Optimal Classification Tiling Algorithm

This work presents a max-margin tiling algorithm to construct multi-layer perceptrons with perfect performance for all training patterns. Each perceptron distinguishes a portion of a single class patterns from all the rest patterns, as large as possible. The process is a divide and conquer approach therefore the size of the portion gradually reduced and the algorithm accelerate accordingly. Each layer of such perceptrons encodes different class patterns with different codes, maintaining faithful representations. The max-margin separation boundary is optimal to against noise therefore this construction provides resolution of challenging classification of noisy patterns such as seriously corrupted images. To our knowledge, it gives the best performance for noisy testing patterns among all existing methods. We applied the algorithm on highly sparse data of genetic mutations and identified not only gene NF1, which had been previously found by monogenic analysis, but also a list of genes whose deletions may polygenically associate with a group of breast cancer patients.