Pattern Discovery In Complex System

Computational mechanics is a new theory frame to analyze how geometric state space structures support computation in dynamics systems. Professor Crutchfield of Santa Fe Institute has developed this frame since 1980s. Epsilon machine is a theory tool of computational mechanics, and its goal is to discover patterns intrinsic to a process about process's structure with little priori assumptions. So in this paper Epsilon machine is called a theory of pattern discovery.Discovering hidden patterns or structures is a very important method to study complex systems. Actually, the process of discovery is to reconstruct causal states for the system. A new reconstruction algorithm, causal state splitting reconstruction (CSSR) was presented by Shalizi in 2004, which is fit for any stationary symbol time serials. There are three procedures in CSSR: initialize, homogenize and determinize, and probability statistics is its main tools, i.e. conditional probability and KS test. Every causal state comprises many strings, which have the same morphs.Epsilon machine is strange and mysterious to most people, and applying it to engineering problem is an instructive challenge. Two different problems, anomaly detection and reinforcement learning are studied based on epsilon machine. Several examples demonstrate that epsilon machine is effective and universal.The new anomaly detection algorithm includes a primary assumption and two important steps. The assumption is that the behavior of the system changes slowly and it can be detected from time series. The first step is time series symbolization and the second is structure vector (SV) model.Causal state can only be reconstructed using symbol series, but most time series is real, not symbol. So symbolization is necessary. Statistical complexity comes from epsilon machine, and it's a good choice to evaluate kinds of symbolization ways. Eight groups of time series are symbolized by several ways and many empirical results are presented.Geometry structures can be inferred from symbol series by CSSR, which reflect...