cdsc_reddit/similarities/README.md

Subreddit similarity

This directory holds the code that computes pairwise similarities between subreddits — both term-based (from TF-IDF over comment text) and author-based (from overlapping commenter sets). Similarity matrices produced here feed downstream clustering (../clustering/) and density analysis (../density/).

Datasets

Subreddit similarity datasets based on comment terms and comment authors are available on Hyak in /gscratch/comdata/output/reddit_similarity. The overall approach to subreddit similarity seems to work reasonably well and the code is stabilizing. If you want help using these similarities in a project, just reach out to Nate.

By default, the scripts here take a TopN parameter which selects the subreddits to include in the similarity dataset according to how many total comments they have. You can alternatively pass a value to the included_subreddits parameter for a file with the names of the subreddits you would like to include on each line.

Scripts

Script	What it does
tfidf.py	Builds TF-IDF vectors for subreddits. Fire CLI subcommands for authors, terms, authors_weekly, terms_weekly.
cosine_similarities.py	Computes cosine similarities between subreddit TF-IDF vectors. Fire CLI subcommands author, term, author-tf.
weekly_cosine_similarities.py	Same idea but operating on the weekly TF-IDF vectors.
wang_similarity.py	A variant similarity computation based on user overlaps in the style of Wang et al.
top_subreddits_by_comments.py	Produces the subreddits_by_num_comments.csv ranking used to pick the top-N subreddits for the similarity matrices.
similarities_helper.py	Shared helpers for building TF-IDF datasets, reindexing, and selecting the top-N subreddits.
Makefile	Wires everything together with the canonical Hyak output paths.

Methods

TF-IDF is a common and simple information-retrieval technique that we can use to quantify the topic of a subreddit. The goal of TF-IDF is to build a vector for each subreddit that scores every term (or phrase) according to how characteristic it is of the overall lexicon used in that subreddit. For example, the most characteristic terms in the subreddit /r/christianity in the current version of the TF-IDF model are:

Term	tf_idf
christians	0.581
christianity	0.569
kjv	0.568
bible	0.557
scripture	0.55

TF-IDF stands for "term frequency — inverse document frequency" because it is the product of two terms "term frequency" and "inverse document frequency." Term frequency quantifies the amount that a term appears in a subreddit (document). Inverse document frequency quantifies how much that term appears in other subreddits (documents). As you can see on the Wikipedia page, there are many possible ways of constructing and combining these terms.

I chose to normalize term frequency by the maximum (raw) term frequency for each subreddit:

\mathrm{tf}_{t,d} = \frac{f_{t,d}}{\max_{t' \in d}{f_{t',d}}}

I use the log inverse document frequency:

\mathrm{idf}_{t} = \log\frac{N}{|\{d \in D : t \in d\}|}

I then combine them using some smoothing to get:

\mathrm{tfidf}_{t,d} = (0.5 + 0.5 \cdot \mathrm{tf}_{t,d}) \cdot \mathrm{idf}_{t}

(Other normalization strategies are worth trying — see the note in TODO.)

Building TF-IDF vectors

The process for building TF-IDF vectors has four steps:

1. Extracting terms using ../ngrams/tf_comments.py
2. Detecting common phrases using ../ngrams/top_comment_phrases.py
3. Extracting terms and common phrases using ../ngrams/tf_comments.py --mwe-pass='second'
4. Building IDF and TF-IDF scores in tfidf.py

Running tf_comments.py on the backfill queue

The main reason that I did it in four steps instead of one is to take advantage of the backfill queue for running tf_comments.py. This step requires reading all of the text in every comment and converting it to a bag of words at the subreddit level. This is a lot of computation that is easily parallelizable. The script ../ngrams/run_tf_jobs.sh partially automates running steps 1 (or 3) on the backfill queue.

Phrase detection using pointwise mutual information

TF-IDF is simple, but only uses single words (unigrams). Sequences of multiple words can be important to account for how words have different meanings in different contexts or how sequences of words refer to distinct things like names. Dealing with context or longer sequences of words is a common challenge in natural language processing since the number of possible n-grams grows like crazy as n gets bigger. Phrase detection helps this problem by limiting the set of n-grams to those most informative.

But how do we detect phrases? I implemented pointwise mutual information, which is a pretty simple way but seems to work pretty well.

PMI is a quantity derived from information theory. The intuition is that if two words occur together quite frequently compared to how often they appear separately then the cooccurrance is likely to be informative.

\operatorname{pmi}(x;y) \equiv \log\frac{p(x,y)}{p(x)\,p(y)} = \log\frac{p(x|y)}{p(x)} = \log\frac{p(y|x)}{p(y)}

In ../ngrams/tf_comments.py if --mwe-pass=first then a 10% sample of 1-4-grams (sequences of terms up to length 4) will be written to a file to be consumed by ../ngrams/top_comment_phrases.py. top_comment_phrases.py computes the PMI for these possible phrases and writes those that occur at least 3500 times in the sample of n-grams and have a PMI of at least 3 (about 65000 expressions).

tf_comments.py --mwe-pass=second then uses the detected phrases and adds them to the term frequency data.

Cosine similarity

Once the TF-IDF vectors are built, making a similarity score between two subreddits is straightforward using cosine similarity.

\text{similarity} = \cos(\theta) = \frac{\mathbf{A} \cdot \mathbf{B}}{\|\mathbf{A}\|\,\|\mathbf{B}\|} = \frac{\sum_{i=1}^{n}{A_i\,B_i}}{\sqrt{\sum_{i=1}^{n}{A_i^2}}\,\sqrt{\sum_{i=1}^{n}{B_i^2}}}

Intuitively, we represent two subreddits as lines in a high-dimensional space (TF-IDF vectors). In linear algebra, the dot product (\cdot) between two vectors takes their weighted sum (e.g. linear regression is a dot product of a vector of covariates and a vector of weights). The vectors might have different lengths — if one subreddit has more words in comments than the other — so in cosine similarity the dot product is normalized by the magnitude (length) of the vectors. It turns out that this is equivalent to taking the cosine of the two vectors. So cosine similarity in essence quantifies the angle between the two lines in high-dimensional space. If the cosine similarity between two subreddits is greater then their TF-IDF vectors are more correlated.

Cosine similarity with TF-IDF is popular (indeed it has been applied to Reddit in research several times before) because it quantifies the correlation between the most characteristic terms for two communities.

Compared to other approaches to similarity like those using word embeddings or topic models it may struggle to handle polysemy, synonymy, or correlations between different terms. Using phrase detection helps with this a little bit. The advantages of this approach are simplicity and scalability. I'm thinking about using latent semantic analysis as an intermediate step to improve upon similarities based on raw TF-IDFs.

Even still, computing similarities between a large number of subreddits is computationally expensive and requires n(n-1)/2 dot-product evaluations. This can be sped up by passing similarity-threshold=X where X>0 into cosine_similarities.py. I used a cosine similarity function that's built into the spark matrix library which supports the DIMSUM algorithm for approximating matrix-matrix products. This algorithm is commonly used in industry (i.e. at Twitter, Google) for large-scale similarity scoring.

See also

The CDSC wiki page CommunityData:CDSC_Reddit is the landing page for this project on the wiki. The methods writeup above used to live there; it now lives here so that doc and code stay in sync.