Diffrence in SOM Significance Degree due to its Node Geometory - part II

Abstract

Most information obtained from the external world is derived from samples, and the accuracy of these judgments is determined using statistical tests. This process commonly employs the concept of probability, known as the significance level. Tokuoka et al. have proposed a novel concept of significance, which differs from the classical statistical approach. They argue that ”significance originally refers to the magnitude relationship between two data class elements.” Applying this new method to the classification of multidimensional data has the potential to yield valuable information. Despite the potential applications of this proposed method, its fundamental properties remain insufficiently understood due to its novelty. In this study, we examined the properties of significance using the Wine benchmark data within the context of Self-Organizing Maps (SOMs). Specifically, we investigated how the number of prototypes and data points affects the accuracy of significance. In SOM analysis, the number of nodes must be appropriately set according to the data size. Tokuoka et al. ’s previous research primarily focused on experiments with spherical SOMs. However, the significance of other node configurations, such as planar and toroidal prototypes, has not been evaluated. Thus, the dependency of SOM significance on node configuration has yet to be thoroughly examined. This study aims to elucidate the differences in significance among spherical, toroidal, and planar SOM node configurations.