Visualizing Topic Models with Force-Directed Graphs

headlineForce-directed graphs are tricky.  At their best, the perspective they offer can be very helpful; data points cluster into formations that feel intuitive and look approachable. At their worst, though, they can be too cluttered, and the algorithms that make everything fall into place can deceive as much as they clarify.

But there’s still a good chance that, despite the problems that come along with making a network model of anything (and the problems introduced by making network models of texts), they can still be helpful for interpreting topic models.  Visualizations aren’t exactly analysis, so what I share below is meant to raise more questions than answers.  We also tried to represent as many aspects of the data as possible without breaking (or breaking only a little) the readability of the visualizations.  There were some very unsuccessful tries before we arrived at what is below.

A Few Remarks on Method

As part of our work together, Ted has run some topic models on his 19th century literature dataset and computed the correlation of each topic to other topics.  We decided to try this out to see topic distribution among genres, and to get a feel for how topics clustered with one another.  Which documents belong to what topic aren’t important for now, although in time I’d like to have the nodes link to the text of the documents.  Ted has also calculated the predominant genre to which each topic belongs. And, after building a network model where topic correlation equals edge value, I’ve run the Girvan-Newman algorithm to assess how the topics would cluster by their associations with other topics (I like this approach to grouping better than others for examinations of overall graph structure like this one, as we’re not as interested in  individual cliques or clusters).  What we get then, is two different ways to categorize the topic: on the one hand we have the genre the topic appears in most (with the genres being assigned to individual documents by a human expert), and on the other we see groupings based on co-occurence with other topics.

The visualizations shown here are all built using d3.js, the excellent open source javascript library created by Mike Bostock.  Each of the graphs are force-directed: all nodes possess a negative charge and repel from one another.  All links bond to these nodes and hold them together.  Many force-directed models set their links to behave like springs and contract to the shortest possible distance between nodes, but these graphs below don’t exactly use Hooke’s law to calculate bond length. Instead, they aim for a specific bond length (in this case, 20 pixels) and draw a link as close as possible to that length given the charges acting on it.

I wanted physical proximity of nodes to one another to means something, so the graphs below have variable bond strengths, which means that depending on the value of the bond (which in these graphs is a function of the correlation of a topic with the topic to which it is linked), it will resist or cooperate with being “stretched” (or really, drawn at a longer distance as other stronger bonds take precedence in being drawn closer to the ideal length of 20px).  This has implications for how to interpret distance between nodes in these images.  The X and Y axes have no set value, so distance does not equal correlation. This is more of a Newtonian than Euclidean space,  which means that a short link can indicate a strong bond between nodes, but strong bonds can also be stretched by opposing forces (like other bonds) exerted on nodes at either end of the bond. So distance between nodes can be significant, but only once considered in context of the whole model and its constitutive metaphor of a physical system. Click on the image below for a sample of what we’re talking about:

Main TM

D3 allows this is to be an interactive visual, and mousing over an individual node will reveal the first ten words of the topic it represents.  Also, clicking on a node allows for pulling and rearranging the graph.  Doing this a few times helps reinforce the idea that distance between nodes is the result of a set of simulated physical properties.  The colors assigned to the Newman groups are arbitrary, but there’s a key on the left to help distinguish among similar colors.

Comparing Two Graphs

Network graphs are more useful when you can compare them to other network graphs.  We split the dataset into two halves, and Ted generated 100 topics for each half of the century.  We used slightly different genre labels, but we calculated Newman groups again to produce the two graphs below (again, click through to interact with the graph):

cellplot49cellplot99

Like the first graph, Newman color assignments are arbitrary; what’s purple in the first 50 years of topics has nothing to do with what’s purple in the next 50 years of topics.  I’ve modified these graphs in two key ways to help with reading them.  Firstly, bond thickness now variable, and it is a function of bond strength (bond strength derived from correlation).  This helps assess if a bond is longer because it’s being stretched or because it’s weak, or both.  Secondly, I’ve added node “halos” to emphasize the degree to which the nodes cluster, as well as highlight the Newman groups.

Here’s an alternative graph that colors the nodes by genre instead of Newman group, leaving only the halo to represent group affiliation:

cellalt49

I won’t pretend that any of these are easy to read immediately, but one of our experiments in this was to try to represent as many dimensions as possible to create an exploratory framework for a topic model.  Halo and node diameter are set, but the two elements on the visualization are independent and could represent topic size, degree of genre predominance in a topic, etc.

My hope is that these visualizations can be insightful and might help us work through the benefits and disadvantages of force-directed layouts for visualizing topic models.

As for interpretation and analysis, here is the part where I punt to domain experts in 19th century literature and history…