A theoretical consideration of multiclass pattern recognition problems: Derivation of an effective formula for the expected accuracy

Abstract

In this paper, we consider multiclass pattern recognition problems theoretically. We first provide a universal set of classes, for example, for all categories of Chinese characters, then we select M classes from the set to make an M‐class recognition problem. The expected accuracy, that is, the mean value of the accuracies of all of the M‐class recognition problems, has been estimated by the Monte Carlo method up to now. However, it is difficult to calculate it precisely because of the combinational explosion. Thus, we derive a formula for the expected accuracy using properties of the universal set. The formula is very effective because of its small computational complexity. We finally show the effectiveness of the formula by applying it to two examples with concrete distributions. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(12): 45–55, 1997