Text analysis of Trump tweets


This post is to proclaim the MathematicaVsR at GitHub project “Text analysis of Trump tweets” in which we compare Mathematica and R over text analyses of Twitter messages made by Donald Trump (and his staff) before the USA president elections in 2016.

The project follows and extends the exposition and analysis of the R-based blog post "Text analysis of Trump’s tweets confirms he writes only the (angrier) Android half" by David Robinson at VarianceExplained.org; see [1].

The blog post [1] links to several sources that claim that during the election campaign Donald Trump tweeted from his Android phone and his campaign staff tweeted from an iPhone. The blog post [1] examines this hypothesis in a quantitative way (using various R packages.)

The hypothesis in question is well summarized with the tweet:

Every non-hyperbolic tweet is from iPhone (his staff).
Every hyperbolic tweet is from Android (from him). pic.twitter.com/GWr6D8h5ed
— Todd Vaziri (@tvaziri) August 6, 2016

This conjecture is fairly well supported by the following mosaic plots, [2]:

TextAnalysisOfTrumpTweets-iPhone-MosaicPlot-Sentiment-Device TextAnalysisOfTrumpTweets-iPhone-MosaicPlot-Device-Weekday-Sentiment

We can see the that Twitter messages from iPhone are much more likely to be neutral, and the ones from Android are much more polarized. As Christian Rudder (one of the founders of OkCupid, a dating website) explains in the chapter "Death by a Thousand Mehs" of the book "Dataclysm", [3], having a polarizing image (online persona) is as a very good strategy to engage online audience:

[…] And the effect isn’t small-being highly polarizing will in fact get you about 70 percent more messages. That means variance allows you to effectively jump several "leagues" up in the dating pecking order – […]

(The mosaic plots above were made for the Mathematica-part of this project. Mosaic plots and weekday tags are not used in [1].)

Concrete steps

The Mathematica-part of this project does not follow closely the blog post [1]. After the ingestion of the data provided in [1], the Mathematica-part applies alternative algorithms to support and extend the analysis in [1].

The sections in the R-part notebook correspond to some — not all — of the sections in the Mathematica-part.

The following list of steps is for the Mathematica-part.

  1. Data ingestion
    • The blog post [1] shows how to do in R the ingestion of Twitter data of Donald Trump messages.

    • That can be done in Mathematica too using the built-in function ServiceConnect, but that is not necessary since [1] provides a link to the ingested data used [1]:

    • Which leads to the ingesting of an R data frame in the Mathematica-part using RLink.

  2. Adding tags

    • We have to extract device tags for the messages — each message is associated with one of the tags "Android", "iPad", or "iPhone".

    • Using the message time-stamps each message is associated with time tags corresponding to the creation time month, hour, weekday, etc.

    • Here is summary of the data at this stage:


  3. Time series and time related distributions

    • We can make several types of time series plots for general insight and to support the main conjecture.

    • Here is a Mathematica made plot for the same statistic computed in [1] that shows differences in tweet posting behavior:


    • Here are distributions plots of tweets per weekday:


  4. Classification into sentiments and Facebook topics

    • Using the built-in classifiers of Mathematica each tweet message is associated with a sentiment tag and a Facebook topic tag.

    • In [1] the results of this step are derived in several stages.

    • Here is a mosaic plot for conditional probabilities of devices, topics, and sentiments:


  5. Device-word association rules

    • Using Association rule learning device tags are associated with words in the tweets.

    • In the Mathematica-part these associations rules are not needed for the sentiment analysis (because of the built-in classifiers.)

    • The association rule mining is done mostly to support and extend the text analysis in [1] and, of course, for comparison purposes.

    • Here is an example of derived association rules together with their most important measures:


In [1] the sentiments are derived from computed device-word associations, so in [1] the order of steps is 1-2-3-5-4. In Mathematica we do not need the steps 3 and 5 in order to get the sentiments in the 4th step.


Using Mathematica for sentiment analysis is much more direct because of the built-in classifiers.

The R-based blog post [1] uses heavily the "pipeline" operator %>% which is kind of a recent addition to R (and it is both fashionable and convenient to use it.) In Mathematica the related operators are Postfix (//), Prefix (@), Infix (~~), Composition (@*), and RightComposition (/*).

Making the time series plots with the R package "ggplot2" requires making special data frames. I am inclined to think that the Mathematica plotting of time series is more direct, but for this task the data wrangling codes in Mathematica and R are fairly comparable.

Generally speaking, the R package "arules" — used in this project for Associations rule learning — is somewhat awkward to use:

  • it is data frame centric, does not work directly with lists of lists, and

  • requires the use of factors.

The Apriori implementation in “arules” is much faster than the one in “AprioriAlgorithm.m” — “arules” uses a more efficient algorithm implemented in C.


[1] David Robinson, "Text analysis of Trump’s tweets confirms he writes only the (angrier) Android half", (2016), VarianceExplained.org.

[2] Anton Antonov, "Mosaic plots for data visualization", (2014), MathematicaForPrediction at WordPress.

[3] Christian Rudder, Dataclysm, Crown, 2014. ASIN: B00J1IQUX8 .

Classification and association rules for census income data


In this blog post I am going to show (some) analysis of census income data — the so called “Adult” data set, [1] — using three types of algorithms: decision tree classification, naive Bayesian classification, and association rules learning. Mathematica packages for all three algorithms can be found at the project MathematicaForPrediction hosted at GitHub, [2,3,4].

(The census income data set is also used in the description of the R package “arules”, [7].)

In the census data every record represents a person with 14 attributes, the last element of a record is one of the labels {“>=50K”,”<50K”}. The relationships between the categorical variables in that data set was described in my previous blog post, “Mosaic plots for data visualization”.

For this data the questions I am most interested in are:
Question 1: Which of the variables (age, occupation, sex, etc.) are most decisive for determining the income of a person?
Question 2: Which values for which variables form conditions that would imply high income or low income? (I.e. “>50K” or “<=50K”.)
Question 3: What conclusions or confirmations we can get from answering the previous two questions?

One way to answer Question 1 is to use following steps, [8].
1. Build a classifier with the training set.
2. Verify using the test set that good classification results are obtained.
3. If the number of variables (attributes) is k for each i, 1<=i<=k :
3.1. Shuffle the values of the i-th column of the test data and find the classification success rates.
4. Compare the obtained k classification success rates between each other and with the success rates obtained by the un-shuffled test data.
5. The variables for which the classification success rates are the worst are the most decisive.

Following these steps with a decision tree classifier, [2], I found that “marital-status” and “education-num” (years of education) are most decisive to give good prediction for the “>50K” label. Using a naive Bayesian classifier, [3], the most significant variables are “marital-status” and “relationship”. (More details are given in the sections “Application of decision trees” and “Application of naive Bayesian classifier”.)

One way to answer Question 2 is to find which values of the variables (e.g. “Wife”, “Peru”, “HS-grad”, “Exec-managerial”) associate most frequently with “>50K” and “<=50K” respectively and apply different Bayesian probability statistics on them. This is what the application of Associative rules learning gives, [9]. Another way is to use mosaic plots, [5,9], and prefix trees (also known as “tries”) [6,11,12].

In order to apply Association rule learning we need to make the numerical variables categorical — we need to partition them into non-overlapping intervals. (This derived, “all categorical” data is also amenable to be input data for mosaic plots and prefix trees.)

Insights about the data set using Mosaic Plots can be found in my previous blog post “Mosaic plots for data visualization”, [13]. The use of Mosaic Plots in [13] is very similar to the Naive Bayesian Classifiers application discussed below.

Data set

The data set can be found and taken from http://archive.ics.uci.edu/ml/datasets/Census+Income, [1].

The description of the data set is given in the file “adult.names” of the data folder. The data folder provides two sets with the same type of data “adult.data” and “adult.test”; the former is used for training, the latter for testing.

The total number of records in the file “adult.data” is 32561; the total number of records in the file “adult.test” is 16281.

Here is how the data looks like:
Adult census income data sample

Since I did not understand the meaning of the column “fnlwgt” I dropped it from the data.

Here is a summary of the data:
Adult census income data summary

As it was mentioned in the introduction, only 24% of the labels are “>50K”. Also note that 2/3 of the records are for males.

Scatter plots and mosaic plots

Often scatter plots and mosaic plots can give a good idea of the general patterns that hold in the data. This sub-section has a couple of examples, but presenting extensive plots is beyond the scope of this blog post. Let me point out that it might be very beneficial to use these kind of plots with Mathematica‘s dynamic features (like Manipulate and Tooltip), or make a grid of mosaic plots.

Mosaic plots of the categorical variables of the data can be seen in my previous blog post “Mosaic plots for data visualization”.

Here is a table of the histograms for “age”, “education-num”, and “hours-per-week”:

Here is a table with scatter plots for all numerical variables of the data:

Application of decision trees

The building and classification with decision trees is straightforward. Since the label “>50K” is only a quarter of the records I consider the classification success rates for “>50K” to be more important.


I experimented with several sets of parameters for decision tree building. I did not get a classification success rate for “>50K” better than 0.644 . Using pruning based on the Minimal Description Length (MDL) principle did not give better results. (I have to say I find MDL pruning to be an elegant idea, but I am not convinced that it works that
well. I believe decision tree pruning based on test data would produce much better results. Only the MDL decision tree pruning is implemented in [2].)

The overall classification success rate is in line with the classification success ratios listed in explanation of the data set; see the file “adult.names” in [1].

Here is a table with the results of the column shuffling experiments described in the introduction (in red is the name of the data column shuffled):

Here is a plot of the “>50K” success rates from the table above:

We can see from the table and the plot that variables “marital-status”, “education-num”, “capital-gain”, “age”, and “occupation” are very decisive when it comes to determining high income. The variable “marital-status” is significantly more decisive than the others.

While considering the decisiveness of the variable “marital-status” we can bring the following questions:
1. Do people find higher paying jobs after they get married?
2. Are people with high paying jobs more likely to marry and stay married?

Both questions are probably answered with “Yes” and probably that is why “marital-status” is so decisive. It is hard to give quantified answers to these questions just using decision trees on this data — we would need to know the salary and marital status history of the individuals (different data) or to be able to imply it (different algorithm).

We can see the decisiveness of “age”, “education-num”, “occupation”, and “hours-per-week” as natural. Of course one is expected to receive a higher pay if he has studied longer, has a high paying occupation, is older (more experienced), and works more hours per week. Note that this statement explicitly states the direction of the correlation: we do assume that longer years of study bring higher pay. It is certainly a good idea to consider the alternative direction of the correlation, that people first get high paying jobs and that these high paying jobs allow them to get older and study longer.

Application of naive Bayesian classifiers

The naive Bayesian classifier, [3], produced better classification results than the decision trees for the label “>50K”:

Here is a table with the results of the column shuffling experiments described in the introduction (in red is the name of the data column shuffled):

Here is a plot of the “>50K” success rates from the table above:

In comparison with the decision tree importance of variables experiments we can notice that:
1. “marital-status” is very decisive and it is the second most decisive variable;
2. the most decisive variable is “relationship” but it correlates with “marital-status”;
3. “age”, “occupation”, “hours-per-week”, “capital-gain”, and “sex” are decisive.

Shuffled classification rates plots comparison

Here are the two shuffled classification rates plots stacked together for easier comparison:

Data modification

In order to apply the association rules finding algorithm Apriori, [4], the data set have to be modified. The modification is to change the numerical variables “age”, “education-num”, and “age” into categorical. I just partitioned them into non-overlapping intervals, labeled the intervals, and assigned the labels according the variable values. Here is the summary of the modified data for just these variables:

Finding association rules

Using the modified data I found a large number of association rules with the Apriori algorithm, [4]. I used the measure called “confidence” to extract the most significant rules. The confidence of an association rule AC with antecedent A and consequent C is defined to be the ratio P(AC)/P(C). The higher the ratio the more confidence we have in the rule. (If the ratio is 1 we have a logical rule, CA.)

Here is a table showing the rules with highest confidence for the consequent being “>50K”:

From the table we can see for example that 2.1% of the data records (or 693 records) show that for a married man who has studied 14 years and originally from USA there is a 0.79 probability that he earns more than $50000.

Here is a table showing the rules with highest confidence for the consequent being “<=50K”:

The association rules in these tables confirm the findings with the classifiers: marital status, age, and education are good predictors of income labels “>50K” and “<=50K”.


The analysis confirmed (and quantified) what is considered common sense:

Age, education, occupation, and marital status (or relationship kind) are good for predicting income (above a certain threshold).

Using the association rules we see for example that
(1) if a person earns more than $50000 he is very likely to be a married man with large number of years of education;
(2) single parents, younger than 25 years, who studied less than 10 years, and were never-married make less than $50000.


[1] Bache, K. & Lichman, M. (2013). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science. Census Income Data Set, URL: http://archive.ics.uci.edu/ml/datasets/Census+Income .

[2] Antonov, A., Decision tree and random forest implementations in Mathematica, source code at https://github.com/antononcube/MathematicaForPrediction, package AVCDecisionTreeForest.m, (2013).

[3] Antonov, A., Implementation of naive Bayesian classifier generation in Mathematica, source code at GitHub, https://github.com/antononcube/MathematicaForPrediction, package NaiveBayesianClassifier.m, (2013).

[4] Antonov, A., Implementation of the Apriori algorithm in Mathematica, source code at https://github.com/antononcube/MathematicaForPrediction, package AprioriAlgorithm.m, (2013).

[5] Antonov, A., Mosaic plot for data visualization implementation in Mathematica, source code at GitHub, https://github.com/antononcube/MathematicaForPrediction, package MosaicPlot.m, (2014).

[6] Antonov, A., Tries with frequencies Mathematica package, source code at GitHub, https://github.com/antononcube/MathematicaForPrediction, package TriesWithFrequencies.m, (2013).

[7] Hahsler, M. et al., Introduction to arules [Dash] A computational environment for mining association rules and frequent item sets, (2012).

[8] Breiman, L. et al., Classification and regression trees, Chapman & Hall, 1984.

[9] Wikipedia, Association rules learning, http://en.wikipedia.org/wiki/Association_rule_learning .

[10] Antonov, A., Mosaic plots for data visualization, (March, 2014), MathematicaForPrediction at GitHub, URL: https://github.com/antononcube/MathematicaForPrediction/blob/master/Documentation/Mosaic%20plots%20for%20data%20visualization.pdf .

[11] Wikipedia, Trie, http://en.wikipedia.org/wiki/Trie .

[12] Antonov, A., Tries, (December, 2013), URL: https://github.com/antononcube/MathematicaForPrediction/blob/master/Documentation/Tries.pdf .

[13] Antonov, A., Mosaic plots for data visualization, (March, 2014) MathematicaForPrediction at WordPress.

Movie genre associations

In this post we are going to look at genre associations deduced by extracting association rules from a catalog of movies. For example, we might want to confirm that most romance movies are also dramas, and we want to find similar rules. For more details see this user guide https://github.com/antononcube/MathematicaForPrediction/blob/master/Documentation/MovieLens%20genre%20associations.pdf at Mathematica for Prediction at GitHub .

The movie data was taken from the page MovieLens Data Sets (http://www.grouplens.org/taxonomy/term/14) of the site GroupLens Research (http://www.grouplens.org). More precisely, the data set named “MovieLens 10M Data Set” was taken.

We are interested in the movie-genre relations only and if we look only at the movie-genre relations of “MovieLens 10M Data Set” the movies are poorly interconnected. Approximately 40% of the movies have only one genre. We use MovieLens since it is publicly available, easy to ingest, and the presented results can be reproduced.

Here is a sample of the movie-genre data:
MovieLens 10k movie-genre data sample

Let us first look into some descriptive statistics of the data set.

We have 10681 movies, and 18 genres. Here is a breakdown of the movies across the genres:
MovieLens 10k movie-genre data genre breakdown

Here are a table of descriptive statistics and a histogram of the distribution of the number of genres:
MovieLens 10k Descriptive statistics for the number of genres

Here are a table of descriptive statistics and a histogram with the distribution of the movies across the release years:
MovieLens 10k Release years descriptive statistics

I applied to the movie-genre data the algorithm Apriori which is an associative rules learning algorithm. The Mathematica implementation is available at this link: https://github.com/antononcube/MathematicaForPrediction/blob/master/AprioriAlgorithm.m

With the Apriori algorithm we can find frequent association genre sets. In order to apply Apriori from each data row only the genres are taken. In this way we can see each movie as a “basket” of genres or as a “transaction” of genres, and the total movie catalog as a set of transactions.

In order to extract association rules from each frequent set we apply different measures. The GitHub package provides five measures: Support, Confidence, Lift, Leverage, and Conviction. The measure Support follows the standard mathematical definition (fraction of the total number of transactions) and it is used to find the association sets. Conviction is considered to be the best for uncovering interesting rules. The definition and interpretation of the measures are given in these tables:
Tables of definitions and properties of association rules measures

I implemented a dynamic interface to browse the association sets that have support higher than 0.25% :
Association sets dynamic interface

This 2×2 table of interface snapshots shows the association sets that have the largest support:
Association sets interface snapshots

We can see that — as expected — “Romance” and “Drama” are highly associated. Other expected associations are {“Comedy”, “Drama”, “Romance”} , {“Crime”, “Drama”, “Thriller”}, and {“Action”, “Crime”, “Thriller”}.

I also implemented a dynamic interface for browsing the association rules extracted from the frequent sets. Here is a list of snapshots of that interface:
1. Association rules of 2 items for all genres ordered by Conviction:
2 item rules for All ordered by Conviction
2. Association rules of 3 items for all genres ordered by Conviction:
3 item rules for All ordered by Conviction
3. Association rules of 2 items with “Drama” ordered by Conviction:
2 item rules for Drama ordered by Conviction
4. Association rules of 3 items with “Drama” ordered by Conviction:
3 item rules for Drama ordered by Conviction

Again, the results we see are expected. For example, looking at the measure Confidence we can see that for the MovieLens 10k catalog 82% of the romance-war movies are also dramas, and 73% of the war movies are dramas. In a certain sense, “War” and {“Romance”, “War”} function like sub-genres of “Drama”.