Extension of fixed point clustering A cluster criterion.pdfVIP

a r X i v : n l i n / 0 1 0 2 0 3 2 v 1 [ n l i n .C D ] 2 4 F e b 2 0 0 1 Extension of fixed point clustering: A cluster criterion A. Hutt1, F. Kruggel Max Planck-Institute of Cognitive Neuroscience, Stephanstrasse 1a, 04103 Leipzig, Germany The present report extends the method of fixed point clustering [7] by intro- ducing an indirect criterion for the number of clusters. The derived probability function allows an objective distinction of clustered data and data in between clusters. Applications on simulated data illustrate the clustering method and the probability function. PACS numbers: 02.60.-x, 45.10.-b 1 Introduction The dynamics of spatially extended systems can be measured by sets of multi- detector arrays. Most spatio-temporal analysis methods fitting multi-dimensional dynamical models [1, 2, 3, 4, 5, 6] consider data over the full time range. In [7], a method was described for partitioning spatio-temporal signals into time seg- ments, in which the signal can be modeled by deterministic ordinary differential equations near fixed points. Each dynamical system is determined by a non- linear spatio-temporal analysis [6]. The earlier proposed algorithm in [7] works with an arbitrary number of clusters k. Since results are dependant on k, an objective criterion for the number of clusters is necessary. The present report introduces a different segmentation algorithm and aims to derive an indirect criterion for the number of temporal segments. In the present report, we use the K-Means algorithm [9, 10] for segmenting data, which addresses each data point to a single cluster. Since K-Means works with an arbitrary number of clusters and this number is crucial to clustering results, we derive a probability function representing the degree of membership of a data point at time t to a cluster. It addresses data to clusters or transition parts between clusters and hence determines the number of necessary clusters. Applications to simulated non-stationary data