Which analysis for a set of (0/1)binary variables alone? I have a dataset I would like to analyze and plot
It consists of 100 binary variables (0/1) for about 2,000,000 observations
There is absolutely no quantitative variable, nor anything I could use as an explained variable for a regression analysis.
Actually, the dataset represents the patronage of 2 billion customers for 100 stores. It equals 1 if the consumer go to the store, 0 if he doesn't. With no further information. Consumers can of course visit several stores.
As the variable look like factors (0/1), I thought I could go for a Mutliple Correspondence Analysis (MCA). However, the resulting plot consists of 2 points for each variable (one for 1 and one for 0) which is not easily interpretable. (or is there a method for not plotting certain points in MCA? - in R)
I also tried to consider my dataset as a bipartite network (consumer-store). However, the plot is not really insightful, as I am especially looking for links between stores. (kind of "if a consumer go to that store, he probably also goes to this one...")
So, I have a simple question: which method you would choose for computing and plotting the links between a set of binary variable?
 A: I would start by making a matrix of stores*stores (this would be 100*100, but you only need a "triangle" of the data, so it's really less than half that size). In each cell, I would put 1) the number of people who went to both stores. 2) The expected number of people in that cell if stores were unrelated. (Row marginal*column marginal/total). This, by itself, may give some insight. 
For a more analytic approach, I would look into social network analysis. This would allow you to find more complex patterns in the data (e.g. are there groups of stores that tend to be visited by the same people?)  It's a whole field in and of itself. I used to be up on the literature, but it has been a decade since I looked at it. There are packages in R that do a nice job; there are also stand alone programs (some of them shareware, some low cost, some quite pricey).
A: Actually, frequent itemset mining may be a better choice than clustering on such data.
The usual vector-oriented set of algorithms does not make a lot of sense. K-means for example will produce means that are no longer binary.
A: I recently suggested latent class analyisis for a similar question. See here, for more details. If you specific questions, leave a comment, and I'll edit this accordimgly.
