Section: New Results

Axis 1: Co-clustering: A versatile way to perform clustering in high dimension

Participant : Christophe Biernacki.

Standard model-based clustering is known to be very efficient for low-dimensional data sets, but it fails for properly addressing high dimension (HD) ones, where it suffers from both statistical and computational drawbacks. In order to counterbalance this curse of dimensionality, some proposals have been made to take into account redundancy and features utility, but related models are not suitable for too many variables. We advocate that co-clustering, an unsupervised mixture model learning method to define simultaneously groups of rows (individuals) and groups of columns (variables) on a data matrix, is of particular interest to perform HD clustering of individuals even if it is not its primary mission. Indeed, column clustering is recast as a strategy to control the variance of the estimation, the model dimension being driven by the number of groups of variables instead of the number of variables itself. However, the statistical counterpart of this important variance reduction brings naturally some important model bias. The purpose is to access (first in an empirical manner) the trade-off bias-variance of the co-clustering strategy in scenarios involving HD fundaments (correlated variables, irrelevant variables). We show the ability of co-clustering to outperform simple mixture row-clustering, even if co-clustering clearly corresponds to a misspecified model situation, revealing a promising manner to efficiently address (very) HD clustering. An early version of this work has been presented to an international conference [36].

It is a joint work with Christine Keribin from Université Paris-Sud.