Introduction

Abstract

Pattern recognition or discrimination is about guessing or predicting the unknown nature of an observation, a discrete quantity such as black or white, one or zero, sick or healthy, real or fake. An observation is a collection of numerical measurements such as an image (which is a sequence of bits, one per pixel), a vector of weather data, an electrocardiogram, or a signature on a check suitably digitized. More formally, an observation is a d-dimensional vector x. The unknown nature of the observation is called a class. It is denoted by y and takes values in a finite set {1, 2,..., M}. In pattern recognition, one creates a function g(x): ℛ^d → {1,..., M} which represents one’s guess of y given x. The mapping g is called a classifier. Our classifier errs on x if g(x) ≠ y.