing the sample mean and sd will be misleading. Astonishingly enough the sample mean itself will have the (formally exact) same distribution as the single step length p(x). This means that the sample mean is also standard Cauchy distributed implying that with a different Cauchy sample one could have easily observed different sample means far of the presented values in blue.

What sense does it make to present the usual interval x_m \pm sd / \sqrt{N} in such a case? What to do?

The sample median, median absolute difference (mad) and Inter-Quantile-Range (IQR) are more appropriate to describe such a data set including outliers intrinsically. To make this plausible I present the following plot, whereby the median is shown in black, the mad in green and the IQR in orange.

This example shows that the median, mad and IQR converge quickly against their assumed values and contain no major jumps. These quantities do an obviously better job in describing the sample. Even in the presence of outliers they remain robust, whereby the mad converges more quickly than the IQR. Note that a standard Cauchy sample will contain half of its sample in the interval median \pm mad meaning that the IQR is twice the mad.

Drawing a random sample from a PDF that has finite moments

Just for comparison I also show the above quantities for a standard normal (pseudo) sample labeled with the same color as before as a counter example. In this case not only do both the sample mean and median but also the sd and mad converge towards their expected values (see plot below). Here all the quantities describe the data set properly and there is no trap since there are no intrinsic outliers. The sample mean itself follows a standard normal, so that the sd in deed makes sense and one could calculate a standard error \frac{sd}{\sqrt{N}} from it to present the usual stochastic confidence intervals for the sample mean.

A careful observation shows that in contrast to the Cauchy case here the sampled mean and sd converge more quickly than the sample median and the IQR. However still the sampled mad performs about as well as the sd. Again the mad is twice the IQR.

And here are the graphs of the prementioned quantities for a pseudo normal sample:

The take-home-message:

Just be careful when you observe outliers and calculate sample quantities right away, you might miss something. At best one carefully observes how the relevant quantities change with sample size as demonstrated in this article.

Such curves should become of broader interest in order to improve transparency in the Data Science process and reduce fallacies as well.

Thank you for reading.

P.S.: Feel free to play with the set random seed in the R-code below and observe how other quantities behave with rising sample size. Of course you can also try different PDFs at the beginning of the code. You can employ a Cauchy, Gaussian, uniform, exponential or Holtsmark (pseudo) random sample.


QUIZ: Which one of the recently mentioned random samples contains a trap** and why?

**in the context of this article


R-code used to generate the data and for producing plots:



Cross-industry standard process for data mining

Introduced in 1996, the cross-industry standard process for data mining (CRISP-DM) became the most
common procedure for all data mining projects. This method consists of six phases: Business
understanding, Data understanding, Data preparation, Modeling, Evaluation and Deployment (see
Figure 1). It is being used not just as a reference manual but as a user guide as it explains every phase
in detail (Hipp, 2000). The six phases of this model are explained below:

Figure 1: Different phases of CRISP-DM

Business Understanding

It includes understanding the business problem and determining the
objective of the business as well as of the project. It is also important to understand the previous work
done on the project (if any) to achieve the business goals and to examine if the scope of the project has changed.

The job of a Data Scientist is not limited to coding or just make a machine learning model and I guess that’s why this whole lifecycle was developed.  The key points a project owner should take care in this process are:

– Identify stakeholders  and involve them to define the scope your project
– Describe your product (your machine learning model)
– Identify how your product ties into the client’s business processes
– Identify metrics / KPIs for measuring success

Evaluating a model is a different thing as it can only tell you how good are your predictions but identifying the success metric is really important for any data science project because when your model is deployed in production this measure will tell you if your model actually works or not. Now, let’s discuss what is this success metric
Consider that you are working in an e-commerce company where Head of finance ask you to create a machine learning model to predict if a specific product will return or not. The problem is not hard to understand, its a binary classification problem and you know you can do the job. But before you start working with the data you should define a metric to measure the success. What do you think your success metric could be? I would go with the return rate, in other words, calculate the rate for how many orders are actually coming back and if this measure is getting decrease you would know your model works and if not then FIX IT !!

Data understanding

The initial step in this phase is to gather all the data from different sources. It is
then important to describe the data, generate graphs for distribution in order to get familiar with the
data. This phase is important as without enough data or without understanding about the data analysis
cannot be performed. In data mining terms this can be compared to Exploratory data analysis (EDA)
where techniques from descriptive statistics are used to have an insight into the data. For instance, if it is
a time series data it makes sense to know from when until when the data is available before diving deep into
the data.

Data preparation

This phase takes most of the time in data mining project as a lot of methods from
data cleaning, feature subset, feature engineering, the transformation of data etc. are used before the final
dataset is trained for modeling purpose. The single dataset can also be prepared in different forms as some
algorithms can learn more with a certain type of data, some algorithms can deal with imbalance dataset
and for some algorithms, the target variable must be balanced. This phase also requires sometimes to
calculate new KPI’s according to the business need or sometimes to reduce the dimension of the dataset.

Modeling and Evaluation

Various models are selected and build in this process and appropriate hyperparameters are
selected after an intensive grid search.  Once all the models are built it is now time to evaluate and compare performances of all the models.


A model is of no use if it is not deployed into production. Until now you have been doing the job of a data scientist but for deployment, you need some software engineering

skills. There are several ways to deploy a machine learning model or python code. Few of them are:

  • Re-implement your python code in C++, Java etc. (LOL)
  • Save the coefficients and use them to get predictions
  • Serialized objects (REST API with flask, Django)

To understand the concept of deploying an ML model using REST API this post is highly recommended.

Predictive maintenance in Semiconductor Industry: Part 1

The process in the semiconductor industry is highly complicated and is normally under consistent observation via the monitoring of the signals coming from several sensors. Thus, it is important for the organization to detect the fault in the sensor as quickly as possible. There are existing traditional statistical based techniques however modern semiconductor industries have the ability to produce more data which is beyond the capability of the traditional process.

For this article, we will be using SECOM dataset which is available here.  A lot of work has already done on this dataset by different authors and there are also some articles available online. In this article, we will focus on problem definition, data understanding, and data cleaning.

This article is only the first of three parts, in this article we will discuss the business problem in hand and clean the dataset. In second part we will do feature engineering and in the last article we will build some models and evaluate them.

Problem definition

This data which is collected by these sensors not only contains relevant information but also a lot of noise. The dataset contains readings from 590. Among the 1567 examples, there are only 104 fail cases which means that out target variable is imbalanced. We will look at the distribution of the dataset when we look at the python code.

NOTE: For a detailed description regarding this cases study I highly recommend to read the following research papers:

  •  Kerdprasop, K., & Kerdprasop, N. A Data Mining Approach to Automate Fault Detection Model Development in the Semiconductor Manufacturing Process.
  • Munirathinam, S., & Ramadoss, B. Predictive Models for Equipment Fault Detection in the Semiconductor Manufacturing Process.

Data Understanding and Preparation

Let’s start exploring the dataset now. The first step as always is to import the required libraries.

There are several ways to import the dataset, you can always download and then import from your working directory. However, I will directly import using the link. There are two datasets: one contains the readings from the sensors and the other one contains our target variable and a timestamp.

The first step before doing the analysis would be to merge the dataset and we will us pandas library to merge the datasets in just one line of code.

Now let’s check out the distribution of the target variable

Figure 1: Distribution of Target Variable

From Figure 1 it can be observed that the target variable is imbalanced and it is highly recommended to deal with this problem before the model building phase to avoid bias model. Xgboost is one of the models which can deal with imbalance classes but one needs to spend a lot of time to tune the hyper-parameters to achieve the best from the model.

The dataset in hand contains a lot of null values and the next step would be to analyse these null values and remove the columns having null values more than a certain percentage. This percentage is calculated based on 95th quantile of null values.

Figure 2: Missing percentge in each column

Now we calculate the 95th percentile of the null values.

Figure 3: Missing percentage after removing columns with more then 45% Na

From figure 3 its visible that there are still missing values in the dataset and can be dealt by using many imputation methods. The most common method is to impute these values by mean, median or mode. There also exist few sophisticated techniques like K-nearest neighbour and interpolation.  We will be applying interpolation technique to our dataset. 

To prepare our dataset for analysis we should remove some more unwanted columns like columns with near zero variance. For this we can calulate number of unique values in each column and if there is only one unique value we can delete the column as it holds no information.

We have applied few data cleaning techniques and reduced the features from 590 to 444. However, In the next article we will apply some feature engineering techniques and adress problems like the curse of dimensionality and will also try to balance the target variable.

Bleiben Sie dran!!

Fuzzy Matching mit dem Jaro-Winkler-Score zur Auswertung von Markenbekanntheit und Werbeerinnerung

Für Unternehmen sind Markenbekanntheit und Werbeerinnerung wichtige Zielgrößen, denn anhand dieser lässt sich ableiten, ob Konsumenten ein Produkt einer Marke kaufen werden oder nicht. Zielgrößen wie diese werden von Marktforschungsinstituten über Befragungen ermittelt. Dafür wird in regelmäßigen Zeitabständen eine gleichbleibende Anzahl an Personen befragt, ob diese sich an Marken einer bestimmten Branche erinnern oder sich an Werbung erinnern. Die Personen füllen dafür in der Regel einen Onlinefragebogen aus.

Die Ergebnisse der Befragung liegen in einer Datenmatrix (siehe Tabelle) vor und müssen zur Auswertung zunächst bearbeitet werden.

Laufende Nummer Marke 1 Marke 2 Marke 3 Marke 4
1 ING-Diba Citigroup Sparkasse
2 Sparkasse Consorsbank
3 Commerbank Deutsche Bank Sparkasse ING-DiBa
4 Sparkasse Targobank

Ziel ist es aus diesen Daten folgende 0/1 codierte Matrix zu generieren. Wenn eine Marke bekannt ist, wird in die zur Marke gehörende Spalte eine Eins eingetragen, ansonsten eine Null.

Alle Marken ING-Diba Citigroup Sparkasse Targobank
ING-Diba, Citigroup, Sparkasse 1 1 1 0
Sparkasse, Consorsbank 0 0 1 0
Commerzbank, Deutsche Bank, Sparkasse, ING-Diba 1 0 0 0
Sparkasse, Targobank 0 0 1 1

Der Workflow um diese Datentransformation durchzuführen ist oftmals mittels eines Teilstrings einer Marke zu suchen ob diese in einem über alle Nennungen hinweg zusammengeführten String vorkommt oder nicht (z.B. „argo“ bei Targobank). Das Problem dieser Herangehensweise ist, dass viele falsch geschriebenen Wörter so nicht erfasst werden und die Erfahrung zeigt, dass falsch geschriebene Marken in vielfältigster Weise auftreten. Hier mussten in der Vergangenheit Mitarbeiter sich in stundenlangem Kampf durch die Ergebnisse wühlen und falsch zugeordnete oder nicht zugeordnete Marken händisch korrigieren und alle Variationen der Wörter notieren, um für die nächste Befragung das Suchpattern zu optimieren.

Eine Alternative diesen aufwändigen Workflow stellt die Ermittlung von falsch geschriebenen Wörtern mittels des Jaro-Winkler-Scores dar. Dafür muss zunächst die Jaro-Winkler-Distanz zwischen zwei Strings berechnet werden. Diese berechnet sich wie folgt:

d_j = \frac{1}{3}(\frac{m}{|s_1|}+\frac{m}{|s_2|}+\frac{m - t}{m})

  • m: Anzahl der übereinstimmenden Buchstaben
  • s: Länge des Strings
  • t: Hälfte der Anzahl der Umstellungen der Buchstaben die nötig sind, damit Strings identisch sind. („Ta“ und „gobank“ befinden sich bereits in der korrekten Reihenfolge, somit gilt: t = 0)

Aus dem Ergebnis lässt sich der Jaro-Winkler Score berechnen:
d_w = \d_j + (l_p (1 - d_j))
ist dabei die Jaro-Winkler-Distanz, l die Länge der übereinstimmenden Buchstaben von Beginn des Wortes bis zum maximal vierten Buchstaben und p ein konstanter Faktor von 0,1.

Für die Strings „Targobank“ und „Tangobank“ ergibt sich die Jaro-Winkler-Distanz:

d_j = \frac{1}{3}(\frac{8}{9}+\frac{8}{9}+\frac{8 - 0}{9})

Daraus wird im nächsten Schritt der Jaro-Winkler Score berechnet:

d_w = 0,9259 + (2 \cdot 0,1 (1 - 0,9259)) = 0,9407407

Bisherige Erfahrungen haben gezeigt, dass sich Scores ab 0,8 bzw. 0,9 am besten zur Suche von ähnlichen Wörtern eignen. Ein Schwellenwert darunter findet sehr viele Wörter, die sich z.B. auch anderen Wörtern zuordnen lassen. Ein Schwellenwert über 0,9 identifiziert falsch geschriebene Wörter oftmals nicht mehr.

Nach diesem theoretischen Exkurs möchte ich nun zeigen, wie sich das Ganze praktisch anwenden lässt. Da sich das Ganze um ein fiktives Beispiel handelt, werden zur Demonstration der Praxistauglichkeit Fakedaten mit folgendem Code erzeugt. Dabei wird angenommen, dass Personen unterschiedlich viele Banken kennen und diese mit einer bestimmten Wahrscheinlichkeit falsch schreiben.


Nun werden die Inhalte der Spalten in eine einzige Spalte zusammengefasst und jede Marke per Komma getrennt.

Damit Sonderzeichen, Leerzeichen oder Groß- und Kleinschreibung keine Rolle spielen, werden alle Strings vereinheitlicht und störende Zeichen entfernt.

Im nächsten Schritt wird geprüft welche Schreibweisen überhaupt existieren. Dafür eignet sich eine Word-Frequency-Matrix, mit der alle einzigartigen Wörter und deren Häufigkeiten in einem Vektor gezählt wird.

Danach wird eine leere Liste erstellt, in der iterativ für jedes Element des Suchvektors ein Charactervektor erzeugt wird, der Wörter enthält, die einen Jaro-Winker Score von 0,9 oder höher besitzen.

Jetzt wird ein leerer DataFrame erzeugt, der die Zeilenlänge des originalen DataFrames besitzt sowie die Anzahl der Marken als Spaltenlänge.

Im nächsten Schritt wird nun aus den ähnlichen Wörtern mit einer oder-Verknüpfung einen String erzeugt, der alle durch den Jaro-Winkler-Score identifizierten Wörter beinhaltet. Wenn ein Treffer gefunden wird, wird in der Suchspalte eine Eins eingetragen, ansonsten eine Null.

Zuletzt wird eine Spalte erzeugt, in die eine Eins geschrieben wird, wenn keine der Marken gefunden wurde.

Nach der fertigen Berechnung der Matrix können nun die finalen KPI´s berechnet und als Report in eine .xlsx Datei geschrieben werden.

Dieses Vorgehen kann natürlich nicht verhindern, dass sich jemand mit kritischem Auge die Daten anschauen muss. In mehreren Tests ergaben sich bei einer Fallzahl von ~10.000 Antworten Genauigkeiten zwischen 95% und 100%, was bisherige Ansätze um ein Vielfaches übertrifft.9407407

Sentiment Analysis of IMDB reviews

Sentiment Analysis of IMDB reviews

This article shows you how to build a Neural Network from scratch(no libraries) for the purpose of detecting whether a movie review on IMDB is negative or positive.


  • Curating a dataset and developing a "Predictive Theory"

  • Transforming Text to Numbers Creating the Input/Output Data

  • Building our Neural Network

  • Making Learning Faster by Reducing "Neural Noise"

  • Reducing Noise by strategically reducing the vocabulary

Curating the Dataset

In [3]:
def pretty_print_review_and_label(i):
    print(labels[i] + "\t:\t" + reviews[i][:80] + "...")

g = open('reviews.txt','r') # features of our dataset
reviews = list(map(lambda x:x[:-1],g.readlines()))

g = open('labels.txt','r') # labels
labels = list(map(lambda x:x[:-1].upper(),g.readlines()))

Note: The data in reviews.txt we're contains only lower case characters. That's so we treat different variations of the same word, like The, the, and THE, all the same way.

It's always a good idea to get check out your dataset before you proceed.

In [2]:
len(reviews) #No. of reviews
In [3]:
reviews[0] #first review
'bromwell high is a cartoon comedy . it ran at the same time as some other programs about school life  such as  teachers  . my   years in the teaching profession lead me to believe that bromwell high  s satire is much closer to reality than is  teachers  . the scramble to survive financially  the insightful students who can see right through their pathetic teachers  pomp  the pettiness of the whole situation  all remind me of the schools i knew and their students . when i saw the episode in which a student repeatedly tried to burn down the school  i immediately recalled . . . . . . . . . at . . . . . . . . . . high . a classic line inspector i  m here to sack one of your teachers . student welcome to bromwell high . i expect that many adults of my age think that bromwell high is far fetched . what a pity that it isn  t   '
In [4]:
labels[0] #first label

Developing a Predictive Theory

Analysing how you would go about predicting whether its a positive or a negative review.

In [5]:
print("labels.txt \t : \t reviews.txt\n")
labels.txt 	 : 	 reviews.txt

NEGATIVE	:	this movie is terrible but it has some good effects .  ...
POSITIVE	:	adrian pasdar is excellent is this film . he makes a fascinating woman .  ...
NEGATIVE	:	comment this movie is impossible . is terrible  very improbable  bad interpretat...
POSITIVE	:	excellent episode movie ala pulp fiction .  days   suicides . it doesnt get more...
NEGATIVE	:	if you haven  t seen this  it  s terrible . it is pure trash . i saw this about ...
POSITIVE	:	this schiffer guy is a real genius  the movie is of excellent quality and both e...
In [41]:
from collections import Counter
import numpy as np

We'll create three Counter objects, one for words from postive reviews, one for words from negative reviews, and one for all the words.

In [56]:
# Create three Counter objects to store positive, negative and total counts
positive_counts = Counter()
negative_counts = Counter()
total_counts = Counter()

Examine all the reviews. For each word in a positive review, increase the count for that word in both your positive counter and the total words counter; likewise, for each word in a negative review, increase the count for that word in both your negative counter and the total words counter. You should use split(' ') to divide a piece of text (such as a review) into individual words.

In [57]:
# Loop over all the words in all the reviews and increment the counts in the appropriate counter objects
for i in range(len(reviews)):
    if(labels[i] == 'POSITIVE'):
        for word in reviews[i].split(" "):
            positive_counts[word] += 1
            total_counts[word] += 1
        for word in reviews[i].split(" "):
            negative_counts[word] += 1
            total_counts[word] += 1

Most common positive & negative words

In [ ]:

The above statement retrieves alot of words, the top 3 being : ('the', 173324), ('.', 159654), ('and', 89722),

In [ ]:

The above statement retrieves alot of words, the top 3 being : ('', 561462), ('.', 167538), ('the', 163389),

As you can see, common words like "the" appear very often in both positive and negative reviews. Instead of finding the most common words in positive or negative reviews, what you really want are the words found in positive reviews more often than in negative reviews, and vice versa. To accomplish this, you'll need to calculate the ratios of word usage between positive and negative reviews.

The positive-to-negative ratio for a given word can be calculated with positive_counts[word] / float(negative_counts[word]+1). Notice the +1 in the denominator – that ensures we don't divide by zero for words that are only seen in positive reviews.

In [58]:
pos_neg_ratios = Counter()

# Calculate the ratios of positive and negative uses of the most common words
# Consider words to be "common" if they've been used at least 100 times
for term,cnt in list(total_counts.most_common()):
    if(cnt > 100):
        pos_neg_ratio = positive_counts[term] / float(negative_counts[term]+1)
        pos_neg_ratios[term] = pos_neg_ratio

Examine the ratios

In [12]:
print("Pos-to-neg ratio for 'the' = {}".format(pos_neg_ratios["the"]))
print("Pos-to-neg ratio for 'amazing' = {}".format(pos_neg_ratios["amazing"]))
print("Pos-to-neg ratio for 'terrible' = {}".format(pos_neg_ratios["terrible"]))
Pos-to-neg ratio for 'the' = 1.0607993145235326
Pos-to-neg ratio for 'amazing' = 4.022813688212928
Pos-to-neg ratio for 'terrible' = 0.17744252873563218

We see the following:

  • Words that you would expect to see more often in positive reviews – like "amazing" – have a ratio greater than 1. The more skewed a word is toward postive, the farther from 1 its positive-to-negative ratio will be.
  • Words that you would expect to see more often in negative reviews – like "terrible" – have positive values that are less than 1. The more skewed a word is toward negative, the closer to zero its positive-to-negative ratio will be.
  • Neutral words, which don't really convey any sentiment because you would expect to see them in all sorts of reviews – like "the" – have values very close to 1. A perfectly neutral word – one that was used in exactly the same number of positive reviews as negative reviews – would be almost exactly 1.

Ok, the ratios tell us which words are used more often in postive or negative reviews, but the specific values we've calculated are a bit difficult to work with. A very positive word like "amazing" has a value above 4, whereas a very negative word like "terrible" has a value around 0.18. Those values aren't easy to compare for a couple of reasons:

  • Right now, 1 is considered neutral, but the absolute value of the postive-to-negative rations of very postive words is larger than the absolute value of the ratios for the very negative words. So there is no way to directly compare two numbers and see if one word conveys the same magnitude of positive sentiment as another word conveys negative sentiment. So we should center all the values around netural so the absolute value fro neutral of the postive-to-negative ratio for a word would indicate how much sentiment (positive or negative) that word conveys.
  • When comparing absolute values it's easier to do that around zero than one.

To fix these issues, we'll convert all of our ratios to new values using logarithms (i.e. use np.log(ratio))

In the end, extremely positive and extremely negative words will have positive-to-negative ratios with similar magnitudes but opposite signs.

In [59]:
# Convert ratios to logs
for word,ratio in pos_neg_ratios.most_common():
    pos_neg_ratios[word] = np.log(ratio)

Examine the new ratios

In [14]:
print("Pos-to-neg ratio for 'the' = {}".format(pos_neg_ratios["the"]))
print("Pos-to-neg ratio for 'amazing' = {}".format(pos_neg_ratios["amazing"]))
print("Pos-to-neg ratio for 'terrible' = {}".format(pos_neg_ratios["terrible"]))
Pos-to-neg ratio for 'the' = 0.05902269426102881
Pos-to-neg ratio for 'amazing' = 1.3919815802404802
Pos-to-neg ratio for 'terrible' = -1.7291085042663878

If everything worked, now you should see neutral words with values close to zero. In this case, "the" is near zero but slightly positive, so it was probably used in more positive reviews than negative reviews. But look at "amazing"'s ratio - it's above 1, showing it is clearly a word with positive sentiment. And "terrible" has a similar score, but in the opposite direction, so it's below -1. It's now clear that both of these words are associated with specific, opposing sentiments.

Run the below code to see more ratios.

It displays all the words, ordered by how associated they are with postive reviews.

In [ ]:

The top most common words for the above code : ('edie', 4.6913478822291435), ('paulie', 4.0775374439057197), ('felix', 3.1527360223636558), ('polanski', 2.8233610476132043), ('matthau', 2.8067217286092401), ('victoria', 2.6810215287142909), ('mildred', 2.6026896854443837), ('gandhi', 2.5389738710582761), ('flawless', 2.451005098112319), ('superbly', 2.2600254785752498), ('perfection', 2.1594842493533721), ('astaire', 2.1400661634962708), ('captures', 2.0386195471595809), ('voight', 2.0301704926730531), ('wonderfully', 2.0218960560332353), ('powell', 1.9783454248084671), ('brosnan', 1.9547990964725592)

Transforming Text into Numbers

Creating the Input/Output Data

Create a set named vocab that contains every word in the vocabulary.

In [19]:
vocab = set(total_counts.keys())

Check vocabulary size

In [20]:
vocab_size = len(vocab)

Th following image rpresents the layers of the neural network you'll be building throughout this notebook. layer_0 is the input layer, layer_1 is a hidden layer, and layer_2 is the output layer.

In [1]:

TODO: Create a numpy array called layer_0 and initialize it to all zeros. Create layer_0 as a 2-dimensional matrix with 1 row and vocab_size columns.

In [21]:
layer_0 = np.zeros((1,vocab_size))

layer_0 contains one entry for every word in the vocabulary, as shown in the above image. We need to make sure we know the index of each word, so run the following cell to create a lookup table that stores the index of every word.

TODO: Complete the implementation of update_input_layer. It should count how many times each word is used in the given review, and then store those counts at the appropriate indices inside layer_0.

In [ ]:
# Create a dictionary of words in the vocabulary mapped to index positions 
# (to be used in layer_0)
word2index = {}
for i,word in enumerate(vocab):
    word2index[word] = i

It stores the indexes like this: 'antony': 22, 'pinjar': 23, 'helsig': 24, 'dances': 25, 'good': 26, 'willard': 71500, 'faridany': 27, 'foment': 28, 'matts': 12313,

Lets implement some functions for simplifying our inputs to the neural network.

In [25]:
def update_input_layer(review):
    The element at a given index of layer_0 should represent
    how many times the given word occurs in the review.
    global layer_0
    # clear out previous state, reset the layer to be all 0s
    layer_0 *= 0
    # count how many times each word is used in the given review and store the results in layer_0 
    for word in review.split(" "):
        layer_0[0][word2index[word]] += 1

Run the following cell to test updating the input layer with the first review. The indices assigned may not be the same as in the solution, but hopefully you'll see some non-zero values in layer_0.

In [26]:
array([[ 18.,   0.,   0., ...,   0.,   0.,   0.]])

get_target_for_labels should return 0 or 1, depending on whether the given label is NEGATIVE or POSITIVE, respectively.

In [27]:
def get_target_for_label(label):
    if(label == 'POSITIVE'):
        return 1
        return 0

Building a Neural Network

In [32]:
import time
import sys
import numpy as np

# Encapsulate our neural network in a class
class SentimentNetwork:
    def __init__(self, reviews,labels,hidden_nodes = 10, learning_rate = 0.1):
            reviews(list) - List of reviews used for training
            labels(list) - List of POSITIVE/NEGATIVE labels
            hidden_nodes(int) - Number of nodes to create in the hidden layer
            learning_rate(float) - Learning rate to use while training
        # Assign a seed to our random number generator to ensure we get
        # reproducable results

        # process the reviews and their associated labels so that everything
        # is ready for training
        self.pre_process_data(reviews, labels)
        # Build the network to have the number of hidden nodes and the learning rate that
        # were passed into this initializer. Make the same number of input nodes as
        # there are vocabulary words and create a single output node.
        self.init_network(len(self.review_vocab),hidden_nodes, 1, learning_rate)

    def pre_process_data(self, reviews, labels):
        # populate review_vocab with all of the words in the given reviews
        review_vocab = set()
        for review in reviews:
            for word in review.split(" "):

        # Convert the vocabulary set to a list so we can access words via indices
        self.review_vocab = list(review_vocab)
        # populate label_vocab with all of the words in the given labels.
        label_vocab = set()
        for label in labels:
        # Convert the label vocabulary set to a list so we can access labels via indices
        self.label_vocab = list(label_vocab)
        # Store the sizes of the review and label vocabularies.
        self.review_vocab_size = len(self.review_vocab)
        self.label_vocab_size = len(self.label_vocab)
        # Create a dictionary of words in the vocabulary mapped to index positions
        self.word2index = {}
        for i, word in enumerate(self.review_vocab):
            self.word2index[word] = i
        # Create a dictionary of labels mapped to index positions
        self.label2index = {}
        for i, label in enumerate(self.label_vocab):
            self.label2index[label] = i
    def init_network(self, input_nodes, hidden_nodes, output_nodes, learning_rate):
        # Set number of nodes in input, hidden and output layers.
        self.input_nodes = input_nodes
        self.hidden_nodes = hidden_nodes
        self.output_nodes = output_nodes

        # Store the learning rate
        self.learning_rate = learning_rate

        # Initialize weights

        # These are the weights between the input layer and the hidden layer.
        self.weights_0_1 = np.zeros((self.input_nodes,self.hidden_nodes))
        # These are the weights between the hidden layer and the output layer.
        self.weights_1_2 = np.random.normal(0.0, self.output_nodes**-0.5, 
                                                (self.hidden_nodes, self.output_nodes))
        # The input layer, a two-dimensional matrix with shape 1 x input_nodes
        self.layer_0 = np.zeros((1,input_nodes))
    def update_input_layer(self,review):

        # clear out previous state, reset the layer to be all 0s
        self.layer_0 *= 0
        for word in review.split(" "):
            if(word in self.word2index.keys()):
                self.layer_0[0][self.word2index[word]] += 1
    def get_target_for_label(self,label):
        if(label == 'POSITIVE'):
            return 1
            return 0
    def sigmoid(self,x):
        return 1 / (1 + np.exp(-x))
    def sigmoid_output_2_derivative(self,output):
        return output * (1 - output)
    def train(self, training_reviews, training_labels):
        # make sure out we have a matching number of reviews and labels
        assert(len(training_reviews) == len(training_labels))
        # Keep track of correct predictions to display accuracy during training 
        correct_so_far = 0

        # Remember when we started for printing time statistics
        start = time.time()
        # loop through all the given reviews and run a forward and backward pass,
        # updating weights for every item
        for i in range(len(training_reviews)):
            # Get the next review and its correct label
            review = training_reviews[i]
            label = training_labels[i]
            ### Forward pass ###

            # Input Layer

            # Hidden layer
            layer_1 =

            # Output layer
            layer_2 = self.sigmoid(
            ### Backward pass ###

            # Output error
            layer_2_error = layer_2 - self.get_target_for_label(label) # Output layer error is the difference between desired target and actual output.
            layer_2_delta = layer_2_error * self.sigmoid_output_2_derivative(layer_2)

            # Backpropagated error
            layer_1_error = # errors propagated to the hidden layer
            layer_1_delta = layer_1_error # hidden layer gradients - no nonlinearity so it's the same as the error

            # Update the weights
            self.weights_1_2 -= * self.learning_rate # update hidden-to-output weights with gradient descent step
            self.weights_0_1 -= * self.learning_rate # update input-to-hidden weights with gradient descent step

            # Keep track of correct predictions.
            if(layer_2 >= 0.5 and label == 'POSITIVE'):
                correct_so_far += 1
            elif(layer_2 < 0.5 and label == 'NEGATIVE'):
                correct_so_far += 1
            sys.stdout.write(" #Correct:" + str(correct_so_far) + " #Trained:" + str(i+1) \
                             + " Training Accuracy:" + str(correct_so_far * 100 / float(i+1))[:4] + "%")
    def test(self, testing_reviews, testing_labels):
        Attempts to predict the labels for the given testing_reviews,
        and uses the test_labels to calculate the accuracy of those predictions.
        # keep track of how many correct predictions we make
        correct = 0

        # Loop through each of the given reviews and call run to predict
        # its label. 
        for i in range(len(testing_reviews)):
            pred =[i])
            if(pred == testing_labels[i]):
                correct += 1
            sys.stdout.write(" #Correct:" + str(correct) + " #Tested:" + str(i+1) \
                             + " Testing Accuracy:" + str(correct * 100 / float(i+1))[:4] + "%")
    def run(self, review):
        Returns a POSITIVE or NEGATIVE prediction for the given review.
        # Run a forward pass through the network, like in the "train" function.
        # Input Layer

        # Hidden layer
        layer_1 =

        # Output layer
        layer_2 = self.sigmoid(
        # Return POSITIVE for values above greater-than-or-equal-to 0.5 in the output layer;
        # return NEGATIVE for other values
        if(layer_2[0] >= 0.5):
            return "POSITIVE"
            return "NEGATIVE"

Run the following code to create the network with a small learning rate, 0.001, and then train the new network. Using learning rate larger than this, for example 0.1 or even 0.01 would result in poor performance.

In [ ]:
mlp = SentimentNetwork(reviews[:-1000],labels[:-1000], learning_rate=0.001)

Running the above code would have given an accuracy around 62.2%

Reducing Noise in Our Input Data

Counting how many times each word occured in our review might not be the most efficient way. Instead just including whether a word was there or not will improve our training time and accuracy. Hence we update our update_input_layer() function.

In [ ]:
def update_input_layer(self,review):
    self.layer_0 *= 0
    for word in review.split(" "):
        if(word in self.word2index.keys()):
            self.layer_0[0][self.word2index[word]] =1

Creating and running our neural network again, even with a higher learning rate of 0.1 gave us a training accuracy of 83.8% and testing accuracy(testing on last 1000 reviews) of 85.7%.

Reducing Noise by Strategically Reducing the Vocabulary

Let us put the pos to neg ratio's that we found were much more effective at detecting a positive or negative label. We could do that by a few change:

  • Modify pre_process_data:
    • Add two additional parameters: min_count and polarity_cutoff
    • Calculate the positive-to-negative ratios of words used in the reviews.
    • Change so words are only added to the vocabulary if they occur in the vocabulary more than min_count times.
    • Change so words are only added to the vocabulary if the absolute value of their postive-to-negative ratio is at least polarity_cutoff
In [ ]:
def pre_process_data(self, reviews, labels, polarity_cutoff, min_count):
        positive_counts = Counter()
        negative_counts = Counter()
        total_counts = Counter()

        for i in range(len(reviews)):
            if(labels[i] == 'POSITIVE'):
                for word in reviews[i].split(" "):
                    positive_counts[word] += 1
                    total_counts[word] += 1
                for word in reviews[i].split(" "):
                    negative_counts[word] += 1
                    total_counts[word] += 1

        pos_neg_ratios = Counter()

        for term,cnt in list(total_counts.most_common()):
            if(cnt >= 50):
                pos_neg_ratio = positive_counts[term] / float(negative_counts[term]+1)
                pos_neg_ratios[term] = pos_neg_ratio

        for word,ratio in pos_neg_ratios.most_common():
            if(ratio > 1):
                pos_neg_ratios[word] = np.log(ratio)
                pos_neg_ratios[word] = -np.log((1 / (ratio + 0.01)))

        # populate review_vocab with all of the words in the given reviews
        review_vocab = set()
        for review in reviews:
            for word in review.split(" "):
                if(total_counts[word] > min_count):
                    if(word in pos_neg_ratios.keys()):
                        if((pos_neg_ratios[word] >= polarity_cutoff) or (pos_neg_ratios[word] <= -polarity_cutoff)):

        # Convert the vocabulary set to a list so we can access words via indices
        self.review_vocab = list(review_vocab)
        # populate label_vocab with all of the words in the given labels.
        label_vocab = set()
        for label in labels:
        # Convert the label vocabulary set to a list so we can access labels via indices
        self.label_vocab = list(label_vocab)
        # Store the sizes of the review and label vocabularies.
        self.review_vocab_size = len(self.review_vocab)
        self.label_vocab_size = len(self.label_vocab)
        # Create a dictionary of words in the vocabulary mapped to index positions
        self.word2index = {}
        for i, word in enumerate(self.review_vocab):
            self.word2index[word] = i
        # Create a dictionary of labels mapped to index positions
        self.label2index = {}
        for i, label in enumerate(self.label_vocab):
            self.label2index[label] = i

Our training accuracy increased to 85.6% after this change. As we can see our accuracy saw a huge jump by making minor changes based on our intuition. We can keep making such changes and increase the accuracy even further.


Download the Data Sources

The data sources used in this article can be downloaded here:

The Inside Out of ML Based Prescriptive Analytics

With the constantly growing number of data, more and more companies are shifting towards analytic solutions. Analytic solutions help in extracting the meaning from the huge amount of data available. Thus, improving decision making.

Decision making is an important aspect of businesses, and technologies like Machine Learning are enhancing it further. The growing use of Machine Learning has changed the way of prescriptive analytics. In order to optimize the efforts, companies need to be more accurate with the historical and present data. This is because the historical and present data are the essentials of analytics. This article helps describe the inside out of Machine Learning-based prescriptive analytics.

Phases of business analytics

Descriptive analytics, predictive analytics, and prescriptive analytics are the three phases of business analytics. Descriptive analytics, being the first one, deals with past performance. Historical data is mined to understand past performance. This serves as a way to look for the reasons behind past success and failure. It is a kind of post-mortem analysis and most management reporting like sales, marketing, operations, and finance etc. make use of this.

The second one is a predictive analysis which answers the question of what is likely to happen. The historical data is now combined with rules, algorithms etc. to determine the possible future outcome or likelihood of a situation occurring.

The final phase, well known to everyone, is prescriptive analytics. It can continually take in new data and re-predict and re-prescribe. This improves the accuracy of the prediction and prescribes better decision options.  Professional services or technology or their combination can be chosen to perform all the three analytics.

More about prescriptive analytics

The analysis of business activities goes through many phases. Prescriptive analytics is one such. It is known to be the third phase of business analytics and comes after descriptive and predictive analytics. It entails the application of mathematical and computational sciences. It makes use of the results obtained from descriptive and predictive analysis to suggest decision options. It goes beyond predicting future outcomes and suggests actions to benefit from the predictions. It shows the implications of each decision option. It anticipates on what will happen when it will happen as well as why it will happen.

ML-based prescriptive analytics

Being just before the prescriptive analytics, predictive analytics is often confused with it. What actually happens is predictive analysis leads to prescriptive analysis. Thus, a Machine Learning based prescriptive analytics goes through an ML-based predictive analysis first. Therefore, it becomes necessary to consider the ML-based predictive analysis first.

ML-based predictive analytics:

A lot of things prevent businesses from achieving predictive analysis capabilities.  Machine Learning can be a great help in boosting Predictive analytics. Use of Machine Learning and Artificial Intelligence algorithms helps businesses in optimizing and uncovering the new statistical patterns. These statistical patterns form the backbone of predictive analysis. E-commerce, marketing, customer service, medical diagnosis etc. are some of the prospective use cases for Machine Learning based predictive analytics.

In E-commerce, machine learning can help in predicting the usual choices of the customer. Thus, presenting him/her according to his/her likes and dislikes. It can also help in predicting fraudulent transaction. Similarly, B2B marketing also makes good use of Machine learning based predictive analytics. Customer services and medical diagnosis also benefit from predictive analytics. Thus, a prediction and a prescription based on machine learning can boost various business functions.

Organizations and software development companies are making more and more use of machine learning based predictive analytics. The advancements like neural networks and deep learning algorithms are able to uncover hidden information. This all requires a well-researched approach. Big data and progressive IT systems also act as important factors in this.

Language Detecting with sklearn by determining Letter Frequencies

Of course, there are better and more efficient methods to detect the language of a given text than counting its lettes. On the other hand this is a interesting little example to show the impressing ability of todays machine learning algorithms to detect hidden patterns in a given set of data.

For example take the sentence:

“Ceci est une phrase française.”

It’s not to hard to figure out that this sentence is french. But the (lowercase) letters of the same sentence in a random order look like this:


Still sure it’s french? Regarding the fact that this string contains the letter “ç” some people could have remembered long passed french lessons back in school and though might have guessed right. But beside the fact that the french letter “ç” is also present for example in portuguese, turkish, catalan and a few other languages, this is still a easy example just to explain the problem. Just try to guess which language might have generated this:


While this looks simply confusing to the human eye and it seems practically impossible to determine the language it was generated from, this string still contains as set of hidden but well defined patterns from which the language could be predictet with almost complete (ca. 98-99%) certainty.

First of all, we need a set of texts in the languages our model should be able to recognise. Luckily with the package NLTK there comes a big set of example texts which actually are protocolls of the european parliament and therefor are publicly availible in 11 differen languages:

  •  Danish
  •  Dutch
  •  English
  •  Finnish
  •  French
  •  German
  •  Greek
  •  Italian
  •  Portuguese
  •  Spanish
  •  Swedish

Because the greek version is not written with the latin alphabet, the detection of the language greek would just be too simple, so we stay with the other 10 languages availible. To give you a idea of the used texts, here is a little sample:

“Resumption of the session I declare resumed the session of the European Parliament adjourned on Friday 17 December 1999, and I would like once again to wish you a happy new year in the hope that you enjoyed a pleasant festive period.
Although, as you will have seen, the dreaded ‘millennium bug’ failed to materialise, still the people in a number of countries suffered a series of natural disasters that truly were dreadful.”

Train and Test

The following code imports the nessesary modules and reads the sample texts from a set of text files into a pandas.Dataframe object and prints some statistics about the read texts:

Above you see a sample set of random rows of the created Dataframe. After removing very short text snipplets (less than 200 chars) we are left with 56481 snipplets. The function clean_eutextdf() then creates a lower case representation of the texts in the coloum ‘ltext’ to facilitate counting the chars in the next step.
The following code snipplet now extracs the features – in this case the relative frequency of each letter in every text snipplet – that are used for prediction:

Now that we have calculated the features for every text snipplet in our dataset, we can split our data set in a train and test set:

After doing that, we can train a k-nearest-neigbours classifier and test it to get the percentage of correctly predicted languages in the test data set. Because we do not know what value for k may be the best choice, we just run the training and testing with different values for k in a for loop:

As you can see in the output the reliability of the language classifier is generally very high: It starts at about 97.5% for k = 1, increases for with increasing values of k until it reaches a maximum level of about 98.5% at k ≈ 10.

Using the Classifier to predict languages of texts

Now that we have trained and tested the classifier we want to use it to predict the language of example texts. To do that we need two more functions, shown in the following piece of code. The first one extracts the nessesary features from the sample text and predict_lang() predicts the language of a the texts:

With this classifier it is now also possible to predict the language of the randomized example snipplet from the introduction (which is acutally created from the first paragraph of this article):

The KNN classifier of sklearn also offers the possibility to predict the propability with which a given classification is made. While the probability distribution for a specific language is relativly clear for long sample texts it decreases noticeably the shorter the texts are.

Background and Insights

Why does a relative simple model like counting letters acutally work? Every language has a specific pattern of letter frequencies which can be used as a kind of fingerprint: While there are almost no y‘s in the german language this letter is quite common in english. In french the letter k is not very common because it is replaced with q in most cases.

For a better understanding look at the output of the following code snipplet where only three letters already lead to a noticable form of clustering:


Even though every single letter frequency by itself is not a very reliable indicator, the set of frequencies of all present letters in a text is a quite good evidence because it will more or less represent the letter frequency fingerprint of the given language. Since it is quite hard to imagine or visualize the above plot in more than three dimensions, I used a little trick which shows that every language has its own typical fingerprint of letter frequencies:

What more?

Beside the fact, that letter frequencies alone, allow us to predict the language of every example text (at least in the 10 languages with latin alphabet we trained for) with almost complete certancy there is even more information hidden in the set of sample texts.

As you might know, most languages in europe belong to either the romanian or the indogermanic language family (which is actually because the romans conquered only half of europe). The border between them could be located in belgium, between france and germany and in swiss. West of this border the romanian languages, which originate from latin, are still spoken, like spanish, portouguese and french. In the middle and northern part of europe the indogermanic languages are very common like german, dutch, swedish ect. If we plot the analysed languages with a different colour sheme this border gets quite clear and allows us to take a look back in history that tells us where our languages originate from:

As you can see the more common letters, especially the vocals like a, e, i, o and u have almost the same frequency in all of this languages. Far more interesting are letters like q, k, c and w: While k is quite common in all of the indogermanic languages it is quite rare in romanic languages because the same sound is written with the letters q or c.
As a result it could be said, that even “boring” sets of data (just give it a try and read all the texts of the protocolls of the EU parliament…) could contain quite interesting patterns which – in this case – allows us to predict quite precisely which language a given text sample is written in, without the need of any translation program or to speak the languages. And as an interesting side effect, where certain things in history happend (or not happend): After two thousand years have passed, modern machine learning techniques could easily uncover this history because even though all these different languages developed, they still have a set of hidden but common patterns that since than stayed the same.

Sentiment Analysis using Python

One of the applications of text mining is sentiment analysis. Most of the data is getting generated in textual format and in the past few years, people are talking more about NLP. Improvement is a continuous process and many product based companies leverage these text mining techniques to examine the sentiments of the customers to find about what they can improve in the product. This information also helps them to understand the trend and demand of the end user which results in Customer satisfaction.

As text mining is a vast concept, the article is divided into two subchapters. The main focus of this article will be calculating two scores: sentiment polarity and subjectivity using python. The range of polarity is from -1 to 1(negative to positive) and will tell us if the text contains positive or negative feedback. Most companies prefer to stop their analysis here but in our second article, we will try to extend our analysis by creating some labels out of these scores. Finally, a multi-label multi-class classifier can be trained to predict future reviews.

Without any delay let’s deep dive into the code and mine some knowledge from textual data.

There are a few NLP libraries existing in Python such as Spacy, NLTK, gensim, TextBlob, etc. For this particular article, we will be using NLTK for pre-processing and TextBlob to calculate sentiment polarity and subjectivity.

The dataset is available here for download and we will be using pandas read_csv function to import the dataset. I would like to share an additional information here which I came to know about recently. Those who have already used python and pandas before they probably know that read_csv is by far one of the most used function. However, it can take a while to upload a big file. Some folks from  RISELab at UC Berkeley created Modin or Pandas on Ray which is a library that speeds up this process by changing a single line of code.

After importing the dataset it is recommended to understand it first and study the structure of the dataset. At this point we are interested to know how many columns are there and what are these columns so I am going to check the shape of the data frame and go through each column name to see if we need them or not.


There are so many columns which are not useful for our sentiment analysis and it’s better to remove these columns. There are many ways to do that: either just select the columns which you want to keep or select the columns you want to remove and then use the drop function to remove it from the data frame. I prefer the second option as it allows me to look at each column one more time so I don’t miss any important variable for the analysis.

Now let’s dive deep into the data and try to mine some knowledge from the remaining columns. The first step we would want to follow here is just to look at the distribution of the variables and try to make some notes. First, let’s look at the distribution of the ratings.

Graphs are powerful and at this point, just by looking at the above bar graph we can conclude that most people are somehow satisfied with the products offered at Amazon. The reason I am saying ‘at’ Amazon is because it is just a platform where anyone can sell their products and the user are giving ratings to the product and not to Amazon. However, if the user is satisfied with the products it also means that Amazon has a lower return rate and lower fraud case (from seller side). The job of a Data Scientist relies not only on how good a model is but also on how useful it is for the business and that’s why these business insights are really important.

Data pre-processing for textual variables


Before we move forward to calculate the sentiment scores for each review it is important to pre-process the textual data. Lowercasing helps in the process of normalization which is an important step to keep the words in a uniform manner (Welbers, et al., 2017, pp. 245-265).

Special characters

Special characters are non-alphabetic and non-numeric values such as {!,@#$%^ *()~;:/<>\|+_-[]?}. Dealing with numbers is straightforward but special characters can be sometimes tricky. During tokenization, special characters create their own tokens and again not helpful for any algorithm, likewise, numbers.


Stop-words being most commonly used in the English language; however, these words have no predictive power in reality. Words such as I, me, myself, he, she, they, our, mine, you, yours etc.


Stemming algorithm is very useful in the field of text mining and helps to gain relevant information as it reduces all words with the same roots to a common form by removing suffixes such as -action, ing, -es and -ses. However, there can be problematic where there are spelling errors.

This step is extremely useful for pre-processing textual data but it also depends on your goal. Here our goal is to calculate sentiment scores and if you look closely to the above code words like ‘inexpensive’ and ‘thrilled’ became ‘inexpens’ and ‘thrill’ after applying this technique. This will help us in text classification to deal with the curse of dimensionality but to calculate the sentiment score this process is not useful.

Sentiment Score

It is now time to calculate sentiment scores of each review and check how these scores look like.

As it can be observed there are two scores: the first score is sentiment polarity which tells if the sentiment is positive or negative and the second score is subjectivity score to tell how subjective is the text. The whole code is available here.

In my next article, we will extend this analysis by creating labels based on these scores and finally we will train a classification model.