Hyperbolic Quotient Feature Map for Competitive Learning Neural Networks

Abstract

In this paper, we present a new learning method called hyperbolic quotient feature map for competitive learning neural networks. The previous neural network learning algorithms didn’t consider their topological properties, and thus their dynamics were not clearly defined. We show that the weight vectors obtained by competitive learning decompose the input vector space and map it to the quotient space X/R. In addition, we define a quotient function which maps [1, ∞) ⊂ R ⁿ to [0,1) and induce the proposed algorithm from the performance measure with the quotient function. Experimental results for pattern recognition of remote sensing data indicate the superiority of the proposed algorithm in comparison to the conventional competitive learning methods.