A matrix approach to data base exploration: Analysis of classifier results

Exploratory pattern analysis is an iterative process. In many instances, numerous iterations are required before a practical model or classification scheme can be concisely stated and adequately analyzed. There are at least three distinct functions that are required for solving the important and difficult pattern recognition problems. These are: (1) conceptualization of a classification model; (2) mathematical modeling and analyzing the practical and theoretical implications of the model; (3) testing the model on actual data. These tasks are interdependent and the investigation proceeds in what often appears to be an unsystematic approach to problem solving. This paper will address the third task and consequently, by association, hopefully affect the other two in a beneficial and constructive manner.The purpose of this article is to illustrate a general methodology, based on a matrix approach, that can be used in organizing, formatting and statistically analyzing classifier results. The discussion is intended for all individuals interested in analyzing pattern analysis and classification experiments, however, it should be of particular interest to those involved in designing interactive pattern recognition software packages. The discussion proceeds from a matrix algebra study of classifier results to techniques for statistical analysis using Cohen's kappa and Cochran's Q statistics. An example from nuclear medicine is used to illustrate the methodology.