High dimensional data clustering from a dynamical systems point of view

We provide a short survey of some recent progress towards subspace clustering of high dimensional data (both numerical and categorical) from the viewpoint of dynamical systems. The novel idea behind the dynamical system based approach is the possible connection between the centers of different clusters in a given data set and the local attractors of a dynamical system to be constructed, and the connection between the clustering criteria not given a priori and the boundaries of domains of attraction of the aforementioned local attractors. The essential difficulty is, for a given data set, that one needs to construct the dynamical system and to discover the structures of the clusters (including the subspaces where these clusters are formed) simultaneously. We will present the related neural network architectures, the modeling dynamical systems, the qualitative analysis of the dynamical systems, the resulting clustering algorithms and their performance analysis and applications (to gene expression data analysis and to neural signal spike trains clustering), the connection to the bifurcation and pattern formation theory, and the mathematical and neurophysiological foundation in terms of adaptive delay in signal transmissions.