Analyzing Political Discourse on Reddit

8/10/2019 Analyzing Political Discourse on Reddit

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Network Analysis Final Report

Max Candocia

December 12, 2014

Abstract

This papers purpose is to show how to apply semi-supervised generative models to clas-

sify the political ideologies of users in an online network and then analyze the interactions

thoughout the website using homophily measures. For this study, Reddit, a large social me-

dia website, is used as the sample source. The model uses two sets of variables: the various

parts of the website where users post comments and whether or not it is positively received,

and various n-grams used within these comments. Oftentimes users of the Internet will dis-

cuss and debate various topics relating to politics, but the manner in which they take place

varies greatly. After classifying users, analyzing the homophily between different portions

of the website will provide insight into how diversity of ideologies (or lack thereof) plays a

role in facilitating discussions. In addition, the amount of positively-scored comments be-

tween people of different or similar ideologies is used as a way of detecting hostilities between

groups. For the generative model, one of the interesting results is which n-grams are used

more often by people of differing ideologies. While these words do not include context, the

second set of variables that involve posting locations help provide that aspect using Reddits

website structure and scoring system. Hyperparameter controls aid in how sharply different

variable sets discriminate between classes, and are shown to reduce both error and impurity

when using 5-fold cross-validation. Finally, the limitations of an algorithm are discussed, as

comment histories are treated as corpora, which can be tens of thousands of words long.

Introduction

User interactions on websites is often a topic of interest. However, the amount of data

one can gather on a particular user is often limited, especially if they do not have much

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information publicly available or have a large amount of text available for analysis. For the

purposes of this project, Reddit is used. Reddit, one of the largest social media websites

in the United States, hosts tens of millions of discussions between millions of users. Many

of these users have extensive posting histories, and they are divided up into sections of the

website called Subreddits. Subreddits are sections of the website for which content revolves

around a single topic, which can be either specific, such as a sports team in Germany, or

broad, such as US politics. There are Subreddits for a variety of topics, and they are usually

named by putting /r/ (pronounced as the English letter r is pronounced) before them,

such as /r/politics, /r/Conservative, or /r/DebateCommunism. Anecdotally, these

communities have biases in them, but no attempt has been made to measure this bias in

terms of political ideology or affiliation. While it is relatively obvious to any user who

traverses the site in general, attempts to quantify this have not been made, largely due to

the difficulty of classifying the ideologies of tens of thousands of users.With these results, it is possible to analyze the compositions of various Subreddits, as

well as quantify interactions between users of different ideologies in them. The results may

be interpretable on a scale of -1 to 1, where -1 indicates that a Subreddit is adebating

grounds (i.e., the sole purpose of commenting is to argue with someone of a different political

ideology), while 1 indicates that it is a pure hive mind (i.e., believers of an ideology only

discuss amongst themselves). Of course, the limitations of the classification algorithm should

be taken into account whenever analyzing the results.

Background

Ideologies

For this study, users are grouped into five different ideological categories. This is not a 100%

accurate representation of the political spectrum, but the groups are general enough to apply

to a large number of people, and they are different enough in terms of philosophical aspects

that they can be considered distinct. These terms are relatively unambiguous when used in

the context of United States politics.

Anarcho-Captialism

Anarcho-Capitalism is a subset of libertarianism as it is described below. Generally speak-

ing, it is the belief that all interactions between humans should be facilitated according to

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principles of laissez-faire capitalism and that government does not exist.

Conservatism

In this context, conservatism refers to conservatism in the United States. Generally speaking,

it is the belief that the government should not have as large of a role in economic issues.

As far as social issues go, there are varying degrees of belief that government should control

certain social interactions between people, but on Reddit, the number of conservatives who

believe in strong government control over social interactions is relatively small compared to

the number of conservatives. Most of the followers of this ideology on Reddit lean towards

the US Republican party.

Liberalism

In this context, liberalism refers to what is generally known as left-liberalism, which consists

of the beliefs of less involvement of government in social affairs between people and more

government involvement in peoples well-being and regulation of businesses. Most of the

followers of this ideology on Reddit lean towards the US Democratic party.

Libertarianism

In this context, libertarianism refers to what is generally known as right-libertarianism, which

is the belief that government should have minimal involvement in both social and economicaffairs of people. While anarcho-capitalism is a subspace of this ideology, it is excluded from

this category because of the divisiveness between the idea of minimal government and no

government.

Socialism

In this context, socialism mostly refers to communism, but it can also refer to the ideologies

of social democrats, who prefer more gradual change than other socialists, who often describe

themselves as anarchists. One of the common goals of socialism is to eliminate hierarchy insociety via the elimination of capitalism.

Learning Algorithm

Learning algorithms for large networks require relatively simple models that can support a

large number of parameters. For this reason, generative models are often used to accomplish

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this. Nigam et al. describes a basic framework for working with a semi-supervised model

in general. Wang et al. describes some different hyperparameter choices, such as link type

importance, that are used in this methodology. However, CATHYHIN, as described in

Wang et al. is an unsupervised learning method that is designed to work on bibliographic

data, as well as creating subtopics for clustering (clusters within clusters). While this could

certainly be possible with ideologies (e.g., Anarcho-Capitalism is treated as a subtopic of

Libertarianism), this aspect of the algorithm will be ignored for the purposes of exploring a

simpler model.

Homophilies of Online Communities

Homophilies of online communities are of great interest to researchers, as data is easier to

gather and far more abundant than real life data. Generally those measuring homophily

use race, gender, and location as attribute variables. However, Bisgin et al. describes

how online communities have the potential to attract people of similar interests due to the

very low barrier of entry. Bisgin describes methods for describing pairwise similarity using

Jaccard similarity coefficients, as the similarity attribute is the shared interests between

users. However, for this data, we rely on clustering in order to determine if users are similar

or not, so that method cannot be applied here. Granted, by definition of the generative

model used, users who use similar words or post in similar places will have a tendency to be

clustered together.

Data

Sampling

The data was collected fromhttp://www.reddit.com/using the Reddit API over the course

of two weeks. The scraper sequentially cycled through 24 different subreddits and grabbed

the most recent post with at least 1 comment reply that was at least 2 days old. The

reason for the cutoff is that most posts do not acquire new comments after 1 day. Within

each comment thread, each comment is collected, as well as the commenting history (last

200 comments) of the user who posted the comment. There are cutoffs for threads with

an abnormally high amount of comments. However, this occurs very rarely, and most of

these comments have less substance to them and no replies to them, making them less

meaningful. This is partly due to Reddits ranking algorithm, which places more recent and

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http://www.reddit.com/http://www.reddit.com/


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more positively-voted comments most visibly.

Labeling

Since ideologies are not labeled a priori, they were manually labeled by selecting a randomsample from the set of all users. Their entire comment histories were analyzed, and a deci-

sion was made regarding classification. Some users could not be classified due to insufficient

information, so they were skipped. The group sizes from this classification were used to con-

struct priors for the generative model. The group sizes for anarcho-capitalism, conservatism,

liberalism, libertarianism, and socialism were 53, 80, 296, 87, and 59, respectively, for a total

of 578 users. This equates to priors of 9.2%, 13.9%, 51.5%, 15.1%, and 10.3%. Note that

this prior is specific to the sample, not to Reddit as a whole.

Description

A total of 18,545 users were recorded, with up to 200 comments in their comment histories

recorded, with a time-cutoff of 4 months from the date of collection. 116,810 comments from

100 different Subreddits were used in the learning algorithm. 3,550 different threads were

analyzed, with a total of 70,738 comments between users. Note that this value is the sum of

all weighted edges between users.

The n-grams used for the general algorithm were hand-selected, as topical clustering can

occur in many other ways. For example, people from all ideologies might talk about the ebolavirus, ISISs invasion of Iraq, or other current events that arent politically lopsided. Also,

note that the values for Subreddits were weighted logarithmically in order to give more weight

to comments that are recieved more positively or negatively by the community. Additionally,

the Subreddit variables were divided into two parts: positively-scored comments on the

Subreddit and negatively-scored comments. This increases the number of Subreddits from

100 to 200.

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Method

Semi-Supervised Classification

Symbol Meaning

b the set of ideologiess the set of Subreddits

t the set of n-grams

bk kth ideology

si ith Subreddit

ti ith n-gram

vt the relative importance of terms versus Subreddits

Ws the initial weight of manually labeled data versus the entire data set for Subreddits

Wt the initial weight of manually labeled data versus the entire data set for n-grams

ds the exponential decay rate for the weight of manually labeled data for Subreddits

dt the exponential decay rate for the weight of manually labeled data for n-grams

ws the minimum weight of manually labeled data after applying decay for Subreddits

wt the minimum weight of manually labeled data after applying l decay for n-grams

s the calculated weight of trained data for Subreddits

t the calculated weight of trained data for n-grams

s the raw count added to each ideologys Subreddit count; a smoothing parameter

t the raw count added to each ideologys n-gram count; a smoothing parameter

sik the probability ofsi appearing in bk

tik the probability ofti appearing in bk

ui theith user

usij the weighted value ofsj for ui

utij the weighted value oftj forui

ubi the ideology ofui

ubik the likelihood ofbk forui

ubik the probability ofbk for ui

q the iteration number of the EM algorithm, starting at 0

N the total number of users

Ns the total number of Subreddits

Nt the total number of n-grams

M the total number of manually labeled users

um the set of manually labeled users

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Assumptions

1. Each user will post a certain number of comments with no relation to their ideology

2. Each user will use a certain number of n-grams with no relation to their ideology

3. When a user who follows bk posts a comment in a Subreddit, there is a sik probability

that the user would post in Subreddit si.

4. When a user who followsbk uses a key n-gram in a comment, there is a tik probability

that that particular n-gram is ti.

5. For any randomly selected user, there is a pk chance that they belong to bk, where pk

is the prior probability.

Algorithm

For each iteration number q, we first estimate the weights of manually labeled data,

s=NWsmax(e

qds , ws)

M

s=NWtmax(e

qdt , wt)

M

Normally algorithms run in supervised modeThen we calculate the Subreddit and n-gram probabilties for each ideology,

sjk =s+

ui|ubi=bk

(1 +sI(ui um)) usij

s Ns +

sls

ui|ubi=bk

s+ (1 +sI(ui um)) usil

tjk =t+

ui|ubi=bk

(1 +tI(ui um)) utij

t Nt +

tlt

ui|ubi=bk

t+ (1 +tI(ui um)) util

Using these values, we then calculate the ideology membership likelihoods of different

users.

ubik =

sjs

sjkusij

tjt

tjkutij

vt

Then the probabilities are calculated by dividing each likelihood by the sum of likelihoods:

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ubik =ubikblb

ubil

Then new memberships are assigned by selecting the ideology with the maximum prob-

ability,

ubi =bargmax(k,ubik

)

This process is repeated several times (usually one to two dozen) for convergence. Note

that logarithms are preferred for computational purposes, but the mathematics is the same.

Additionally, class priors were not updated, as they usually are in generative models. Doing

so favors the largest groups, which disproportionately increases error in other groups.

Variable Selection

Because variables were initially selected without much regard for their usefulness from a

statistical perspective, a simple and efficient method is used to reduce the number of Sub-

reddit and n-gram variables: After the generative model algorithm is run, it is rerun, but

with any variable that does not have a factor of at least 20 between the highest and lowest

probabilities among its ideologies. This means that variables must be more discriminatory

in order to be considered in the model. Using cross-validation to evaulate model criteria,

other methods are possible, but this cutoff is the most efficient considering the size of the

dataset.

Validation

Because trained data exists, the model may be validated via n-fold cross-validation.

1. Choose a number k that represents the number of folds (i.e., iterations of validation)

you want to use.

2. Divide the manually labeled data into k partitions.

3. For each partition, run the generative model without having data from that partition

being labeled.

4. Compare the results of the classifications for each partition with their true (manually

labeled) classifications. Record the error rate and the impurity rate for each classifica-

tion.

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Depending on the goal of classification, other loss criteria may be used to quantify the

models accuracy.

Homophily Measures

Note that if one of these variables appears without operating on a Subreddit, it refers to the

entire dataset.

Variable Meaning

f(sk) the frequency matrix of comments from users of one ideology to another in sk

fij(sk) the frequency of comment responses from someone ofbi to someone ofbj insk

fj(sk) the frequency of responses from all users to someone ofbj insk

fi(sk) the frequency of responses from someone ofbi to all users in sk

H(si) the homophily ofsiEij(sk) the expected number of responses from someone ofbi to someone ofbj in sk

assuming that there is no correlation with respect to i and j

ERij(sk) fij(sk)/Eij(sk), defined as 1 when it would otherwise be 00

Sij(sk) proportion of comment replies from someone ofbi tobj in sk that are positively-score

Overall Homphily

Since homophily was related by class identification, a matrix of responses, f(sk), for which

theith row andj th column refers to the number of comment replies to users ofbi tobj insk,

is used to calculate correlation. The homophily, H(sk), is defined to be

H(sk) =2 trace f(sk)

f(sk)

f(sk)

A value of 1 means that all interactions are between people of similar ideologies, and a

value of -1 means all interactions are between users of different ideologies.

Response Likelihood

Another metric of interest is how likely someone is to respond to someone else in a Subreddit

given both their ideologies, versus what youd expect if they responded completely randomly.

The calculation for the matrix of expected values is as follows:

Eij(sk) =fi(sk) fj(sk) 1

(

f(sk))2

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Then the ratio is calculated,

ERij =fij(sk)

Eij(sk)

Ratios that have large enough cell counts are then reported.

Response Positivity

One final metric that is used, although not directly related to homophily, is the proportion

of responses from users of bi to bj within sk that are positive. This metric is extremely

straightforward to calculate, although it is mostly useful in analyzing specific Subreddits.

The main purpose of this metric is to indicate hostility towards particular groups from

another group, which is useful information when analyzing homophily.

Results

Semi-Supervised Classification

For variable selection, 144 out of the original 200 Subreddits were used in the model, and

154 out of 330 of the original n-grams were used in the model.

For the semi-supervised classification, 5-fold cross-validation was used in order to deter-

mine the error rate and the impurity of each group. The error rate for each group is theproportion of members of each group that were not classified into the proper group. The

impurity rate for each group is the percentage of users classified into a group that do not

belong to that group. In this experiment, the primary goal was to minimize impurity, as it

helps ensure that the subjects used for inference are most likely to have accurate labels.

Anarcho-Captialsim Conservatism Liberalism Libertarianism Socialism

Error 32.8% 61.3% 11.5% 48.1% 39.2%

Impurity 26.7% 34.0% 29.0% 33.8% 21.7%

While these results are significantly better than random guesses, there is still a consider-

able amount of error.

With rows representing actual values and columns representing sorted values, this is the

classification matrix from the cross-validation:

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Anarcho-Capitalism Conservatism Liberalism Libertarianism Sociali

Anarcho-Capitalism 33 0 12 4 4

Conservatism 0 31 43 5 1

Liberalism 7 10 262 13 4

Libertarianism 3 6 32 45 1

Socialism 2 0 20 1 36

Authority Hub

AmericanPolitics

Anarchism

Anarcho_Capitalism

Bad_Cop_No_Donut

BasicIncome

changemyview

Conservative

conspiracy

DebateAnarchism

DebateFascism

Economics

EnoughLibertarianSpam

gunpolitics

Libertarian

MensRights

moderatepolitics

NeutralPolitics

occupywallstreet

PoliticalDiscussion

politics

privacy

progressive

socialism

worldpolitics

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

Subreddit

Ideology

AnarchoCapitalism

Conservatism

Liberalism

Libertarianism

Socialism

Ideology Representation from Top 10 Hub and AuthorityRanked Usersin Each Subreddit

Figure 1: The ideologies of the most important users in various Subreddits. Hub rankings

and authority rankings derived from the HITS algorithm are used here. Users with high hub

rankings tend to respond to more and important individuals, and people with high authority

rankings tend to be responded to by more and important people.

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Homophily Measures

The following results use cross-validated averages combined with the results with all labeled

data used to classify results. Additionally, results were averaged over classification-calculated

ideologies (i.e., values of 1 or 0) and probability-calculated ideologies (derived in the model).The overall homophily for all Subreddits combined was 0.25.

1,957 123 1,762 569 670 5,080

133 1,248 3,081 478 123 5,062

1,740 3,131 34,300 3,893 2,134 45,197

562 482 3,742 1,636 192 6,614

677 113 1,970 191 4,516 7,467

5,068 5,096 44,855 6,767 7,634 69,421

AnarchoCapitalism

Conservatism

Liberalism

Libertarianism

Socialism

Total

AnarchoCapital ism Conservatism Liberal ism Libertarianism Socialism Total

Replier's Ideology

OriginalPoster'sIdeology

0

10000

20000

30000

Number of Comments

Frequency of Replies in Sampled Subreddits by Ideology of Replier and Original Poster

Displayed values are averaged from different algorithms of ideology predicting

Figure 2: The frequencies of various response types across all Subreddits. Note that the

discrepancy between the number of comments in the summary statistics are not the same as

the number here, as some comments are mediated by unclassified users due to various forms

of censoring on the website (e.g., banning, comment removal).

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Figure 3: The homophilies of various Subreddits, ordered from highest to lowest.

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5.3 0.3 0.5 1.1 1.2

0.4 3.4 0.9 1 0.2

0.5 0.9 1.2 0.9 0.4

1.2 1 0.9 2.5 0.3

1.2 0.2 0.4 0.3 5.5

AnarchoCapitalism

Conservatism

Liberalism

Libertarianism

Socialism

AnarchoCapitalismConservatism Liberalism Libertarianism Socialism

Replier's Ideology

OriginalP

oster'sIdeology

0.1

1.0

10.0

actual replies

expected replies

color is based on a log scale

Ratio of Actual Responses to Expected Responses on Sampled Subreddits

Figure 4: The ratios of actual responses to expected responses for the entire network, by

ideologies of replier and original poster.

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89.5% 80.9% 86.3% 87.9% 84.5%

83.7% 82.4% 80.9% 84.9% 78.2%

83.5% 76.6% 82.5% 80.3% 84.1%

87.1% 84.0% 80.3% 83.7% 80.4%

82.8% 78.6% 86.3% 79.8% 87.3%

AnarchoCapitalism

Conservatism

Liberalism

Libertarianism

Socialism

AnarchoCapitalism Conservatism Liberalism Libertarianism Socialism

Replier's Ideology

OriginalPo

ster'sIdeology

75%

80%85%

90%

95%

100%% Positive

Percentage of PositivelyScored Responsesby Ideology of Responder and Original Poster

Figure 5: The percent of responses scored positively by ideologies of the replier and orig-

inal poster. Lower values mean that comment replies recieve negative feedback from the

community it was posted in, and likely the original poster, as well.

Some specific results for Subreddits that will be used as examples in the conclusion:

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1,766 5 324 221 306 2,623

18 0 4 1 1 24

323 2 69 48 55 496

212 0 46 32 37 328

320 1 56 38 69 485

2,639 8 499 340 468 3,955

AnarchoCapitalism

Conservatism

Liberalism

Libertarianism

Socialism

Total

AnarchoCapitalism Conservatism Liberalism Libertarianism Socialism Total

Replier's Ideology


0

500

1000

1500

Number of Comments

Frequency of Replies in /r/Anarcho_Capitalism by Ideology of Replier and Original Poster


60 22 235 221 13 552

23 12 108 92 7 243

238 92 912 799 59 2,100

228 91 745 814 39 1,917

12 5 49 40 4 110

561 222 2,050 1,965 122 4,922

AnarchoCapitalism

Conservatism

Liberalism

Libertarianism

Socialism

Total

AnarchoCapitalism Conservatism Liberalism Libertarianism Socia lism Total

Replier's Ideology


0

250

500

750

Number of Comments

Frequency of Replies in /r/Libertarian by Ideology of Replier and Original Poster


Figure 6: Frequencies of /r/Anarcho Capitalism and /r/Libertarian comment replies by

ideology of replier and original poster.

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86% 66% 81% 87% 94%

75% 78% 78% 76% 84%

75% 64% 78% 72% 84%

83% 76% 81% 82% 91%

82% 40% 70% 64% 88%

AnarchoCapitalism

Conservatism

Liberalism

Libertarianism

Socialism

AnarchoCap ital ism Conse rvat ism L iberal ism L iber ta rian ism Soc ia lism

Replier's Ideology


0.00

0.25

0.50

0.75

1.00% Positive Replies

Percentage of Comment Reply Scores that are Positive for /r/politics

Blank cells have too few entries to display.

Figure 7: Percentage of comments with positive scores by ideologies of replier and original

poster in /r/politics.

Conclusions

Classification

The semi-supervised classification algorithm was fairly effective at classifying liberals cor-

rectly, but across the board, the error rate was somewhat high, even for a classification

problem with 5 different groups. There is not too much to say about the algorithm without

using a competing algorithm and comparing results. The primary purpose of classification

is to have the labels as opposed to testing the algorithm.

Homophily

Unsurprisingly, the majority of interactions on the sampled Subreddits are facilitated by

liberals. This effect can be seen as a majority of Subreddits have high homophilies. Two

notable exceptions are /r/Anarcho-Capitalism and /r/Libertarian. Upon closer inspection,

viewing the frequency tables for the specific subreddits can detail what is happening. In

the case of /r/Anarcho-Capitalism, Anarcho-Capitalists tend to respond to many people of

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differing ideologies, which lowers the homophily significantly. In the case of /r/Libertarian,

the majority of users (not seen in the graphics below) are libertarians, but most of the

interactions are facilitated by liberals. This means that there are many liberals responding

to libertarians and vice-versa, which makes /r/Libertarian a heterophilic Subreddit.

While the sampling procedures introduce bias into statistics generalized to the whole

website, each ideology demonstrated that its users had a level of preferential self-attachment,

as is seen in Figure 4. What is most notable, though, is the tendency for anarcho-capitalists

and Socialists to communicate much less frequently with those of other ideologies. There

is an obvious exception, where anarcho-capitalists are slightly more likely to respond to

libertarians and socialists and vice-versa, but with the majority of the website consisting of

liberals, clustering is obvious.

Finally, looking at the tendency for comments to have a positive score, it is obvious that

there is some hostility for conservatives by liberals, but this effect is averaged over the entiresample. If you take a look at the main politics Subreddit, /r/politics in Figure 7, the story

becomes much more clear. It is obvious here that conservatives are not very welcome by

socialists, liberals, or anarcho-capitalists in /r/politics. Looking at these results by Subreddit

reduces biases caused by sampling and allows for a much more precise understanding of how

interactions take place in a community.

As far as practicality behind these results, individuals can use these to decide which

sections of the website are more hospitable to discussion given their ideology, and for content-

makers (e.g., blog writers), the general census results of the Subreddits can be used tostrategically post content targetting the appropriate audience.

Limitations and Future Work

There are many limitations of this analysis, the largest one being the error introduced by the

learning algorithm. Oftentimes people post little information about their beliefs, so it is very

difficult to classify them. Additionally, even when it is more obvious to a human, machine

learning algorithms become very complicated when a high level of accuracy is desired.One possible solution in future experiments is to shift the model to use natural language

processing to establish variables, rather than rely purely on n-grams, which are much noisier

in the context of comments on social media. Additionally, a model with hyperparameters for

each class, such as those implemented in CATHYHIN in Wang et al., would allow for more

flexibility in discriminating between ideologies. Also, akin to the topical heirarchies that are

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created in CATHYHIN, a more advanced model could find subclusters within ideologies so

that top-level groups do not have to be as homogenous with respect to their parameters.

There is also the question of how dissimilar users are in their beliefs, regardless of ide-

ology. If two users have one political viewpoint in common and discuss it with each other,

should that be considered heterophilic? Coincidentally, that type of process is described by

Damon Cantola in Homophily, Cultural Drift, and the Co-Evolution of Cultural Groups

as one that can actually bridge groups together. However, trying to extend this model to a

network evolution model would be very difficult given the Reddit API limitations and the

vast amounts of data that would need to be collected.

Lastly, while the sample size was sufficient for the analysis that was done, a larger sample

size would enable more complex algorithms to be used, since the number of parameters is very

high for such models. One major difficulty of this is the time-consuming task of manually

labeling users, but perhaps the nature of semi-supervised learning would not necessitate animpractically large training size.

References

1. Bisgin, Hail; Agarwal, Nitin; and Xu, Xiaowei. Investigating Homophily in Online

Social Networks. http://www.researchgate.net/publication/221158453 Investigating

Homophily in Online Social Networks/links/0fcfd5089ae5348b1c000000

2. Centola, Damon et al. Homophily, Cultural Drift, and the Co-Evolution of Cultural

Groups. http://nsr.asc.upenn.edu/files/Centola-et-al-2007-JCR.pdf

3. H. Wickham. ggplot2: elegant graphics for data analysis. Springer New York, 2009.

4. Hadley Wickham (2014). scales: Scale functions for graphics. Rpackage version 0.2.4.

http://CRAN.R-project.org/package=scales.

http://nsr.asc.upenn.edu/files/Centola-et-al-2007-JCR.pdf

5. Nigam, Kamal; McCallum, Andrew; and Mitchell, Tom M. Semi-Supervised TextClassification Using EM.http://people.cs.umass.edu/ mccallum/papers/semisup-em.pdf

6. R Core Team (2014). R: A language and environment for statistical computing. R

Foundation for Statistical Computing, Vienna, Austria. URLhttp://www.R-project.org/.

7. Wang et al. Constructing Topical Hierarchies in Heterogeneous Information Networks.

http://web.engr.illinois.edu/ hanj/pdf/icdm13 cwang.pdf

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http://www.researchgate.net/publication/221158453_Investigating_Homophily_in_Online_Social_Networks/links/0fcfd5089ae5348b1c000000http://www.researchgate.net/publication/221158453_Investigating_Homophily_in_Online_Social_Networks/links/0fcfd5089ae5348b1c000000http://nsr.asc.upenn.edu/files/Centola-et-al-2007-JCR.pdfhttp://cran.r-project.org/package=scaleshttp://nsr.asc.upenn.edu/files/Centola-et-al-2007-JCR.pdfhttp://people.cs.umass.edu/~mccallum/papers/semisup-em.pdfhttp://www.r-project.org/http://web.engr.illinois.edu/~hanj/pdf/icdm13_cwang.pdfhttp://web.engr.illinois.edu/~hanj/pdf/icdm13_cwang.pdfhttp://www.r-project.org/http://people.cs.umass.edu/~mccallum/papers/semisup-em.pdfhttp://nsr.asc.upenn.edu/files/Centola-et-al-2007-JCR.pdfhttp://cran.r-project.org/package=scaleshttp://nsr.asc.upenn.edu/files/Centola-et-al-2007-JCR.pdfhttp://www.researchgate.net/publication/221158453_Investigating_Homophily_in_Online_Social_Networks/links/0fcfd5089ae5348b1c000000http://www.researchgate.net/publication/221158453_Investigating_Homophily_in_Online_Social_Networks/links/0fcfd5089ae5348b1c000000


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Appendix

Figure 8: Visualization of comment replies in sample. Gold = anarcho-capitalist, Red =

conservative, Blue = liberal, Green = libertarian, Pink = socialist, Black = unlabeled.

Layout created using Yifan-Hu algorithm in Gephi.

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Documents

Analyzing Political Discourse on Reddit