Self-organizing feature maps with perfect organization

The self-organizing feature maps (SOFMs) introduced by Kohonen (1990) have found use in a wide variety of signal processing applications. The goal of SOFMs is to allow encoding of high-dimensional data vectors in such a manner that a vector's relative position in the codebook is related to the information in the vector in as simple a fashion as possible. One measure of the SOFM's performance in achieving this goal has been proposed by Zrehen and Blayo (1992). According to this measure, many feature maps produced by previous algorithms were disorganized. We review the Zrehen disorganization measure and some of its characteristics. We then show how our version of the SOFM algorithms can accept some simple modifications to produce feature maps which achieve perfect organization under the Zrehen measure of feature map performance. We discuss the emergent geometric properties of resulting feature maps, and illustrate the results using industrial drill vibration data. We note that applying the Zrehen-constrained algorithm to a data set implies certain assumptions about the set's distribution. We discuss the implications of these assumptions in the context of a feature extraction system for industrial milling data.