Statistical Pattern Classification with Binary Variables

Binary random variables are regarded as random vectors in a binary-field (modulo-2) linear vector space. A characteristic function is defined and related results derived using this formulation. Minimax estimation of probability distributions using an entropy criterion is investigated, which leads to an A-distribution and bilinear discriminant functions. Nonparametric classification approaches using Hamming distances and their asymptotic properties are discussed. Experimental results are presented.