# Text analysis of Trump tweets

## Introduction

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 .

The blog post  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  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, :

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", , having a polarizing image (online persona) is 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 .)

## Concrete steps

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

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  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  provides a link to the ingested data used :

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

• 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  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  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  and, of course, for comparison purposes.

• Here is an example of derived association rules together with their most important measures: In  the sentiments are derived from computed device-word associations, so in  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.

## Comparison

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

The R-based blog post  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.

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

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

 Christian Rudder, Dataclysm, Crown, 2014. ASIN: B00J1IQUX8 .

# Pareto principle adherence examples

This post (document) is made to provide examples of the Pareto principle manifestation in different datasets.

The Pareto principle is an interesting law that manifests in many contexts. It is also known as “Pareto law”, “the law of significant few”, “the 80-20 rule”.

For example:

• “80% of the land is owned by 20% of the population”,
• “10% of all lakes contain 90% of all lake water.”

For extensive discussion and studied examples see the Wikipedia entry “Pareto principle”, .

It is a good idea to see for which parts of the analyzed data the Pareto principle manifests. Testing for the Pareto principle is usually simple. For example, assume that we have the GDP of all countries:

``````countries = CountryData["Countries"];
gdps = {CountryData[#, "Name"], CountryData[#, "GDP"]} & /@ countries;
gdps = DeleteCases[gdps, {_, _Missing}] /. Quantity[x_, _] :> x;

Grid[{RecordsSummary[gdps, {"country", "GDP"}]}, Alignment -> Top, Dividers -> All]`````` In order to test for the manifestation of the Pareto principle we have to (i) sort the GDP values in descending order, (ii) find the cumulative sums, (iii) normalize the obtained vector by the sum of all values, and (iv) plot the result. These steps are done with the following two commands:

``````t = Reverse@Sort@gdps[[All, 2]];
ListPlot[Accumulate[t]/Total[t], PlotRange -> All, GridLines -> {{0.2} Length[t], {0.8}}, Frame -> True]`````` In this document we are going to use the special function `ParetoLawPlot` defined in the next section and the package . Most of the examples use data that is internally accessible within Mathematica. Several external data examples are considered.

See the package  for the function `RecordsSummary`. See the source file  for R functions that facilitate the plotting of Pareto principle graphs. See the package  for the outlier detection functions used below.

## Definitions

This simple function makes a list plot that would help assessing the manifestation of the Pareto principle. It takes the same options as `ListPlot`.

``````Clear[ParetoLawPlot]
Options[ParetoLawPlot] = Options[ListPlot];
ParetoLawPlot[dataVec : {_?NumberQ ..}, opts : OptionsPattern[]] := ParetoLawPlot[{Tooltip[dataVec, 1]}, opts];
ParetoLawPlot[dataVecs : {{_?NumberQ ..} ..}, opts : OptionsPattern[]] := ParetoLawPlot[MapThread[Tooltip, {dataVecs, Range[Length[dataVecs]]}], opts];
ParetoLawPlot[dataVecs : {Tooltip[{_?NumberQ ..}, _] ..}, opts : OptionsPattern[]] :=
Block[{t, mc = 0.5},
t = Map[Tooltip[(Accumulate[#]/Total[#] &)[SortBy[#[], -# &]], #[]] &, dataVecs];
ListPlot[t, opts, PlotRange -> All, GridLines -> {Length[t[[1, 1]]] Range[0.1, mc, 0.1], {0.8}}, Frame -> True, FrameTicks -> {{Automatic, Automatic}, {Automatic, Table[{Length[t[[1, 1]]] c, ToString[Round[100 c]] <> "%"}, {c, Range[0.1, mc, 0.1]}]}}]
];``````

This function is useful for coloring the outliers in the list plots.

``````ClearAll[ColorPlotOutliers]
ColorPlotOutliers[] := # /. {Point[ps_] :> {Point[ps], Red, Point[ps[[OutlierPosition[ps[[All, 2]]]]]]}} &;
ColorPlotOutliers[oid_] := # /. {Point[ps_] :> {Point[ps], Red, Point[ps[[OutlierPosition[ps[[All, 2]], oid]]]]}} &;``````

These definitions can be also obtained by loading the packages MathematicaForPredictionUtilities.m and OutlierIdentifiers.m; see [1,3].

``````Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/MathematicaForPredictionUtilities.m"]
Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/OutlierIdentifiers.m"]``````

## Units

Below we are going to use the metric system of units. (If preferred we can easily switch to the imperial system.)

``\$UnitSystem = "Metric";(*"Imperial"*)``

## CountryData

We are going to consider a typical Pareto principle example — weatlh of income distribution.

### GDP

This code find the Gross Domestic Product (GDP) of different countries:

``````gdps = {CountryData[#, "Name"], CountryData[#, "GDP"]} & /@CountryData["Countries"];
gdps = DeleteCases[gdps, {_, _Missing}] /. Quantity[x_, _] :> x;``````

The corresponding Pareto plot (note the default grid lines) shows that 10% of countries have 90% of the wealth:

``ParetoLawPlot[gdps[[All, 2]], ImageSize -> 400]`` Here is the log histogram of the GDP values.

``Histogram[Log10@gdps[[All, 2]], 20, PlotRange -> All]`` The following code shows the log plot of countries GDP values and the found outliers.

``````Manipulate[
DynamicModule[{data = Transpose[{Range[Length[gdps]], Sort[gdps[[All, 2]]]}], pos},
pos = OutlierPosition[modFunc@data[[All, 2]], tb@*opar];
If[Length[pos] > 0,
ListLogPlot[{data, data[[pos]]}, PlotRange -> All, PlotTheme -> "Detailed", FrameLabel -> {"Index", "GDP"}, PlotLegends -> SwatchLegend[{"All", "Outliers"}]],
ListLogPlot[{data}, PlotRange -> All, PlotTheme -> "Detailed", FrameLabel -> {"Index", "GDP"}, PlotLegends -> SwatchLegend[{"All", "Outliers"}]]
]
],
{{opar, SPLUSQuartileIdentifierParameters, "outliers detector"}, {HampelIdentifierParameters, SPLUSQuartileIdentifierParameters}},
{{tb, TopOutliers, "bottom|top"}, {BottomOutliers, TopOutliers}},
{{modFunc, Identity, "data modifier function"}, {Identity, Log}}
]`````` This table gives the values for countries with highest GDP.

``````Block[{data = gdps[[OutlierPosition[gdps[[All, 2]], TopOutliers@*SPLUSQuartileIdentifierParameters]]]},
Row[Riffle[#, " "]] &@Map[Grid[#, Dividers -> All, Alignment -> {Left, "."}] &, Partition[SortBy[data, -#[[-1]] &], Floor[Length[data]/3]]]
]`````` ### Population

Similar data retrieval and plots can be made for countries populations.

``````pops = {CountryData[#, "Name"], CountryData[#, "Population"]} & /@CountryData["Countries"];
unit = QuantityUnit[pops[[All, 2]]][];
pops = DeleteCases[pops, {_, _Missing}] /. Quantity[x_, _] :> x;``````

In the following Pareto plot we can see that 15% of countries have 80% of the total population:

``ParetoLawPlot[pops[[All, 2]], PlotLabel -> Row[{"Population", ", ", unit}]]`` Here are the countries with most people:

``````Block[{data = pops[[OutlierPosition[pops[[All, 2]], TopOutliers@*SPLUSQuartileIdentifierParameters]]]},
Row[Riffle[#, " "]] &@Map[Grid[#, Dividers -> All, Alignment -> {Left, "."}] &, Partition[SortBy[data, -#[[-1]] &], Floor[Length[data]/3]]]
]`````` ### Area

We can also see that the Pareto principle holds for the countries areas:

``````areas = {CountryData[#, "Name"], CountryData[#, "Area"]} & /@CountryData["Countries"];
areas = DeleteCases[areas, {_, _Missing}] /. Quantity[x_, _] :> x;
ParetoLawPlot[areas[[All, 2]]]`````` ``````Block[{data = areas[[OutlierPosition[areas[[All, 2]], TopOutliers@*SPLUSQuartileIdentifierParameters]]]},
Row[Riffle[#, " "]] &@Map[Grid[#, Dividers -> All, Alignment -> {Left, "."}] &, Partition[SortBy[data, -#[[-1]] &], Floor[Length[data]/3]]]
]`````` ### Time series-wise

An interesting diagram is to plot together the curves of GDP changes for different countries. We can see China and Poland have had rapid growth.

``````res = Table[
(t = CountryData[countryName, {{"GDP"}, {1970, 2015}}];
t = Reverse@Sort[t["Path"][[All, 2]] /. Quantity[x_, _] :> x];
Tooltip[t, countryName])
, {countryName, {"USA", "China", "Poland", "Germany", "France", "Denmark"}}];

ParetoLawPlot[res, PlotRange -> All, Joined -> True, PlotLegends -> res[[All, 2]]]`````` #### Manipulate

This dynamic interface can be used for a given country to compare (i) the GDP evolution in time and (ii) the corresponding Pareto plot.

``````Manipulate[
DynamicModule[{ts, t},
ts = CountryData[countryName, {{"GDP"}, {1970, 2015}}];
t = Reverse@Sort[ts["Path"][[All, 2]] /. Quantity[x_, _] :> x];
Grid[{{"Date list plot of GDP values", "GDP Pareto plot"}, {DateListPlot[ts, ImageSize -> Medium],
ParetoLawPlot[t, ImageSize -> Medium]}}]
], {countryName, {"USA", "China", "Poland", "Germany", "France", "Denmark"}}]`````` ## Country flag colors

The following code demonstrates that the colors of the pixels in country flags also adhere to the Pareto principle.

``````flags = CountryData[#, "Flag"] & /@ CountryData["Countries"];

flags[[1 ;; 12]]`````` ``````ids = ImageData /@ flags;

pixels = Apply[Join, Flatten[ids, 1]];

Clear[ToBinFunc]
ToBinFunc[x_] := Evaluate[Piecewise[MapIndexed[{#2[], #1[] < x <= #1[]} &, Partition[Range[0, 1, 0.1], 2, 1]]]];

pixelsInt = Transpose@Table[Map[ToBinFunc, pixels[[All, i]]], {i, 1, 3}];

pixelsIntTally = SortBy[Tally[pixelsInt], -#[[-1]] &];

ParetoLawPlot[pixelsIntTally[[All, 2]]]`````` ## TunnelData

Loking at lengths in the tunnel data we can see the manifestation of an exaggerated Pareto principle.

``````tunnelLengths = TunnelData[All, {"Name", "Length"}];
tunnelLengths // Length

(* 1552 *)

t = Reverse[Sort[DeleteMissing[tunnelLengths[[All, -1]]] /. Quantity[x_, _] :> x]];

ParetoLawPlot[t]`````` Here is the logarithmic histogram of the lengths:

``Histogram[Log10@t, PlotRange -> All, PlotTheme -> "Detailed"]`` ## LakeData

The following code gathers lakes data and makes the Pareto principle plots for surface areas, volumes, and fish catch. We can see that the lakes volumes data manifests an “exaggerated” Pareto principle adherence.

``````lakeAreas = LakeData[All, "SurfaceArea"];
lakeVolumes = LakeData[All, "Volume"];
lakeFishCatch = LakeData[All, "CommercialFishCatch"];

data = {lakeAreas, lakeVolumes, lakeFishCatch};
t = N@Map[DeleteMissing, data] /. Quantity[x_, _] :> x;

opts = {PlotRange -> All, ImageSize -> Medium}; MapThread[ParetoLawPlot[#1, PlotLabel -> Row[{#2, ", ", #3}], opts] &, {t, {"Lake area", "Lake volume", "Commercial fish catch"}, DeleteMissing[#][[1, 2]] & /@ data}]`````` ## City data

One of the examples given in  is that the city areas obey the Power Law. Since the Pareto principle is a kind of Power Law we can confirm that observation using Pareto principle plots.

The following grid of Pareto principle plots is for areas and population sizes of cities in selected states of USA.

``````res = Table[
(cities = CityData[{All, stateName, "USA"}];
t = Transpose@Outer[CityData, cities, {"Area", "Population"}];
t = Map[DeleteMissing[#] /. Quantity[x_, _] :> x &, t, {1}];
ParetoLawPlot[MapThread[Tooltip, {t, {"Area", "Population"}}], PlotLabel -> stateName, ImageSize -> 250])
, {stateName, {"Alabama", "California", "Florida", "Georgia", "Illinois", "Iowa", "Kentucky", "Ohio", "Tennessee"}}];

Legended[Grid[ArrayReshape[res, {3, 3}]], SwatchLegend[Cases[res[], _RGBColor, Infinity], {"Area", "Population"}]]`````` ## Movie ratings in MovieLens datasets

Looking into the MovieLens 20M dataset, , we can see that the Pareto princple holds for (1) most rated movies and (2) most active users. We can also see the manifestation of an exaggerated Pareto law — 90% of all ratings are for 10% of the movies. “MovieLens20M-MDensity-and-Pareto-plots”

The following plot taken from the blog post “PIN analysis”, , shows that the four digit passwords people use adhere to the Pareto principle: the first 20% of (the unique) most frequently used passwords correspond to the 70% of all passwords use.

``ColorNegate[Import["http://www.datagenetics.com/blog/september32012/c.png"]]`` ## References

 Anton Antonov, “MathematicaForPrediction utilities”, (2014), source code MathematicaForPrediction at GitHub, https://github.com/antononcube/MathematicaForPrediction, package MathematicaForPredictionUtilities.m.

 Anton Antonov, Pareto principle functions in R, source code MathematicaForPrediction at GitHub, https://github.com/antononcube/MathematicaForPrediction, source code file ParetoLawFunctions.R .

 Anton Antonov, Implementation of one dimensional outlier identifying algorithms in Mathematica, (2013), MathematicaForPrediction at GitHub, URL: https://github.com/antononcube/MathematicaForPrediction/blob/master/OutlierIdentifiers.m .

 Wikipedia entry, “Pareto principle”, URL: https://en.wikipedia.org/wiki/Pareto_principle .

 Wikipedia entry, “Power law”, URL: https://en.wikipedia.org/wiki/Power_law .

 GroupLens Research, MovieLens 20M Dataset, (2015).

 “PIN analysis”, (2012), DataGenetics.

# Handwritten digits recognition by matrix factorization

## Introduction

This MathematicaVsR at GitHub project is for comparing Mathematica and R for the tasks of classifier creation, execution, and evaluation using the MNIST database of images of handwritten digits.

Here are the bases built with two different classifiers:

• Singular Value Decomposition (SVD) • Non-Negative Matrix Factorization (NNMF) Here are the confusion matrices of the two classifiers:

• SVD • NNMF The blog post "Classification of handwritten digits" (published 2013) has a related more elaborated discussion over a much smaller database of handwritten digits.

## Concrete steps

The concrete steps taken in scripts and documents of this project follow.

1. Ingest the binary data files into arrays that can be visualized as digit images.
• We have two sets: 60,000 training images and 10,000 testing images.
1. Make a linear vector space representation of the images by simple unfolding.

2. For each digit find the corresponding representation matrix and factorize it.

3. Store the matrix factorization results in a suitable data structure. (These results comprise the classifier training.)

• One of the matrix factors is seen as a new basis.
1. For a given test image (and its linear vector space representation) find the basis that approximates it best. The corresponding digit is the classifier prediction for the given test image.

2. Evaluate the classifier(s) over all test images and compute accuracy, F-Scores, and other measures.

## Scripts

There are scripts going through the steps listed above:

## Documents

The following documents give expositions that are suitable for reading and following of steps and corresponding results.

## Observations

### Ingestion

I figured out first in R how to ingest the data in the binary files of the MNIST database. There were at least several online resources (blog posts, GitHub repositories) that discuss the MNIST binary files ingestion.

After that making the corresponding code in Mathematica was easy.

### Classification results

Same in Mathematica and R for for SVD and NNMF. (As expected.)

### NNMF

NNMF classifiers use the MathematicaForPrediction at GitHub implementations: NonNegativeMatrixFactorization.m and NonNegativeMatrixFactorization.R.

### Parallel computations

Both Mathematica and R have relatively simple set-up of parallel computations.

### Graphics

It was not very straightforward to come up in R with visualizations for MNIST images. The Mathematica visualization is much more flexible when it comes to plot labeling.

## Going further

### Comparison with other classifiers

Using Mathematica’s built-in classifiers it was easy to compare the SVD and NNMF classifiers with neural network ones and others. (The SVD and NNMF are much faster to built and they bring comparable precision.)

It would be nice to repeat that in R using one or several of the neural network classifiers provided by Google, Microsoft, H2O, Baidu, etc.

### Classifier ensembles

Another possible extension is to use classifier ensembles and Receiver Operation Characteristic (ROC) to create better classifiers. (Both in Mathematica and R.)

### Importance of variables

Using classifier agnostic importance of variables procedure we can figure out :

• which NNMF basis vectors (images) are most important for the classification precision,

• which image rows or columns are most important for each digit, or similarly

• which image squares of a, say, 4×4 image grid are most important.