On empirical capacity, random coding bound, and probability of outage of an object recognition system under constraint of PCA-encoding

The problem of determining the limits of a pattern or object recognition system can often be approached from Information Theoretic point of view. Given source encoded data, the constrained recognition capacity and random coding bound are fundamental characteristics of a recognition channel. They indicate the limiting relationship between the number of classes that a recognition system can maintain, the length of encoded data describing an object/pattern (or its template) at a specific level of noise and distortion and the probability of recognition error. We define recognition channel as an environment that transforms an object template into a query template to be recognized. In this work we assume that images are encoded using an empirical version of Karhunen-Loeve expansion known in the literature as Principal Component Analysis (PCA).We numerically evaluate the empirical capacity and random coding bound of a PCA-based recognition system using two datasets, FRGC 2006 and COIL-100. We further analyze the relationship between these performance measures and the probability of information outage often used in practice to characterize capabilities of a nonergodic communication channel. Our conclusions are supported by the results of the numerical analysis.