LSA is a marvellous tool, but literary historians may want to customize it for their own discipline.

Right now Latent Semantic Analysis is the analytical tool I’m finding most useful. By measuring the strength of association between words or groups of words, LSA allows a literary historian to map themes, discourses, and varieties of diction in a given period.

This approach, more than any other I’ve tried, turns up leads that are useful for me as a literary scholar. But when I talk to other people in digital humanities, I rarely hear enthusiasm for it. Why doesn’t LSA get more love? I see three reasons:

1. The word “semantic” is a false lead: it points away from the part of this technique that would actually interest us. It’s true that Latent Semantic Analysis is based on the observation that a word’s distribution across a collection of documents works remarkably well as a first approximation of its meaning. A program running LSA can identify English synonyms on the TOEFL as well as the average student applying to college from a non-English-speaking country. [1]

But for a literary historian, the value of this technique does not depend on its claim to identify synonyms and antonyms. We may actually be more interested in contingent associations (e.g., “sensibility” — “rousseau” in the list on the left) than we are in the core “meaning” of a word.

I’ll return in a moment to this point. It has important implications, because it means that we want LSA to do something slightly different than linguists and information scientists have designed it to do. The “flaws” they have tried to iron out of the technique may not always be flaws for our purposes.

2. People who do topic-modeling may feel that they should use more-recently-developed Bayesian methods, which are supposed to be superior on theoretical grounds. I’m acknowledging this point just to set it aside; I’ve mused out loud about it once already, and I don’t want to do more musing until I have rigorously compared the two methods. I will say that from the perspective of someone just getting started, LSA is easier to implement than Bayesian topic modeling: it runs faster and scales up more easily.

3. The LSA algorithm provided by an off-the-shelf package is not necessarily the best algorithm for a literary historian. At bottom, that’s why I’m writing this post: humanists who want to use LSA are going to need guidance from people in their own discipline. Computer scientists do acknowledge that LSA requires “tuning, which is viewed as a kind of art.” [2] But they also offer advice about “best practices,” and some of those best practices are defined by disciplinary goals that humanists don’t share.

For instance, the power of LSA is often said to come from “reducing the dimensionality of the matrix.” The matrix in question is a term-document matrix — documents are listed along one side of the matrix, and terms along the other, and each cell of the matrix (tfi,j) records the number of times term i appears in document j, modified by a weighting algorithm described at the end of this post.

A (very small) term-document matrix.

That term-document matrix in and of itself can tell you a lot about the associations between words; all you have to do is measure the similarity between the vectors (columns of numbers) associated with each term. But associations of this kind won’t always reveal synonyms. For instance, “gas” and “petrol” might seem unrelated, because they substitute for each other in different sociolects and are rarely found together. To address that problem, you can condense the matrix by factorizing it with a technique called singular value decomposition (SVD). I’m not going to get into the math here, but the key is that condensing the matrix partially fuses related rows and columns — and as a result, the compressed matrix is able to measure transitive kinds of association. The words “gas” and “petrol” may rarely appear together. But they both appear with the same kinds of other words. So when dimensionality reduction “merges” the rows representing similar documents, “gas” and “petrol” will end up being strongly represented in the same merged rows. A compressed matrix is better at identifying synonyms, and for that reason at information retrieval. So there is a lot of consensus among linguists and information scientists that reducing the number of dimensions in the matrix is a good idea.

But literary historians approach this technique with a different set of goals. We care a lot about differences of sociolect and register, and may even be more interested in those sources of “noise” than we are in purely semantic relations. “Towering,” for instance, is semantically related to “high.” But I could look that up in a dictionary; I don’t need a computer program to tell me that! I might be more interested to discover that “towering” belongs to a particular subset of poetic diction in the eighteenth century. And that is precisely the kind of accident of distribution that dimensionality-reduction is designed to filter out. For that reason, I don’t think literary applications of LSA are always going to profit from the dimensionality-reduction step that other disciplines recommend.

For about eight months now, I’ve been using a version of LSA without dimensionality reduction. It mines associations simply by comparing the cosine-similarity of term vectors in a term-document matrix (weighted in a special way to address differences of document size). But I wanted to get a bit more clarity about the stakes of that choice, so recently I’ve been comparing it to a version of LSA that does use SVD to compress the matrix.

Comparing 18c associations for "delicacy" generated by two different algorithms.

Here’s a quick look at the results. (I’m using 2,193 18c volumes, mostly produced by TCP-ECCO; volumes that run longer than 100,000 words get broken into chunks that can range from 50k-100k words.) In many cases, the differences between LSA with and without compression are not very great. In the case of “delicacy,” for instance, both algorithms indicate that “delicate” has the strongest association. “Politeness” and “tenderness” are also very high on both lists. But compare the second row. The algorithm with compression produces “sensibility” — a close synonym. On the left-hand side, we have “woman.” This is not a synonym for “delicacy,” and if a linguist or computer scientist were evaluating these algorithms, it would probably be rejected as a mistake. But from a literary-historical point of view, it’s no mistake: the association between “delicacy” and femininity is possibly the most interesting fact about the word.

The 18c associations of "high" and "towering," in an uncompressed term-document matrix.

In short, compressing the matrix with SVD highlights semantic relationships at the cost of slightly blurring other kinds of association. In the case of “delicacy,” the effect is fairly subtle, but in other cases the difference between the two approaches is substantial. For instance, if you measure the similarity of term vectors in a matrix without compression, “high” and “towering” look entirely different. The main thing you discover about “high” is that it’s used for physical descriptions of landscape (“lies,” “hills”), and the main thing you discover about “towering” is that it’s used in poetic contexts (“flowery,” “glittering”).

The 18c. associations of "high" and "towering," as measured in a term-document matrix that has undergone SVD compression.

In a matrix that has undergone dimensionality reduction with SVD, associations have a much more semantic character, although they are still colored by other dimensions of context. Which of these two algorithms is more useful for humanistic purposes? I think the answer is going to depend on the goals being pursued in a given research project — if you’re interested in “topics” that are strictly semantic, you might want to use an algorithm that reduces dimensionality with SVD. If you’re interested in discourses, sociolects, genres, or types of diction, you might use LSA without dimensionality reduction.

My purpose here isn’t to choose between those approaches; it’s just to remind humanists that the algorithms we borrow from other disciplines are often going to need to be customized for our own disciplinary purposes. Information scientists have designed topic-modeling algorithms that produce semantically unified topics, because semantic categorization is important for them. But in literary history, we also care about other dimensions of language, and we don’t have to judge topic-modeling algorithms by strictly semantic criteria. How should we judge them? It will probably take decades for us to answer that question fully, but the short answer is just — by how well, in practice, they help us locate critically and historically interesting patterns.

A couple of technical notes: A fine point of LSA that can matter a great deal is how you weight the individual cells in the term-document matrix. For the normal LSA algorithm that uses dimensionality reduction, the consensus is that “log-entropy weighting” works well. You take the log of each frequency, and multiply the whole term vector by the entropy of the vector. I have found that this also works well for humanistic purposes.

For LSA without dimensionality reduction, I would recommend weighting cells by subtracting the expected frequency from the observed frequency. This formula “evens the playing field” between common and uncommon words — and it does so, vitally, in a way that gives a word’s absence from a long document more weight than its absence from a short one. (Much of LSA’s power actually comes from learning where a given word tends not to appear. [3]) I have tried various ways of applying log-entropy weighting without compressing the matrix, and I do not recommend it. Those two techniques belong together.

For reasons that remain somewhat mysterious (although the phenomenon itself is widely discussed), dimensionality reduction seems to work best when the number of dimensions retained is in the range of 250-350. Intuitively, it would seem possible to strike a sort of compromise between LSA methods that do and don’t compress the matrix by reducing dimensionality less drastically (perhaps only, say, cutting it by half). But in practice I find that doesn’t work very well; I suspect compression has to reach a certain threshold before the noise inherent in the process starts to cancel itself out and give way to a new sort of order.

[1] Thomas K. Landauer, Peter W. Foltz, and Darrell Latham, An Introduction to Latent Semantic Analysis, Discourse Processes 25 (1998): 259-84. Web reprint, p. 22.
[2] Preslav Nakov, Elena Valchanova, and Galia Angelova, “Towards Deeper Understanding of Latent Sematic Analysis Performance,” Recent Advances in Natural Language Processing, ed. Nicolas Nicolov (Samokov, Bulgaria: John Benjamins, 2004), 299.
[3] Landauer, Foltz, and Latham, p. 24.

Topics tend to be trends. Really: p < .05!

While I’m fascinated by cases where the frequencies of two, or ten, or twenty words closely parallel each other, my conscience has also been haunted by a problem with trend-mining — which is that it always works. There are so many words in the English language that you’re guaranteed to find groups of them that correlate, just as you’re guaranteed to find constellations in the night sky. Statisticians call this the problem of “multiple comparisons”; it rests on a fallacy that’s nicely elucidated in this classic xkcd comic about jelly beans.

Simply put: it feels great to find two conceptually related words that correlate over time. But we don’t know whether this is a significant find, unless we also know how many potentially related words don’t correlate.

One way to address this problem is to separate the process of forming hypotheses from the process of testing them. For instance, we could use topic modeling to divide the lexicon up into groups of terms that occur in the same contexts, and then predict that those terms will also correlate with each other over time. In making that prediction, we turn an undefined universe of possible comparisons into a finite set.

Once you create a set of topics, plotting their frequencies is simple enough. But plotting the aggregate frequency of a group of words isn’t the same thing as “discovering a trend,” unless the individual words in the group actually correlate with each other over time. And it’s not self-evident that they will.

The top 15 words in topic #91, "Silence/Listened," and their cosine similarity to the centroid.

So I decided to test the hypothesis that they would. I used semi-fuzzy clustering to divide one 18c collection (TCP-ECCO) into 200 groups of words that tend to appear in the same volumes, and then tested the coherence of those topics over time in a different 18c collection (a much-cleaned-up version of the Google ngrams dataset I produced in collaboration with Loretta Auvil and Boris Capitanu at the NCSA). Testing hypotheses in a different dataset than the one that generated them is a way of ensuring that we aren’t simply rediscovering the same statistical accidents a second time.

To make a long story short, it turns out that topics have a statistically significant tendency to be trends (at least when you’re working with a century-sized domain). Pairs of words selected from the same topic correlated significantly with each other even after factoring out other sources of correlation*; the Fisher weighted mean r for all possible pairs was 0.223, which measured over a century (n = 100) is significant at p < .05.

In practice, the coherence of different topics varied widely. And of course, any time you test a bunch of hypotheses in a row you're going to get some false positives. So the better way to assess significance is to control for the "false discovery rate." When I did that (using the Benjamini-Hochberg method) I found that 77 out of the 200 topics cohered significantly as trends.

There are a lot of technical details, but I'll defer them to a footnote at the end of this post. What I want to emphasize first is the practical significance of the result for two different kinds of researchers. If you're interested in mining diachronic trends, then it may be useful to know that topic-modeling is a reliable way of discovering trends that have real statistical significance and aren’t just xkcd’s “green jelly beans.”

The top 15 terms in topic #89, "Enemy/Attacked," and their cosine similarity to the centroid.

Conversely, if you're interested in topic modeling, it may be useful to know that the topics you generate will often be bound together by correlation over time as well. (In fact, as I’ll suggest in a moment, topics are likely to cohere as trends beyond the temporal boundaries of your collection!)

Finally, I think this result may help explain a phenomenon that Ryan Heuser, Long Le-Khac, and I have all independently noticed: which is that groups of words that correlate over time in a given collection also tend to be semantically related. I've shown above that topic modeling tends to produce diachronically coherent trends. I suspect that the converse proposition is also true: clusters of words linked by correlation over time will turn out to have a statistically significant tendency to appear in the same contexts.

Why are topics and trends so closely related? Well, of course, when you’re topic-modeling a century-long collection, co-occurrence has a diachronic dimension to start with. So the boundaries between topics may already be shaped by change over time. It would be interesting to factor time out of the topic-modeling process, in order to see whether rigorously synchronic topics would still generate diachronic trends.

I haven’t tested that yet, but I have tried another kind of test, to rule out the possibility that we’re simply rediscovering the same trends that generated the topics in the first place. Since the Google dataset is very large, you can also test whether 18c topics continue to cohere as trends in the nineteenth century. As it turns out, they do — and in fact, they cohere slightly more strongly! (In the 19c, 88 out of 200 18c topics cohered significantly as trends.) The improvement is probably a clue that Google’s dataset gets better in the nineteenth century (which god knows, it does) — but even if that’s true, the 19c result would be significant enough on its own to show that topic modeling has considerable predictive power.

Practically, it’s also important to remember that “trends” can play out on a whole range of different temporal scales.

For instance, here’s the trend curve for topic #91, “Silence / Listened,” which is linked to the literature of suspense, and increases rather gradually and steadily from 1700 to the middle of the nineteenth century.

By contrast, here’s the trend curve for topic #89, “Enemy/Attacked,” which is largely used in describing warfare. It doesn’t change frequency markedly from beginning to end; instead it bounces around from decade to decade with a lot of wild outliers. But it is in practice a very tightly-knit trend: a pair of words selected from this topic will have on average 31% of their variance in common. The peaks and outliers are not random noise: they’re echoes of specific armed conflicts.

* Technical details: Instead of using Latent Dirichlet Allocation for topic modeling, I used semi-fuzzy c-means clustering on term vectors, where term vectors are defined in the way I describe in this technical note. I know LDA is the standard technique, and it seems possible that it would perform even better than my clustering algorithm does. But in a sufficiently large collection of documents, I find that a clustering algorithm produces, in practice, very coherent topics, and it has some other advantages that appeal to me. The “semi-fuzzy” character of the algorithm allows terms to belong to more than one cluster, and I use cosine similarity to the centroid to define each term’s “degree of membership” in a topic.

I only topic-modeled the top 5000 words in the TCP-ECCO collection. So in measuring pairwise correlations of terms drawn from the same topic, I had to calculate it as a partial correlation, controlling for the fact that terms drawn from the top 5k of the lexicon are all going to have, on average, a slight correlation with each other simply by virtue of being drawn from that larger group.

Trends, topics, and trending topics.

I’ve developed a text-mining strategy that identifies what I call “trending topics” — with apologies to Twitter, where the term is used a little differently. These are diachronic patterns that I find practically useful as a literary historian, although they don’t fit very neatly into existing text-mining categories.

A “topic,” as the term is used in text-mining, is a group of words that occur together in a way that defines a thematic focus. Cameron Blevin’s analysis of Martha Ballard’s diary is often cited as an example: Blevin identifies groups of words that seem to be associated, for instance, with “midwifery,” “death,” or “gardening,” and tracks these topics over the course of the diary.

“Trends” haven’t received as much attention as topics, but we need some way to describe the pattern that Google’s ngram viewer has made so visible, where groups of related words rise and fall together across long periods of time. I suspect “trend” is as a good a name for this phenomenon as we’ll get.

blue, red, green, yellow, in the English corpus 1750-2000

From 1750 to 1920, the prominence of color vocabulary increases by a factor of three, for instance: and when it does, the names of different colors track each other very closely. I would call this a trend. Moreover, it’s possible to extend the principle that conceptually related words rise and fall together beyond cases like the colors and seasons where we’re dealing with an obvious physical category.

Google data graphed with my own viewer; if you compare this to Google's viewer, remember that I'm merging capitalized and uncapitalized forms, as well as ardor/ardour.

“Animated,” “attentive,” and “ardour” track each other almost as closely as the names of primary colors (the correlation coefficients are around 0.8), and they characterize conduct in ways that are similar enough to suggest that we’re looking at the waxing and waning not just of a few random words, but of a conceptual category — say, a particular sort of interest in states of heightened receptiveness or expressivity.

I think we could learn a lot by thoughtfully considering “trends” of this sort, but it’s also a kind of evidence that’s not easy to interpret, and that could easily be abused. A lot of other words correlate almost as closely with “attentive,” including “propriety,” “elegance,” “sentiments,” “manners,” “flattering,” and “conduct.” Now, I don’t think that’s exactly a random list (these terms could all be characterized loosely as a discourse of manners), but it does cover more conceptual ground than I initially indicated by focusing on words like “animated” and “ardour.” And how do we know that any of these terms actually belonged to the same “discourse”? Perhaps the books that talked about “conduct” were careful not to talk about “ardour”! Isn’t it possible that we have several distinct discourses here that just happened to be rising and falling at the same time?

In order to answer these questions, I’ve been developing a technique that mines “trends” that are at the same time “topics.” In other words, I look for groups of terms that hold together both in the sense that they rise and fall together (correlation across time), and in the sense that they tend to be common in the same documents (co-occurrence). My way of achieving this right now is a two-stage process: first I mine loosely defined trends from the Google ngrams dataset (long lists of, say, one hundred closely correlated words), and then I send those trends to a smaller, generically diverse collection (including everything from sermons to plays) where I can break the list into clusters of terms that tend to occur in the same kinds of documents.

I do this with the same vector space model and hierarchical clustering technique I’ve been using to map eighteenth-century diction on a larger scale. It turns the list of correlated words into a large, branching tree. When you look at a single branch of that tree you’re looking at what I would call a “trending topic” — a topic that represents, not a stable, more-or-less-familiar conceptual category, but a dynamically-linked set of concepts that became prominent at the same time, and in connection with each other.

one branch of a tree created by finding words that correlate with "manners," and then clustering them based on co-occurrence in 18c books

Here, for instance, is a branch of a larger tree that I produced by clustering words that correlate with “manners” in the eighteenth century. It may not immediately look thematically coherent. We might have expected “manners” to be associated with words like “propriety” or “conduct” (which do in fact correlate with it over time), but when we look at terms that change in correlated ways and occur in the same volumes, we get a list of words that are largely about wealth and rank (“luxury,” “opulence,” “magnificence”), as well as the puzzling “enervated.” To understand a phenomenon like this, you can simply reverse the process that generated it, by using the list as a search query in the eighteenth-century collection it’s based on. What turned up in this case were, pre-eminently, a set of mid-eighteenth-century works debating whether modern commercial opulence, and refinements in the arts, have had an enervating effect on British manners and civic virtue. Typical examples are John Brown’s Estimate of the Manners and Principles of the Times (1757) and John Trusler’s Luxury no Political Evil but Demonstratively Proved to be Necessary to the Preservation and Prosperity of States (1781). I was dimly aware of this debate, but didn’t grasp how central it became to debate about manners, and certainly wasn’t familiar with the works by Brown and Trusler.

I feel like this technique is doing what I want it to do, practically, as a literary historian. It makes the ngram viewer something more than a provocative curiosity. If I see an interesting peak in a particular word, I can can map the broader trend of which it’s a part, and then break that trend up into intersecting discourses, or individual works and authors.

Admittedly, there’s something inelegant about the two-stage process I’m using, where I first generate a list of terms and then use a smaller collection to break the list into clusters. When I discussed the process with Ben Schmidt and Miles Efron, they both, independently, suggested that there ought to be some simpler way of distinguishing “trends” from “topics” in a single collection, perhaps by using Principal Component Analysis. I agree about that, and PCA is an intriguing suggestion. On the other hand, the two-stage process is adapted to the two kinds of collections I actually have available at the moment: on the one hand, the Google dataset, which is very large and very good at mapping trends with precision, but devoid of metadata, on the other hand smaller, richer collections that are good at modeling topics, but not large enough to produce smooth trend lines. I’m going to experiment with Principal Component Analysis and see what it can do for me, but in the meantime — speaking as a literary historian rather than a computational linguist — I’m pretty happy with this rough-and-ready way of identifying trending topics. It’s not an analytical tool: it’s just a souped-up search technology that mines trends and identifies groups of works that could help me understand them. But as a humanist, that’s exactly what I want text mining to provide.

The key to all mythologies.

Well, not really. But it is a classifying scheme that might turn out to be as loopy as Casaubon’s incomplete project in Middlemarch, and I thought I might embrace the comparison to make clear that I welcome skepticism.

In reality, it’s just a map of eighteenth-century diction. I took the 1,650 most common words in eighteenth-century writing, and asked my iMac to group them into clusters that tend to be common in the same eighteenth-century works. Since the clustering program works recursively, you end up with a gigantic branching tree that reveals how closely words are related to each other in 18c practice. If they appear on the same “branch”; they tend to occur in the same works. If they appear on the same “twig,” that tendency is even stronger.

You wouldn’t necessarily think that two words happening to occur in the same book would tell you much, but when you’re dealing with a large number of documents, it seems there’s a lot of information contained in the differences between them. In any case, this technique produced a detailed map of eighteenth-century topics that seemed — to me, anyway — surprisingly illuminating. To explore a couple of branches, or just marvel at this monument of digital folly, click here, or on the illustration to the right. That’ll take you through to a page where you can click on whichever branches interest you. (Click on the links in the right-hand margin, not the annotations on the tree itself.) To start with, I recommend Branch 18, which is a sort of travel narrative, Branch 13, which is 18c poetic diction in a nutshell, and Branch 5, which is saying something about gender and/or sexuality that I don’t yet understand.

If you want to know exactly how this was produced, and contrast it to other kinds of topic modeling, I describe the technique in this “technical note.” I should also give thanks to the usual cast of characters. Ryan Heuser and Ben Schmidt have produced analogous structures which gave me the idea of attempting this. Laura Mandell and 18th Connect helped me obtain the eighteenth-century texts on which the tree was based.