Exploration and reduction of high dimensional spaces with independent component analysis

The application of Independent Component Analysis (ICA) to genomic data is here considered. In recent years, microarrays have delivered to researchers huge series of measurements of gene expression levels under different experimental conditions. This work, for instance, emphasizes exploratory data analysis following experimental work on the popular Escherichia coli; the context is a typical one in which changes in gene expression values are observed after perturbing genes at an initial time and measuring the responses at regular time intervals until the steady state is achieved. The gene temporal patterns are as usual very short, and it is no exception for the application here described, as only six time points are available. This aspect combines with a very large feature space (i.e., the gene dimensionality). Thus, several kinds of fluctuations have to be monitored, and many are discarded because not significantly different from noise. ICA represents a very flexible signal processing tool which attempts to deal with noise as well, although the expected impact involves its most inherent property of delivering a decomposition of the gene profiles according to statistically independent sources of information. The latter are most likely linked to underlying biological processes regulating the genes, but it is not a goal of this paper to characterize these biological aspects, since this is a subject of ongoing research which requires further experimental investigation and tests before drawing any important conclusion. However, the initial computational results which have been obtained are very encouraging, and thus they are presented here together with some interesting problem-specific aspects. i

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