Minimum Probability of Error Signal Representation

The problem of minimum probability of error signal representation (MPE-SR) considering issues of finite training data is revisited and extended in this paper. Results are presented that justify addressing this problem as a complexity-regularized optimization criterion, reflecting the well-known tradeoff between signal representation quality and learning complexity. A rate-distortion type of formulation is proposed to address this optimization problem by finding a sequence of signal representations achieving optimal complexity-fidelity operational points. Finally under specific assumptions, it is shown that the MPE-SR reduces to a version of Fisher linear discriminant analysis.