Clustering Gene Expression Data by Mutual Information with Gene Function

We introduce a simple on-line algorithm for clustering paired samples of continuous and discrete data. The clusters are defined in the continuous data space and become local there, while within-cluster differences between the associated, implicitly estimated conditional distributions of the discrete variable are minimized. The discrete variable can be seen as an indicator of relevance or importance guiding the clustering. Minimization of the Kullback-Leibler divergence-based distortion criterion is equivalent to maximization of the mutual information between the generated clusters and the discrete variable. We apply the method to a time series data set, i.e. yeast gene expressions measured with DNA chips, with biological knowledge about the functions of the genes encoded into the discrete variable.