Chordalysis: a new method to discover the structure of data by Francois Petitjean.
From the post:
…you can’t use log-linear analysis if your dataset has more than, say, 10 variables! This is because the process is exponential in the number of variables. That is where our new work makes a difference. The question was: how can we keep the rigorous statistical foundations of classical log-linear analysis but make it work for datasets with hundreds of variables?
The main part of the answer is “chordal graphs”, which are the graphs made of triangular structures. We showed that for this class of models, the theory is scalable for high-dimensional datasets. The rest of the solution involved melding the classical statistical machinery with advanced data mining techniques from association discovery and graphical modelling.
The result is Chordalysis: a log-linear analysis method for high-dimensional data. Chordalysis makes it possible to discover the structure of datasets with hundreds of variables on a standard computer. So far we’ve applied it successfully to datasets with up to 750 variables. (emphasis added)
Scaling log-linear analysis to high-dimensional data (PDF), by Francois Petitjean, Geoffrey I. Webb and Ann E. Nicholson.
Association discovery is a fundamental data mining task. The primary statistical approach to association discovery between variables is log-linear analysis. Classical approaches to log-linear analysis do not scale beyond about ten variables. We develop an efficient approach to log-linear analysis that scales to hundreds of variables by melding the classical statistical machinery of log-linear analysis with advanced data mining techniques from association discovery and graphical modeling.
Being curious about what was meant by “…a standard computer…” I searched the paper to find:
The conjunction of these features makes it possible to scale log-linear analysis to hundreds of variables on a standard desktop computer. (page 3 of the PDF, the pages are unnumbered)
Not a lot clearer but certainly encouraging!
The data used in the paper can be found at: http://www.icpsr.umich.edu/icpsrweb/NACDA/studies/09915.
The Chordalysis wiki looks helpful.
So, are your clients going to be limited to 10 variables or a somewhat higher number?