Nonlinear methods for clustering and reduction of dimensionality

Analysis of data in computational finance and computational neuroscience share a number of common traits: data are typically massive, noisy, very high dimensional, and governed by complete multi-scale time dynamics. The set of known parameters forms a small subset of the true variates that control the dynamics of the systems from which data is collected. Reduction of dimensionality of the data, and clustering of system parameters according to a relevant measure of independence, and improving signal to noise ratio, are among the core problems of both disciplines. We propose a nonlinear version of independent component analysis for clustering of parameters and separating clusters according to their measure of statistical independence. Analogously, we propose a nonlinear version of principal component analysis for reducing the dimensionality of data. The combination of these two methods forms the basis for a dynamic pattern recognition paradigm. This approach is inspired by a mathematical analogy to a successful method for estimation of patterns of functional connectivity in neuro-imaging