مرکز منطقه ای اطلاع رساني علوم و فناوري - Nonsupervised sequential classification and recognition of patterns

Abstract :

A Bayes approach to nonsupervised pattern recognition is given where $n l$ -dimensional vector samples $X_{1}, X_{2}, \\cdots , X_{n}$ are received unclassified, i.e., any one of $M$ pattern sources $\\omega _{1}, \\omega _{2}, \\cdots , \\omega _{M}$ , with corresponding probabilities of occurrence $Q_{1_{o}}, Q_{2_{o}} , \\cdots , Q_{M_{o}}$ , caused each sample $X_{s}, s=1,2, \\cdots , n$ . The approach utilizes the fact that the cumulative distribution function (c.d.f.) of $X_{s}$ is a mixture c.d.f., $F(X_{s})= \\sum _{i=1}^{M} F(X_{s}|\\omega _{i}) Q_{i_{o}}$ . It is assumed that available a priori knowledge includes knowledge of $M$ and the family ${F(X_{s}|\\omega _{i})}$ , where $F(X_{s}|\\omega _{i})$ is characterized by a vector $B_{i_{o}}$ . In general, $B_{i_{o}}$ and $Q_{i_{o}}, i = 1,2, \\cdots , M$ are considered fixed but unknown, and conditional probability of error in deciding which source caused $X_{n}$ is minimized. When the functional form of $F(X_{s}|\\omega _{i})$ in terms of $B_{i_{o}}$ is unknown, the family ${F(X_{s}|\\omega _{i})}$ is taken to be the family of multinomial c.d.f.\´s--an application of the histogram concept to the nonsupervisory problem. Additional nonparameteric a priori knowledge about the family--such as $F(X_{s}|\\omega _{i})$ is symmetrical, and/or $F(X_{s}|\\omega _{i})$ differs from $F(X_{s}|\\omega _{j})$ only by a translational vector--can be utilized in the Bayes solution.