Organization Component Analysis: The method for extracting insights from the shape of cluster

Clustering analysis is widely used to stratify data in the same cluster when they are similar according to specific metrics. The process of understanding and interpreting clusters is mostly intuitive. However, we observe each cluster has unique shape that comes out of metrics on data, which can represent the organization of categorized data mathematically. In this paper, we apply novel topological based method to study potentially complex high-dimensional categorized data by quantifying their shapes and extracting fine-grain insights about them to interpret the clustering result. We introduce our Organization Component Analysis method for the purpose of the automatic arbitrary cluster-shape study without assumption about the data distribution. Our method explores a topology-preserving map of a data cluster manifold to extract the main organization structure of a cluster by the leveraging of the self-organization map technique. To do this, we represent self-organization map as graph. We introduce organization components to geometrically describe the shape of cluster and their endogenous phenomena. Specifically, we propose an innovative way to measure the alignment between two sequences of momentum changes on geodesic path over the embedded graph to quantify the extent to which the feature is related to a given component. As a result, we can describe variability among stratified data, correlated features in terms of lower number of organization components. We illustrate the utilization of our method by applying it to two quite different types of data, in each case mathematically detecting the organization structure of categorized data which are much profounder and finer than those produced by standard methods.