Task Decomposition and Modular Perceptons with Sigmoid Activation Functions for Solving the Two-Spirals Problem

A complicated learning problem can be decomposed into multiple simple two-class problems. A single-output classifier for separating its represented class from the others really solves a two-class problem and can be trained by all samples from the represented class and a small part from its neighboring classes. The equal sample sizes in the two-class problems thus come into being. Two of solutions are as follows. (A). Add some virtual samples to the smaller classes. (B). Multiply the weight increments in the smaller sides by enlargement factors. If the decision boundaries of single-output perceptrons are open, their effective regions must be limited by adding correction coefficients, which are related to the class means and variances. The result for solving the two-spirals problem shows that the above methods are effective.