Pattern Trajectory Analysis of Nonstationary Multivariate Data

Multivariate data sets with dependency between observations are described using a feature space representation. The resulting ordered set of points in feature space is termed the pattern trajectory. A set of descriptors of the pattern trajectory has been developed. Time-dependent clusters and transition segments form the basic structural description from which both lower level properties, e.g., cluster position, cluster dispersion, transition rate, and higher level properties, e.g., rebound, periodicity, finite state model, may be derived. Two algorithms have been developed for time-dependent cluster analysis. The time-weighted minimum spanning tree (TWMST) algorithm utilizes a composite space-time distance measure and creates clusters by cutting the longest tree branches. The time-dependent Isodata (TD-ISODATA) algorithm utilizes a global clustering to initiate the segmentation into timedependent cluster cores and transition segments. Examples of the applica tion of these algorithms to nonstationary neuronal spike train data and to simulated animal migration data are described. The pattern trajectory approach appears to offer advantages in the analysis of complex nonstationary data sets where conventional time series techniques are insufficient. Time-dependent clustering provides a means to identify a composite source model.