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18c 19c math methodology topic modeling trend mining

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.

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18c 19c fiction methodology

For most literary scholars, text mining is going to be an exploratory tool.

Having just returned from a conference of Romanticists, I’m in a mood to reflect a bit about the relationship between text mining and the broader discipline of literary studies. This entry will be longer than my usual blog post, because I think I’ve got an argument to make that demands a substantial literary example. But you can skip over the example to extract the polemical thesis if you like!

At the conference, I argued that literary critics already practice a crude form of text mining, because we lean heavily on keyword search when we’re tracing the history of a topic or discourse. I suggested that information science can now offer us a wider range of tools for mapping archives — tools that are subtler, more consonant with our historicism, and maybe even more literary than keyword search is.

At the same time, I understand the skepticism that many literary critics feel. Proving a literary thesis with statistical analysis is often like cracking a nut with a jackhammer. You can do it: but the results are not necessarily better than you would get by hand.

One obvious solution would be to use text mining in an exploratory way, to map archives and reveal patterns that a critic could then interpret using nuanced close reading. I’m finding that approach valuable in my own critical practice, and I’d like to share an example of how it works. But I also want to reflect about the social forces that stand in the way of this obvious compromise between digital and mainstream humanists — leading both sides to assume that quantitative analysis ought to contribute instead by proving literary theses with increased certainty.

Part of a topic tree based on a generically diverse collection of 2200 18c texts.

I’ll start with an example. If you don’t believe text mining can lead to literary insights, bear with me: this post starts with some goofy-looking graphs, but develops into an actual hypothesis about the Romantic novel based on normal kinds of literary evidence. But if you’re willing to take my word that text-mining can produce literary leads, or simply aren’t interested in Romantic-era fiction, feel free to skip to the end of this (admittedly long!) post for the generalizations about method.

Several months ago, when I used hierarchical clustering to map eighteenth-century diction on this blog, I pointed to a small section of the resulting tree that intriguingly mixed language about feeling with language about time. It turned out that the words in this section of the tree were represented strongly in late-eighteenth-century novels (novels, for instance, by Frances Burney, Sophia Lee, and Ann Radcliffe). Other sections of the tree, associated with poetry or drama, had a more vivid kind of emotive language, and I wondered why novels would combine an emphasis on feeling or exclamation (“felt,” “cried”) with the abstract topic of duration (“moment,” “longer”). It seemed an oddly phenomenological way to think about emotion.

But I also realized that hierarchical clustering is a fairly crude way of mapping conceptual space in an archive. The preferred approach in digital humanities right now is topic modeling, which does elegantly handle problems like polysemy. However, I’m not convinced that existing methods of topic modeling (LDA and so on) are flexible enough to use for exploration. One of their chief advantages is that they don’t require the human user to make judgment calls: they automatically draw boundaries around discrete “topics.” But for exploratory purposes boundaries are not an advantage! In exploring an archive, the goal is not to eliminate ambiguity so that judgment calls are unnecessary: the goal is to reveal intriguing ambiguities, so that the human user can make judgments about them.

If this is our goal, it’s probably better to map diction as an associative web. Fortunately, it was easy to get from the tree to a web, because the original tree had been based on an algorithm that measured the strength of association between any two words in the collection. Using the same algorithm, I created a list of twenty-five words most strongly associated with the branch that had interested me (“instantly,” “cried,” “felt,” moment,” “longer,”) and then used the strengths of association between those words to model the whole list as a force-directed graph. In this graph, words are connected by “springs” that pull them closer together; the darker the line, the stronger the association between the two words, and the more tightly they will be bound together in the graph. (The sizes of words are loosely proportional to their frequency in the collection, but only very loosely.)

A graph like this is not meant to be definitive: it’s a brainstorming tool that helps me explore associations in a particular collection (here, a generically diverse collection of eighteenth-century writing). On the left side, we see a triangle of feminine pronouns (which are strongly represented in the same novels where “felt,” “moment,” and so on are strongly represented) as well as language that defines domestic space (“quitting,” “room”). On the right side of the graph, we see a range of different kinds of emotion. And yet, looking at the graph as a whole, there is a clear emphasis on an intersection of feeling and time — whether the time at issue is prospective (“eagerly,” “hastily,” “waiting”) or retrospective (“recollected,” “regret”).

In particular, there are a lot of words here that emphasize temporal immediacy, either by naming a small division of time (“moment,” “instantly”), or by defining a kind of immediate emotional response (“surprise,” “shocked,” “involuntarily”). I have highlighted some of these words in red; the decision about which words to include in the group was entirely a human judgment call — which means that it is open to the same kind of debate as any other critical judgment.

But the group of words I have highlighted in red — let’s call it a discourse of temporal immediacy — does turn out to have an interesting historical profile. We already know that this discourse was common in late-eighteenth-century novels. But we can learn more about its provenance by restricting the generic scope of the collection (to fiction) and expanding its temporal scope to include the nineteenth as well as eighteenth centuries. Here I’ve graphed the aggregate frequency of this group of words in a collection of 538 works of eighteenth- and nineteenth-century fiction, plotted both as individual works and as a moving average. [The moving average won’t necessarily draw a line through the center of the “cloud,” because these works vary greatly in size. For instance, the collection includes about thirty of Hannah More’s “Cheap Repository Tracts,” which are individually quite short, and don’t affect the moving average more than a couple of average-sized novels would, although they create an impressive stack of little circles in the 1790s.]

The shape of the curve here suggests that we’re looking at a discourse that increased steadily in prominence through the eighteenth century and peaked (in fiction) around the year 1800, before sinking back to a level that was still roughly twice its early-eighteenth-century frequency.

Why might this have happened? It’s always a good idea to start by testing the most boring hypothesis — so a first guess might be that words like “moment” and “instantly” were merely displacing some set of close synonyms. But in fact most of the imaginable synonyms for this set of words correlate very closely with them. (This is true, for instance, of words like “sudden,” “abruptly,” and “alarm.”)

Another way to understand what’s going on would be to look at the works where this discourse was most prominent. We might start by focusing on the peak between 1780 and 1820. In this period, the works of fiction where language of temporal immediacy is most prominent include

    Charlotte Dacre, Zofloya (1806)
    Charlotte Lennox, Hermione, or the Orphan Sisters (1791)
    M. G. Lewis, The Monk (1796)
    Ann Radcliffe, A Sicilian Romance (1790), The Castles of Athlin and Dunbayne (1789), and The Romance of the Forest (1792)
    Frances Burney, Cecilia (1782) and The Wanderer (1814)
    Amelia Opie, Adeline Mowbray (1805)
    Sophia Lee, The Recess (1785)

There is a strong emphasis here on the Gothic, but perhaps also, more generally, on women writers. The works of fiction where the same discourse is least prominent would include

    Hannah More, most of her “Cheap Repository Tracts” and Coelebs in Search of a Wife (1809)
    Robert Bage, Hermsprong (1796)
    John Trusler, Life; or the Adventures of William Ramble (1793)
    Maria Edgeworth, Castle Rackrent (1800)
    Arnaud Berquin, The Children’s Friend (1788)
    Isaac Disraeli, Vaurien; or, Sketches of the Times (1797)

Many of these works are deliberately old-fashioned in their approach to narrative form: they are moral parables, or stories for children, or first-person retrospective narratives (like Rackrent), or are told by Fieldingesque narrators who feel free to comment and summarize extensively (as in the works by Disraeli and Trusler).

After looking closely at the way the language of temporal immediacy is used in Frances Burney, Cecilia (1782), and Sophia Lee, The Recess (1785), it seems to me that it had both a formal and an affective purpose.

Formally, it foregrounded a newly sharp kind of temporal framing. If we believe Ian Watt, part of the point of the novel form is to emulate the immediacy of first-hand experience — a purpose that can be slightly at odds with the retrospective character of narrative. Eighteenth-century novelists fought the distancing effect of retrospection in a lot of ways: epistolary narrative, discovered journals and so on are ways of bringing the narrative voice as close as possible to the moment of experience. But those tricks have limits; at some point, if your heroine keeps running off to write breathless letters between every incident, Henry Fielding is going to parody you.

By the late eighteenth century it seems to me novelists were starting to work out ways of combining temporal immediacy with ordinary retrospective narration. Maybe you can’t literally have your narrator describe events as they’re taking place, but you can describe events in a way that highlights their temporal immediacy. This is one of the things that makes Frances Burney read more like a nineteenth-century novelist than like Defoe; she creates a tight temporal frame for each event, and keeps reminding her readers about the tightness of the frame. So, a new paragraph will begin “A few moments after he was gone …” or “At that moment Sir Robert himself burst into the Room …” or “Cecilia protested she would go instantly to Mr Briggs,” to choose a few examples from a single chapter of Cecilia (my italics, 363-71). We might describe this vaguely as a way of heightening suspense — but there are of course many different ways to produce suspense in fiction. Narratology comes closer to the question at issue when it talks about “pacing,” but unless someone has already coined a better term, I think I would prefer to describe this late-18c innovation as a kind of “temporal framing,” because the point is not just that Burney uses “scene” rather than “summary” to make discourse time approximate story time — but that she explicitly divides each “scene” into a succession of discrete moments.

There is a lot more that could be said about this aspect of narrative form. For one thing, in the Romantic era it seems related to a particular way of thinking about emotion — a strategy that heightens emotional intensity by describing experience as if it were divided into a series of instananeous impressions. E.g, “In the cruelest anxiety and trepidation, Cecilia then counted every moment till Delvile came …” (Cecilia, 613). Characters in Gothic fiction are “every moment expecting” some start, shock, or astonishment. “The impression of the moment” is a favorite phrase for both Burney and Sophia Lee. On one page of The Recess, a character “resign[s] himself to the impression of the moment,” although he is surrounded by a “scene, which every following moment threatened to make fatal” (188, my italics).

In short, fairly simple tools for mapping associations between words can turn up clues that point to significant formal, as well as thematic, patterns. Maybe I’m wrong about the historical significance of those patterns, but I’m pretty sure they’re worth arguing about in any case, and I would never have stumbled on them without text mining.

On the other hand, when I develop these clues into a published article, the final argument is likely to be based largely on narratology and on close readings of individual texts, supplemented perhaps by a few simple graphs of the kind I’ve provided above. I suppose I could master cutting-edge natural language processing, in order to build a fabulous tool that would actually measure narrative pace, and the division of scenes into incidents. That would be fun, because I love coding, and it would be impressive, since it would prove that digital techniques can produce literary evidence. But the thing is, I already have an open-source application that can measure those aspects of narrative form, and it runs on inexpensive hardware that requires only water, glucose, and caffeine.

The methodological point I want to make here is that relatively simple forms of text mining, based on word counts, may turn out to be the techniques that are in practice most useful for literary critics. Moreover, if I can speak frankly: what makes this fact hard for us to acknowledge is not technophilia per se, but the nature of the social division between digital humanists and mainstream humanists. Literary critics who want to dismiss text mining are fond of saying “when you get right down to it, it’s just counting words.” (At moments like this we seem to forget everything 20c literary theorists ever learned from linguistics, and go back to treating language as a medium that ideally, ought to be immaterial and transparent. Surely a crudely verbal approach — founded on lumpy, ambiguous words — can never tell us anything about the conceptual subtleties of form and theme!) Stung by that critique, digital humanists often feel we have to prove that our tools can directly characterize familiar literary categories, by doing complex analyses of syntax, form, and sentiment.

I don’t want to rule out those approaches; I’m not interested in playing the game “Computers can never do X.” They probably can do X. But we’re already carrying around blobs of wetware that are pretty good at understanding syntax and sentiment. Wetware is, on the other hand, terrible at counting several hundred thousand words in order to detect statistical clues. And clues matter. So I really want to urge humanists of all stripes to stop imagining that text mining has to prove its worth by proving literary theses.

That should not be our goal. Full-text search engines don’t perform literary analysis at all. Nor do they prove anything. But literary scholars find them indispensable: in fact, I would argue that search engines are at least partly responsible for the historicist turn in recent decades. If we take the same technology used in those engines (a term-document matrix plus vector space math), and just turn the matrix on its side so that it measures the strength of association between terms rather than documents, we will have a new tool that is equally valuable for literary historians. It won’t prove any thesis by itself, but it can uncover a whole new range of literary questions — and that, it seems to me, ought to be the goal of text mining.

References
Frances Burney, Cecilia; or, Memoirs of an Heiress, ed. Peter Sabor and Margaret Ann Doody (Oxford: OUP, 1999).
Sophia Lee, The Recess; or, a Tale of Other Times, ed. April Alliston (Lexington: UP of Kentucky, 2000).

[Postscript: This post, originally titled “How to make text mining serve literary history,” is a version of a talk I gave at NASSR 2011 in Park City, Utah, sharpened by the discussion that took place afterward. I’d like to thank the organizers of the conference (Andrew Franta and Nicholas Mason) as well as my co-panelists (Mark Algee-Hewitt and Mark Schoenfield) and everyone in the audience. The original slides are here; sometimes PowerPoint can be clearer than prose.

I don’t mean to deny, by the way, that the simple tools I’m using could be refined in many ways — e.g., they could include collocations. What I’m saying is I that don’t think we need to wait for technical refinements. Our text-mining tools are already sophisticated enough to produce valuable leads, and even after we make them more sophisticated, it will remain true that at some point in the critical process we have to get off the bicycle and walk.]

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Uncategorized

Digital humanities and the spy business.

Flickr / dunechaser (Creative Commons)
I’m surprised more digital humanists haven’t blogged the news that the US Intelligence Advanced Projects Activity wants to fund techniques for mining and categorizing metaphors.

The stories I’ve read so far have largely missed the point of the program. They focus instead on the amusing notion that the government “fancies a huge metaphor repository.” And it’s true that the program description reads a bit like a section of English 101 taught by the men from Dragnet. “The Metaphor Program will exploit the fact that metaphors are pervasive in everyday talk and reveal the underlying beliefs and worldviews of members of a culture.” What is “culture,” you ask? Simply refer to section 1.A.3., “Program Definitions”: “Culture is a set of values, attitudes, knowledge and patterned behaviors shared by a group.”

This seems accurate enough, although the combination of precision and generality does feel a little freaky. “Affect is important because it influences behavior; metaphors have been associated with affect.”

The program announcement is similarly precise about the difference between metaphor and metonymy. (They’re not wild about metonymy.)

(3) Figurative Language: The only types of figurative language that are included in the program are metaphors and metonymy.
• Metonymy may be proposed in addition to but not instead of metaphor analysis. Those interested in metonymy must explain why metonymy is required, what metonymy adds to the analysis and how it complements the proposed work on metaphors.

All this is fun, but the program also has a purpose that hasn’t been highlighted by most of the reporting I’ve seen. The second phase of the program will use statistical analysis of metaphors to “characterize differing cultural perspectives associated with case studies of the types of interest to the Intelligence Community.” One can only speculate about those types, but I imagine that we’re talking about specific political movements and religious groups. The goal is ostensibly to understand their “cultural perspectives,” but it seems quite possible that an unspoken, longer-term goal might involve profiling and automatically identifying members of demographic, vocational, or political groups. (IARPA has inherited some personnel and structures once associated with John Poindexter’s Total Information Awareness program.) The initial phase of the metaphor-mining is going to focus on four languages: “American English, Iranian Farsi, Russian Russian and Mexican Spanish.”

Naturally, my feelings are complex. Automatically extracting metaphors from text would be a neat trick, especially if you also distinguished metaphor from metonymy. (You would have to know, for instance, that “Oval Office” is not a metaphor for the executive branch of the US government.) [UPDATE: Arno Bosse points out that Brad Pasanek has in fact been working on techniques for automatic metaphor extraction, and has developed a very extensive archive. Needless to say, I don’t mean to associate Brad with the IARPA project.]

Going from a list of metaphors to useful observations about a “cultural perspective” would be an even neater trick, and I doubt that it can be automated. My doubts on that score are the main source of my suspicion that the actual deliverable of the grant will turn out to be profiling. That may not be the intended goal. But I suspect it will be the deliverable because I suspect that it’s the part of the project researchers will get to work reliably. It probably is possible to identify members of specific groups through statistical analysis of the metaphors they use.

On the other hand, I don’t find this especially terrifying, because it has a Rube Goldberg indirection to it. If IARPA wants to automatically profile people based on digital analysis of their prose, they can do that in simpler ways. The success of stylometry indicates that you don’t need to understand the textual features that distinguish individuals (or groups) in order to make fairly reliable predictions about authorship. It may well turn out that people in a particular political movement overuse certain prepositions, for reasons that remain opaque, although the features are reliably predictive. I am confident, of course, that intelligence agencies would never apply a technique like this domestically.

Postscript: I should credit Anna Kornbluh for bringing this program to my attention.

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Uncategorized

Why humanists need to understand text mining.

Humanists are already doing text mining; we’re just doing it in a theoretically naive way. Every time we search a database, we use complex statistical tools to sort important documents from unimportant ones. We don’t spend a lot of time talking about this part of our methodology, because search engines hide the underlying math, making the sorting process seem transparent.

But search is not a transparent technology: search engines make a wide range of different assumptions about similarity, relevance, and importance. If (as I’ve argued elsewhere) search engines’ claim to identify obscure but relevant sources has powerfully shaped contemporary historicism, then our critical practice has come to depend on algorithms that other people write for us, and that we don’t even realize we’re using. Humanists quite properly feel that humanistic research ought to be shaped by our own critical theories, not by the whims of Google. But that can only happen if we understand text mining well enough to build — or at least select — tools more appropriate for our discipline.

The AltaVista search page, circa 1996. This was the moment to freak out about text mining.

This isn’t an abstract problem; existing search technology sits uneasily with our critical theory in several concrete ways. For instance, humanists sometimes criticize text mining by noting that words and concepts don’t line up with each other in a one-to-one fashion. This is quite true: but it’s a critique of humanists’ existing search practices, not of embryonic efforts to improve them. Ordinary forms of keyword search are driven by individual words in a literal-minded way; the point of more sophisticated strategies — like topic modeling — is precisely that they pay attention to looser patterns of association in order to reflect the polysemous character of discourse, where concepts always have multiple names and words often mean several different things.

Perhaps more importantly, humanists have resigned themselves to a hermeneutically naive approach when they accept the dart-throwing game called “choosing search terms.” One of the basic premises of historicism is that other social forms are governed by categories that may not line up with our own; to understand another place or time, a scholar needs to begin by eliciting its own categories. Every time we use a search engine to do historical work we give the lie to this premise by assuming that we already know how experience is organized and labeled in, say, seventeenth-century Spain. That can be a time-consuming assumption, if our first few guesses turn out to be wrong and we have to keep throwing darts. But worse, it can be a misleading assumption, if we accept the first or second set of results and ignore concepts whose names we failed to guess. The point of more sophisticated text-mining techniques — like semantic clustering — is to allow patterns to emerge from historical collections in ways that are (if not absolutely spontaneous) at least a bit less slavishly and minutely dependent on the projection of contemporary assumptions.

I don’t want to suggest that we can dispense with search engines; when you already know what you’re looking for, and what it’s called, a naive search strategy may be the shortest path between A and B. But in the humanities you often don’t know precisely what you’re looking for yet, or what it’s called. And in those circumstances, our present search strategies are potentially misleading — although they remain powerful enough to be seductive. In short, I would suggest that humanists are choosing the wrong moment to get nervous about the distorting influence of digital methods. Crude statistical algorithms already shaped our critical practice in the 1990s when we started relying on keyword search; if we want to take back the reins, each humanist is going to need to understand text mining well enough to choose the tools appropriate for his or her own theoretical premises.

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18c 19c visualization

The history of an association, part two.

Here’s another attempt to animate the history of a cluster of associated words — this time as a force-directed graph that folds and unfolds itself as the window of time moves forward, and changing strengths of association create different tensions in the graph.

I had a lot of fun making this clip, but I don’t want to make exaggerated claims for it. These images might not mean very much to me if I hadn’t also read some of the books on which they’re based. The visualization only took a day to build, though, and I think it might turn out to be a useful brainstorming tool. In this instance the clip got me thinking about the different ways time is imagined in the “terror gothic” and in the “horror gothic.”



Association between words is measured here using a vector space model and a collection of more than five hundred works of British fiction. I realize it may seem strange that associations can form and disappear while an eighty-year search window moves forward only sixty years — at the end of this clip the cluster is disappearing while the window still overlaps with the period where the cluster started to emerge. It’s worth recalling that the model isn’t counting words, but measuring the association between them. An early-eighteenth-century work that didn’t use sentimental language at all would do nothing to dilute the association between sentimental terms. But a group of nineteenth-century works that used the same language differently could rapidly obscure earlier patterns.

In short, I suspect that the language of temporal immediacy (“moment,” “suddenly,” “immediately,” and so on) is strongly associated with feeling in the 18c in part because gothic novels, and novels of sensibility, just get to it first. In the nineteenth century other kinds of fiction may take up the same temporal language, diluting its specific connection to tremulous feeling. I can’t prove it yet, but the clues I’m seeing do point in that general direction.

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18c 19c visualization

The history of an association.

[Update May 6th, 2011: The problem I describe here is solved a bit more effectively in a more recent post.] It’s fairly easy to visualize a cluster of associated words. But I’d also like to understand how these associations change, and visualizing that is trickier. For one thing, it’s not easy to define what it means to trace “the same” cluster across time; we need an approach that remains open to the possibility that a particular set of associations could simply weaken or dissolve. The video I’ve embedded below is a first, tentative stab at the problem. Move your mouse pointer away after clicking “play” to see the image without cropping.



I’m trying to understand a late-eighteenth-century convergence between the language of temporality and of feeling. Two words that seemed particularly strongly connected were “moment” and “felt.” So what I’ve done is to proceed five years at a time through a 200-year-long corpus, looking at 80-year-long windows from the corpus. In each “snapshot,” I select the twelve words that associate most strongly in vector space with a vector that’s composed of both “moment” and “felt.” In order to graph them on a coordinate plane, I also measure their association with each term separately. The y axis is association with “moment,” and the x axis is association with “felt.” The reference terms themselves are also plotted. This gives me a way to visualize strength of association in the whole cluster — basically, as everything gets closer to the upper-right-hand corner, the strength of association is getting stronger. At the same time we can get a general sense of the semantic character of the cluster.

I’m working with a relatively small collection here — 538 works of British fiction stretched out between 1700 and 1900. I have a larger 18th-century collection, but in this case I needed continuity over a longer span of time, and in order to achieve that I had to limit the collection to fiction, which reduced its size. It also means that the selection of words you’ll see here is different from the selection of words you saw in previous posts about the “felt-moment” convergence, which were based on a generically diverse collection.

Some of the things that are awkward about this video are consequences of the small collection size. For instance, given the small collection size, I have to choose a pretty long window (80 years out of an overall 200-year-long collection). The window is a bit shorter than that at the beginning of the video — for purely dramatic reasons, so that we don’t reach the “climax” of the clip too rapidly.

Also, of course, the stop-motion animation is rather jerky. With a larger collection, I think it might actually be possible to watch these terms move across the coordinate plane in a smooth and connected fashion. But given the small collection size, smooth motion would be illusory; the data don’t really support that level of precision.

However, even with all those caveats, I feel I’m learning something from the exercise. I think we are glimpsing the transformation of an associative cluster, and looking at the way it changes across time makes me more than ever suspect that — at the moment when it’s strongest — it has something to do with the way late-eighteenth-century fiction imagines suspense. “Anxiety” and “agitation” are durable presences, often in the upper-right-hand corner of the cluster. This interpretation is also, of course, based on reading some of the relevant works, and I think the next stage in exploring the question will be to go back and read them again. As always, I’m inclined to present text-mining more as an exploratory tool or brainstorming technique than as definitive evidence.

It is also a bit interesting to watch the language of gothic agitation turn into language of middle-class striving as we get into the nineteenth century. The intersection between “moment” and “felt” is increasingly occupied not by trembling but by terms like “energy,” “effort,” and “struggle.” I’m not quite sure what to make of that trajectory. Perhaps it helps explain the dissolution of the earlier cluster.

Another way of visualizing clusters like this might be to group terms in a force-directed graph and animate the evolution of the graph across time.

Categories
math methodology

Should we model “topics” as associative clusters, or as statistical factors?

I should say up front that this is going to be a geeky post about things that happen under the hood of the car. Many readers may be better served by scrolling down to “Trends, topics, and trending topics,” which has more to say about the visible applications of text mining.

I’ve developed a clustering methodology that I like pretty well. It allows me to map patterns of usage in a large collection by treating each term as a vector; I assess how often words occur together by measuring the angle between vectors, and then group the words with Ward’s clustering method. This produces a topic tree that seems to be both legible (in the sense that most branches have obvious affinities to a genre or subject category) and surprising (in the sense that they also reveal thematic connections I wouldn’t have expected). It’s a relatively simple technique that does what I want to do, practically, as a literary historian. (You can explore this map of eighteenth-century diction to check it out yourself; and I should link once again to Sapping Attention, which convinced me clustering could be useful.)

But as I learn more about Bayesian statistics, I’m coming to realize that it’s debatable whether the clusters of terms I’m finding count as topics at all. The topic-modeling algorithms that have achieved wide acceptance (for instance, Latent Dirichlet Allocation) are based on a clear definition of what a “topic” is. They hypothesize that the observed complexity of usage patterns is actually produced by a smaller set of hidden variables. Because those variables can be represented as lists of words, they’re called topics. But the algorithm isn’t looking for thematic connections between words so much as resolving a collection into a set of components or factors that could have generated it. In this sense, it’s related to a technique like Principal Component Analysis.

Deriving those hidden variables is a mathematical task of considerable complexity. In fact, it’s impossible to derive them precisely: you have to estimate. I can only understand the math for this when my head is constantly bathed in cool running water to keep the processor from overheating, so I won’t say much more about it — except that “factoring” is just a metaphor I’m using to convey the sort of causal logic involved. The actual math involves Bayesian inference rather than algebra. But it should be clear, anyway, that this is completely different from what I’m doing. My approach isn’t based on any generative model, and can’t claim to reveal the hidden factors that produce texts. It simply clusters words that are in practice associated with each other in a corpus.

I haven’t tried the Bayesian approach yet, but it has some clear advantages. For one thing, it should work better for purposes of classification and information retrieval, because it’s looking for topics that vary (at least in principle) independently of each other.* If you want to use the presence of a topic in a document to guide classification, this matters. A topic that correlated positively or negatively with another topic would become redundant; it wouldn’t tell you much you didn’t already know. It makes sense to me that people working in library science and information retrieval have embraced an approach that resolves a collection into independent variables, because problems of document classification are central to those disciplines.

On the other hand, if you’re interested in mapping associations between terms, or topics, the clustering approach has advantages. It doesn’t assume that topics vary independently. On the contrary, it’s based on a measure of association between terms that naturally extends to become a measure of association between the topics themselves. The clustering algorithm produces a branching tree structure that highlights some of the strongest relationships and contrasts, but you don’t have to stop there: any list of terms can be treated as a vector, and compared to any other list of terms.

A fragment of a larger tree, produced by clustering the top 1650 terms in a collection of 2,193 18c documents. Click through for a larger image giving more context.

Moreover, this flexibility means that you don’t have to treat the boundaries of “topics” as fixed. For instance, here’s part of the eighteenth-century tree that I found interesting: the words on this branch seemed to imply a strange connection between temporality and feeling, and they turned out to be particularly common in late-eighteenth-century novels by female writers. Intriguing, but we’re just looking at five words. Maybe the apparent connection is a coincidence. Besides, “cried” is ambiguous; it can mean “exclaimed” in this period more often than it means “wept.” How do we know what to make of a clue like this? Well, given the nature of the vector space model that produced the tree, you can do this: treat the cluster of terms itself as a vector, and look for other terms that are strongly related to it. When I did that, I got a list that confirmed the apparent thematic connection, and helped me begin to understand it.
A list of terms most strongly associated with the group "instantly, cried, felt, moment, longer" in a generically diverse corpus of 2,193 18c documents ranging from sermons to cookbooks. "Similarity" here is technically measured as the cosine of the angle between two vectors.

This is, very definitely, a list of words associated with temporality (moment, hastily, longer, instantly, recollected) and feeling (felt, regret, anxiety, astonishment, agony). Moreover, it’s fairly clear that the common principle uniting them is something like “suspense” (waiting, eagerly, impatiently, shocked, surprise). Gender is also involved — which might not have been immediately evident from the initial cluster, because gendered words were drawn even more strongly to other parts of the tree. But the associational logic of the clustering process makes it easy to treat topic boundaries as porous; the clusters that result don’t have to be treated as rigid partitions; they’re more appropriately understood as starting-places for exploration of a larger associational web.

[This would incidentally be my way of answering a valid critique of clustering — that it doesn’t handle polysemy well. The clustering algorithm has to make a choice when it encounters a word like “cried.” The word might in practice have different sets of associations, based on different uses (weep/exclaim), but it’s got to go in one branch or another. It can’t occupy multiple locations in the tree. We could try to patch that problem, but I think it may be better to realize that the problem isn’t as important as it appears, because the clusters aren’t end-points. Whether a term is obviously polysemous, or more subtly so, we’re always going to need to make a second pass where we explore the associations of the cluster itself in order to shake off the artificiality of the tree structure, and get a richer sense of multi-dimensional context. When we do that we’ll pick up words like “herself,” which could justifiably be located at any number of places in the tree.]

Much of this may already be clear to people in informatics, but I had to look at the math in order to understand that different kinds of “topic modeling” are really doing different things. Humanists are going to have some tricky choices to make here that I’m not sure we understand yet. Right now the Bayesian “factoring” approach is more prominent, partly because the people who develop text-mining algorithms tend to work in disciplines where classification problems are paramount, and where it’s important to prove that they can be solved without human supervision. For literary critics and historians, the appropriate choice is less clear. We may sometimes be interested in classifying documents (for instance, when we’re reasoning about genre), and in that case we too may need something like Latent Dirichlet Allocation or Principal Component Analysis to factor out underlying generative variables. But we’re just as often interested in thematic questions — and I think it’s possible that those questions may be more intuitively, and transparently, explored through associational clustering. To my mind, it’s fair to call both processes “topic modeling” — but they’re exploring topics of basically different kinds.

Postscript: I should acknowledge that there are lots of ways of combining these approaches, either by refining LDA itself, or by combining that sort of topic-factoring approach with an associational web. My point isn’t that we have to make a final choice between these processes; I’m just reflecting that, in principle, they do different things.

* (My limited understanding of the math behind Latent Dirichlet Allocation is based on a 2009 paper by D.M. Blei and J. D. Lafferty available here.)

Categories
18c 19c methodology ngrams topic modeling

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.

Categories
18c methodology topic modeling

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.

Categories
18c methodology

Revealing the relationships between topics in a corpus.

[UPDATE April 7: The illustrations in this post are now out of date, though some of the explanation may still be useful. The kinds of diction mapped in these illustrations are now mapped better in branches 13-14, 18, and 1 of this larger topic tree.] While trying to understand the question I posed in my last post (why did style become less “conversational” in the 18th century?), I stumbled on a technique that might be useful to other digital humanists. I thought I might pause to describe it.

The technique is basically a kind of topic modeling. But whereas most topic modeling aims to map recurring themes in a single work, this technique maps topics at the corpus level. In other words, it identifies groups of words that are linked by the fact that they tend to occur in the same kinds of books. I’m borrowing this basic idea from Ben Schmidt, who used tf-idf scores to do something similar. I’ve taken a slightly different approach by using a “vector space model,” which I prefer for reasons I’ll describe in some technical notes. But since you’ll need to see results before you care about the how, let me start by showing you what the technique produces.

part of a topic tree based on 2,200 18c works

This branch of a larger tree structure was produced by a clustering program that groups words together when they resemble each other according to some measure of similarity. In this case I defined “similarity” as a tendency to occur in the same eighteenth-century texts. Since the tree structure records the sequence of grouping operations, it can register different nested levels of similarity. In the image above, for instance, we can see that “proud” and “pride” are more likely to occur in the same texts than either is to occur together with “smile” or “gay.” But since this is just one branch of a much larger tree, all of these words are actually rather likely to occur together.

This tree is based on a generically diverse collection of 18c texts drawn from ECCO-TCP with help from 18thConnect, and was produced by applying the clustering program I wrote to the 1350 most common words in that collection. The branch shown above represents about 1/50th of the whole tree. But I’ve chosen this branch to start with because it neatly illustrates the underlying principle of association. What do these words have in common? They’re grouped together because they appear in the same kinds of texts, and it’s fairly clear that the “kinds” in this case are poetic. We could sharpen that hypothesis by using this list of words as a search query to see exactly which texts it turns up, but given the prevalence of syncope (“o’er” and “heav’n”), poetry is a safe guess.

It is true that semantically related words tend to be strongly grouped in the tree. Ease/care, charms/fair and so on, are closely linked. But that isn’t a rule built into the algorithm I’m using; the fact that it happens is telling us something about the way words are in practice distributed in the collection. As a result, you get a snapshot of eighteenth century “poetic diction,” not just in the sense of specialized words like “oft,” but in the sense that you can see which themes counted as “poetic” in the eighteenth century, and possibly gather some clues about the way those themes were divided into groups. (In order to find out whether those divisions were generic or historical, you would need to turn the process around and use the sublists as search queries.)

part of a topic tree based on 2,200 18c works

Here’s another part of the tree, showing words that are grouped together because they tend to appear in accounts of travel. The words at the bottom of the image (from “main” to “ships”) are very clearly connected to maritime travel, and the verbs of motion at the top of the image are connected to travel more generally. It’s less obvious that diurnal rhythms like morning/evening and day/night would be described heavily in the same contexts, but apparently they are.

In trees like these, some branches are transparently related to a single genre or subject category, while others are semantically fascinating but difficult to interpret as reflections of a single genre. They may well be produced by the intersection or overlap of several different generic (or historical) categories, and it’ll require more work to understand the nature of the overlap. In a few days I’ll post an overview of the architecture of the whole 1350-word eighteenth-century tree. It’ll be interesting to see how its architecture changes when I slide the collection forward in time to cover progressively later periods (like, say, 1750-1850). But I’m finding the tree interesting for reasons that aren’t limited to big architectural questions of classification: there are interesting thematic clues at every level of the structure. Here’s a portion of one that I constructed with a slightly different list of words.

part of a topic tree based on 2,200 18c works

Broadly, I would say that this is the language of sentiment: “alarm,” “softened,” “shocked,” “warmest,” “unfeeling.” But there are also ringers in there, and in a way they’re the most interesting parts. For instance, why are “moment” and “instantly” part of the language of sentiment in the eighteenth century?