Character choices in Harry Potter fanfiction

Harry Potter fanfiction is something I find pretty interesting. On FanFiction.net, there are over 700,000 stories, all set within the Harry Potter universe. Not one of the authors expects any sort of financial gain, although it is possible for popular authors to get published.  E.L. James, the author of 50 Shades of Grey, got her start writing fanfiction for the Twilight series. Say what you will about either of those series, but there’s no denying their popularity.

The stories on the FanFiction.net, also called “fics” or “fanfics”, vary wildly in length from poems to short stories to full-length novels. There’s even a few fics that contain more words than all seven Harry Potter books put together. It’s also surprising that the community is still active to this day, considering it’s been eight years since the last book came out and four years since the last movie.

I decided to take a look at the meta-information available on FanFiction.net for these stories. When browsing for fics, you can get lists of descriptions containing the title, author, genre, length, number of reviews, etc. There’s also a short summary written by the author. I wrote a script that scrapes this information from the search results, using the Python lxml module for HTML parsing. I randomly sampled 200,000 fics, so roughly 28% of the total. Here are a few stats from the dataset:

 

I think these are some fairly impressive numbers. Of course, these statistics are a poor summary of the actual data, but for my first post with this dataset, I wanted to look at character choices.

Most popular single characters

Each fic can list up to four characters from a list of 375. Harry Potter has a lot of supporting characters. The first thing I did was count how many times each individual character appeared in a fic and sorted the result. Below are the most popular character choices.

Top 25 character choices. Note that the percentages sum to >100% since each fic can have multiple choices.

Top 25 character choices. Note that the percentages sum to >100% since each fic can have multiple characters

 

It should come as no surprise that Harry is at the top of the list. I do feel a bit bad for Ron, though. It appears that Draco has taken what could arguable be called his spot, and Ron barely made it higher than “OC”, meaning an original character. I think there are multiple reasons for this. First, a large percentage of Harry Potter fanfics are romances: 55% of fics in my sample contain the “Romance” genre label, with the next highest being “Humor” at 21%. I think Draco has that bad boy appeal that makes him popular in romances. I’ve also found that a lot of fics are “do-overs”, i.e. fan re-imaginings of the original plot. In those stories, Ron can be unpopular. The community even has a term for treating a character badly called “bashing”.

The other rankings aren’t too surprising. I kinda wish Fred and George were next to each other, but I understand since there’s also a popular type of story that picks up where the books ended. As an example, if anyone reading this is a Harry Potter fan, I recommend the short story Cauterize by Lady Altair.

Pairings and multiple character groupings

The next thing I wanted to look at was how characters are grouped together. As I mentioned, romance is a very popular genre label, so the most popular grouping is obviously two characters. The community refers to this as a “pairing”, and if a fan likes a particular pairing, they “ship” that pairing. It’s short for “relationship” (used as both a noun and a verb for some reason). There can be fervent debates about “ships” on sites like /r/harrypotter, so I think it’s an interesting thing to look at.

As an aside for those familiar with FanFiction.net, I’ve ignored the use of square brackets [], which are supposed to explicitly denote a romantic pairing. Only 3.2% of fics in my sample use brackets, which goes up slightly to 4.5% if you just consider fics with a Romance genre label. Thus, I found it easier to just ignore them.

To do the analysis, I counted how often each combination of characters occurred and grouped the possible combinations by numbers of characters, i.e. a “double” indicates a fic with two and only two characters. These pairings may be romantic or platonic, but differentiating these cases is impossible from my dataset, since even the summary text may not indicate which pairings are romantic and which aren’t. Regardless, this is such a large dataset that I think the overall trends are still clear.

Stuff

Pie chart of character percentages from a sample of 200,000 fics. The color indicates the number of characters, which are broken up into the most popular character choices for each.

 

A few observations:

  1. Pairings are definitely the most popular type of fic, with Draco pairings claiming the top two spots. I was actually surprised that canon pairings are as popular as they are (Ron/Hermione, Harry/Ginny, etc.).
  2. The “other doubles” category is the single biggest chunk of the graph, but these are all pairings that consist of <1% of the total. In my dataset, there are 2,779 unique pairings, and I’m only showing 12. Of course, this is only a subset of the total possible 70,125 possible pairings given 375 available characters.
  3. Of the solo acts, Snape is the second most popular (after Harry, of course). This seems appropriate to me, since Snape strikes me as a lone wolf character.
  4. The “golden trio”  of Harry, Hermione, and Ron is unsurprisingly the most popular choice for three characters. The value 0.1% may seem small, but remember we’re talking about 700,000 fics, so 0.1% is still in the hundreds.

Summary analysis for different pairings

The last thing I wanted do was see what particular pairings have in common, if anything. The method I chose was comparing the most popular words used in the summaries. I decided to look at just two pairings, specifically the top two that didn’t have a common character (Draco/Hermione and James/Lily). To make the comparison, I took the 100 most popular words in the summaries of each pairing (using the same algorithm as Wordle to count words) and clustered the words by whether they were common to both pairings or not. This doesn’t mean a word specific to a pairing never appears in the opposite pairing, it’s simply not in the top 100. The resulting “Venn diagram” is shown below. Note that I removed explicit mentions to the characters involved since they dominated the counts. For example, I removed words such as Draco, Draco’s, Malfoy, etc. Also, I limited the analysis to fics written in English for obvious reasons.

Word cloud showing the most popular words contained the summaries of fics with either a Draco/Hermione pairing or James/Lily pairing.

“Venn diagram” word cloud showing the most popular words in the summaries of fics with either a Draco/Hermione or James/Lily pairing. The font size for each words is proportional to the total number of times that word appears in summaries with these pairings. Gray words in the center are the most common words that appear in both pairings, blue words on the left are the most common words that appear in Draco/Hermione fics, and red words on the right are the most common words in James/Lily fics.

 

The Venn diagram look may not have panned out as I had originally hoped, but the information is still interesting. Even if it does look like a Pepsi logo.

A few observations:

  1. The top words in both pairings tend to be shared, i.e. there are more gray words than blue or red. This isn’t unique to Draco/Hermione vs. James/Lily. Words like loveHogwarts, and year are common to many types of pairings. There are also common English words like up and out in the center. I automatically remove the most common English (Wordle does the same), but these two aren’t on the list of common words I found online.
  2. You can see that the Draco/Hermione pairing is more popular than James/Lily since its unique words are larger overall. To scale the font size of the words in the center, I averaged the counts from both pairings.
  3. The most common category of unique words are shorthand names for the pairing, e.g. DMHG or LJ. The word Dramione is a portmanteau of Draco and Hermione. I’m not sure if there’s one for James/Lily yet, but my vote is for Limes.
  4. I don’t think the list of unique words is enough to make any claims of thematic differences between the pairings. For example, I could speculate that many Draco/Hermione fics are Romeo-and-Juliet-style stories of star-crossed lovers, whereas James/Lily stories could have the “will-they-or-won’t-they” trope. There might be hints of this (secret and past for Draco/Hermione; finally and hate for James/Lily), but this isn’t enough to make any strong conclusions. I might look at popular phrases/groups of words to really get at this question.

Final thoughts

Character choices in Harry Potter fanfiction can be considered both highly variable (6,950 unique character groupings from a series with essentially three main characters) and highly regular (a randomly selected fic has a 25% chance of having Harry, Hermione, or Draco as a character). I hope to do more analyses like these, and I thought character choices was a good place to start because it’s an easy dimension for clustering fics together. Next, I hope to do more with the summaries. Perhaps use Markov chains to generate pseudorandom summaries like the posts in /r/SubredditSimulator. Please leave suggestions below and thanks for reading!

Analysis of abstracts from a paper library

Author’s note: This is an old journal entry from August 15, 2014.

One thing I really respect about my PhD advisor is his effort to stay up-to-date with the recent literature. At conferences, I always see him talking to several different grad students during the poster sessions, whereas it seems like most senior scientists make it to one or two posters before talking to other PIs. He also keeps an extensive library of journal articles that gets updated regularly. I don’t know if he actually reads every new paper, but I’m nevertheless jealous of his ability to find them. So far I’ve been dissatisfied with services designed to notify me of new articles, whether it’s an RSS feed of a major journal or an email search alert from PubMed/Google Scholar. These services are either too strict and miss relevant articles, or too lax and return way too many results. A new service called PubChase holds promise, but I don’t know how well it works. Regardless, I wanted to see if I could figure out a better way to find new, relevant articles. The first step: analyzing my advisor’s library of papers.

Getting the raw data

My advisor’s paper library has over 13,000 files in it, and I certainly did not want open every file in order to get the raw text from the titles and abstracts. Endnote provided a way to automate this, although it wasn’t successful in extracting the abstracts from every article. I did, however, manage to create a huge text file with the titles and abstracts of 6,687 journal articles. This process was likely biased for newer papers, since I don’t think Pubmed can pull abstracts from scans, but this frankly doesn’t bother me as long as the sampling process was unbiased with respect to the article’s topic, which is hopefully the case. To begin, I used my code based on the Wordle algorithm (see previous post) to identify the 500 most common words and their relative usages. This counting ignores common English words as well as a list of special words, which I omitted somewhat arbitrarily after deciding they would be bad at identifying a paper’s unique content. For example, words like “results”, “effects”, “suggest”, “show”, and “significantly” could show up in any abstract regardless of the topic. Also, I counted each word in the title 3 times in order to give the title more weight. This technique is used by PubMed in its search algorithm, described here. Shown below is a word cloud of the final set of 500 words used for clustering.

Word cloud of 500 most common words in extracted abstracts and titles. The font size is linearly proportional to the number of occurrences. Words appearing in an abstract were counted once, but three times in a title.

Word cloud of 500 most common words in extracted abstracts and titles. The font size is linearly proportional to the number of occurrences. Words appearing in an abstract were counted once, but three times in a title.

Clearly, some of the words are too small to read due to the enormous number of occurrences of  “auditory” (14,431 if you were curious). This illustrates why it is important to scale each word’s weight by its overall usage. Specifically, for document i=1,2,\ldots,N and term j=1,2,\ldots,M, the total weight W_{i,j} was calculated as the product of the global weight G_j of term j and the local weight L_{i,j} of term j in document i. These weights were calculated as follows, described in more detail on the PubMed website.

W_{i,j} = L_{i,j}G_j,
G_j = \sqrt{\ln \left(\frac{N}{n_j}\right)}
L_{i,j} = \frac{10}{1+e^{\alpha\ell_i}\lambda^{k_{i,j}-1}}

N is the total number of documents (6,687), n_j is the number of documents term j appears in, \ell_i is the total number of words in document i (or 250, whichever is larger), and k_{i,j} is the number of times term j is in document i. The constants \alpha = 0.0044 and \lambda = 0.7 were given by PubMed. The total number of terms M was set at 500, resulting in a set of 6,687 feature vectors of length 500 to be clustered.

Note that the above equations have two changes from the description on the PubMed website. First, the third equation above has a factor of 10 in the numerator, not 1. I added this because the local weights in my data set were originally much smaller than the global weights, skewing the clustering process. The second change was adding the square root in the second equation, which was made for the same reason. I don’t know why Pubmed’s global weights are smaller, but perhaps it is because their database of documents is much larger.

Choosing the number of clusters

With over 6,000 articles, you can imagine the breadth of information covered is quite broad. You can find papers in the library on everything from signal processing to basic anatomy to psychology. There’s even oddball papers on topics like particle physics. Any attempt to identify every topic in the library will fall victim to overfitting, but I was confident that I could separate a small number of topics that were well-represented and identify the words that best separate topics from each other.

I started with principal component analysis to reduce the dimensionality. The figure below shows the percent of explainable variance as a function of the number of components, and you can see how multidimensional this data set is. We need over 100 components to explain just 50% of the variance! This is a testament to how variable the term usages are between papers.

Cumulative variance explained by principal components

Cumulative variance explained by principal components

To help decide on the number of components to include and eventually perform the clustering, I used Matlab’s implementation of the EM algorithm for Gaussian mixture models (gmdistribution.fit). This allowed me to make some judgements on relative model quality using the Akaike information criterion (AIC). This value decreases as the likelihood of the model increases but contains an added penalty for increasing the number of free parameters. Therefore, a lower AIC value is desirable. You can see how the AIC value changes as a function of both the number of components and the number of clusters below

Akaike information criterion (AIC) for Gaussian mixture model as a function of the number of clusters. Each line represents a different number of principal components used.

Akaike information criterion (AIC) for Gaussian mixture model as a function of the number of clusters. Each line represents a different number of principal components used.

There are two obvious trends. First, increasing the number of components appears to increase the AIC value in an approximately linear fashion (lines appear offset from each other), which is due to increasing the number of free parameters. Second, increasing the number of clusters appear to decrease the AIC, which is due to increasing the likelihood of the model. Another interesting trend appears when you normalize these line by their max AIC value, as shown below

Values of Akaike information criterion (AIC) as a function of the number of clusters. The values are normalized by the maximum value for each line, i.e. when every paper was assigned to a single cluster.

Values of Akaike information criterion (AIC) as a function of the number of clusters. The values are normalized by the maximum value for each line, i.e. when every paper was assigned to a single cluster.

Here you can see that the AIC value decreases at the same relative rate when the number of components is ≥15, implying that adding additional components to these models will not significantly improve the likelihood. Therefore, I chose 15 components to be used in the final clustering. These components represent approximately 19.5% percent of the variance.

Finally, to choose the number of clusters, I used the fairly arbitrary elbow method to select a value of 8. This method is very subjective, but as the above figure demonstrates, adding additional clusters decreases the AIC value, but not by much.

Determining cluster keywords

The final result is a set of 8 clusters, each with 500-1200 papers. To identify what each cluster’s “topic” might be, I summed the feature vectors for every paper within a cluster and sorted the result in order to obtain the words with the highest weights for each cluster. I then created a word cloud with the top 20 words in each cluster, shown below, where the color indicates cluster identity.

Word cloud showing the top 20 words within each of the 8 clusters of papers, calculated by summing the feature vectors across members of a cluster. The color indicates cluster identity, and the font size is proportional to the summed weight of the word.

Word cloud showing the top 20 words within each of the 8 clusters of papers, calculated by summing the feature vectors across members of a cluster. The color indicates cluster identity, and the font size is proportional to the summed weight of the word.

Before making any claims about how the words are related within clusters, there are several general observations I’ve made:

  1. The weights are fairly evenly distributed, i.e. all the words have a somehwhat similar font size. This is especially true when compared to the earlier word cloud constructed with the raw word counts.
  2. The top words from the earlier word cloud (auditory, cochlear, and neurons) are still prominent in several of the clusters here, indicating that despite scaling for the overall usage, these words still occur often enough to produce a large summed weight within that cluster.
  3. Different forms of words are commonly grouped together, e.g. cell and cells, implant and implantation, inhibition and inhibitory, etc. This could indicate that these words co-localize in the same or very related documents. The white cluster (middle-left) even has a triplet: neurons, neural, and neuronal.

Describing the clusters

The real question is whether the top twenty words in each cluster actually say something about the papers in their cluster. If the clustering process actually separated the papers by topic, then we would assume that’s the case. You can see in the word cloud there’s certainly repetitions of words between clusters, but I do think the words can be interpreted into an overarching theme. There has to be outliers in each cluster (where do the particle physics papers go?), but I think the eight clusters break down into the following groups:
  • Cluster 1 (dark red, top left): Auditory neurophysiology, electric hearing, cochlear implants. This cluster seems to focus on neural responses (response, activity, evoked) in auditory centers (auditory nerve, nucleus, cortex, inferior colliculus) from electric stimulation (electrical, stimulation, cochlear implant). Compare this to Cluster 8, which seems to focus on the speech recognition performance of CI users, or Cluster 3, which seems to involve neural responses due to acoustic stimulation.
  • Cluster 2 (dark blue, top middle): Auditory neurophysiology, binaural hearing. This cluster certainly involves binaural neural processing (both binaural and interaural are present), especially in the inferior colliculus (note the abbreviation IC ). It is also the only cluster with inhibitory, which certainly has an important role in binaural processing.
  • Cluster 3 (orange, top right): Auditory processing, neuroimaging. This cluster seems to focus on higher-order auditory processing (speech, pitch, perception, complex), so it likely contains the neuroimaging papers. This is supported by the presence of the anatomical terms: primary, cortex, cortical, but there’s nothing to suggest neurophysiology at the cellular level.
  • Cluster 4 (white, center left): General systems neuroscience. This cluster appears to involve involve general principles of neuroscience (spike, information, model, synaptic), including the aforementioned trifecta of neurons, neuronal, and neural. With regards to anatomy, this cluster is probably focused more on the neocortex (cortex, cortical), since no brainstem terms are mentioned. This is also the only cluster with a non-auditory word (visual), which is understandable given that a larger percentage of papers on the visual system involve cortical processing than the auditory system.
  • Cluster 5 (yellow, center left): Cochlear implants, psychophysics. This cluster definitely focuses on cochlear implants (implant, implantation, CI, pulse), but also has many classic psychophysical terms (subjects, listeners, masking, noise). Compare this to Cluster 8, which seems to focus more on CI performance and less on the basic psychophysics.
  • Cluster 6 (blue, bottom left): Inner ear biology, auditory periphery. This cluster seems to focus on the periphery (cochlea, hair cells, cochlear nucleus) with perhaps more of a biological focus than some of the neural coding clusters (synapses, membrane, synaptic, cell). However, there is certainly a neural component (nerve, fibers).
  • Cluster 7 (light brown, bottom middle): Pyschophysics. This once is definitely a psychophysics cluster. Pretty much every word is indicative of this (masking, cues, thresholds, detection, target, signal, noise). There is also a binaural component (binaural, interaural, localization, time, level).
  • Cluster 8 (light blue, bottom right): Cochlear implant performance. This cluster certainly involves cochlear implants (electrode, stimulation, multichannel), but compared with the other two putative CI clusters (1 and 5), this cluster seems to focus on how well CIs actually work (speech, recognition, perception, performance, scores). It is certainly the must humanized cluster (children, patients, subjects, users). Given both children and age, this cluster likely also contains papers on how CIs affect development.

Final thoughts

While my research involves cochlear implants, I am still somewhat surprised that 3 of the 8 clusters seem to include them, since they’re really only one aspect of my advisor’s interests. I was, however, pleased to see that each CI cluster seems to have a separate focus (neurophysiology, psychophsyics, or general performance). This could indicate that the clustering worked well, although the notion of a singular topic per cluster is certainly something I arbitrarily imposed. Overall, I think the eight topics do cover my advisor’s research interests nicely, and I bet he’s even been an author on a paper in each cluster. In the future, it would be interesting to approach this problem with hierarchical clustering, since it might reveal subtopics within the larger clusters. For example, Cluster 7 might separate into topics on localization and signal detection. It would also be interesting to see where the outliers were assigned, since these 8 topics certainly don’t cover every paper in the library. Regardless, I think this was a fun and informative exercise. I did make several new PubMed email alerts as a result, but I’ll have to wait a few weeks to see how well they work. Who knows, maybe I’ll even read a paper or two, instead of just thinking of ways to find them.

Update: I set up around 5 PubMed alerts as a result of this work, each containing 3-5 search terms. They’ve been pretty effective at alerting me to papers, and I definitely prefer them to reading a bunch of table of contents from multiple journals. Now if only I had the motivation to read all those papers…

 

Word Clouds!

Author’s note: This is an old journal entry from July 29, 2014 that I never did anything with, so now it’s going to become my first blog post.

I recently discovered Wordle, a site which allows you to create beautiful word clouds, a type of graphic consisting of words where the font size is proportional to how often the word appears in a given body of text. I thought it would be fun trying to use Wordle to analyze some abstract books from scientific conferences, but that may have been a bit overambitious. Who knew you could crash Chrome by trying to copy and paste 15,000+ pages of text?

Undeterred (i.e. too much time on my hands), I decided to write some Matlab code to make my own. This allowed me to analyze very large bodies of text and also have more control in the final graphic creation. I had to learn some regular expressions as well as use Matlab’s Computer Vision Toolbox in a manner in which it certainly wasn’t designed, but hey, it works. Below are two word clouds, showing the most common 200 words in the ARO 2014 and SfN 2013 abstract books, respectively. ARO stands for the Association of Research in Otolaryngology, and it’s definitely the largest conference devoted to hearing research. It pales in size, however, compared to the annual SfN meeting (Society for Neuroscience), which draws in about 30,000 people.

Word cloud from ARO 2014

Word cloud from ARO 2014

Word cloud from SfN 2013

Word cloud from SfN 2013

To make the word clouds, I simply counted word frequencies like Wordle, but in addition to ignoring common English words (“the”, “and”, etc.), I also removed nonspecific scientific words like “abstract” and “methods.” The result certainly isn’t as pretty as those from Wordle, but look, a brain! and sort of a cochlea! The clouds from Wordle have much nicer inter-word spacing due to the way they handle collision detection, but I had to be more flexible since I wanted the words to fit into an arbitrary shape.

Observations so far? Despite obtaining the #3 spot on the ARO cloud, the word “auditory” barely made it into the SfN cloud, achieving spot #196 and losing terribly to “visual” at #47. Oh well, at least the sensory neuroscientists can be bitter together, since they were beaten by other systems, namely #19 “memory” and #21 “motor.” In case you were wondering, the word “neurons” was used 17,452 times in the SfN abstract book, an order of magnitude increase from the #1 word in the ARO cloud: “cells,” which was used 1,846 times. This isn’t all that surprising given the huge size of SfN relative to ARO.

Lastly, for a summary of the data, here are some basic counts on the text analysis.