Applying an Improved MRPS-GMM Method to Detect Temporal Patterns in Dynamic Data System

Shaobo Wang, Marquette University


The purpose of this thesis is to introduce an improved approach for the temporal pattern detection, which is based on the Multivariate Reconstructed Phase Space (MRPS) and the Gaussian Mixture Model (GMM), to overcome the disadvantage caused by the diversity of shapes among different temporal patterns in multiple nonlinear time series. Moreover, this thesis presents an applicable software program developed with MATLAB for users to utilize this approach. A major study involving dynamic data systems is to understand the correspondence between events of interest and predictive temporal patterns in the output observations, which can be used to develop a mechanism to predict the occurrence of events. The approach introduced in this thesis employs Expectation-Maximization (EM) algorithm to fit a more precise distribution for the data points embedded in the MRPS. Furthermore, it proposes an improved algorithm for the pattern classification process. As a result, the computational complexity will be reduced. A recently developed software program, MATPAD, is presented as a deliverable application of this approach. The GUI of this program contains specific functionalities so that users can directly implement the procedure of MRPS embedding and fit data distribution with GMM. Moreover, it allows users to customize the related parameters for specific problems so that users will be able to test their own data.