Identification of dinamic complex trajectories using gershgorin´s theorem in principal component analysis

Abstract

The main motivation of this paper is to develop some methods or techniques that will allow us to study complex systems (in the sense of finding their under lying structure or their similarity to others). If we have these techniques, we will be able to tackle a series of real life problem that until now has had no reliable solution. Examples of such problems are 3D-object recognition, handwritten word recognition, interpretation of bio-medical signal and speech recognition. In this paper, we will present one techniques to analyze dynamical system based on their behavior, where that behavior can be determined from the system output tr ajectories. We will use dynamic pattern recognition and principal component analysis concepts for dynamic system analysis. The purpose is to find vectors basis using such similarity structur al where the sequences of the state var iables can be segmented and each segment can be described as a lineal combination of vectors basis.