Clustering Change Sign Detection by Fusing Mixture Complexity

TL;DR

This paper introduces a method for detecting changes in the cluster structure by examining the transition of MC fusion, and demonstrates the effectiveness of the method through empirical analysis using both artificial and real-world datasets.

Abstract

This paper proposes an early detection method for cluster structural changes. Cluster structure refers to discrete structural characteristics, such as the number of clusters, when data are represented using finite mixture models, such as Gaussian mixture models. We focused on scenarios in which the cluster structure gradually changed over time. For finite mixture models, the concept of mixture complexity (MC) measures the continuous cluster size by considering the cluster proportion bias and overlap between clusters. In this paper, we propose MC fusion as an extension of MC to handle situations in which multiple mixture numbers are possible in a finite mixture model. By incorporating the fusion of multiple models, our approach accurately captured the cluster structure during transitional periods of gradual change. Moreover, we introduce a method for detecting changes in the cluster structure by examining the transition of MC fusion. We demonstrate the effectiveness of our method through empirical analysis using both artificial and real-world datasets.

Figures (9)

• Figure 1: Transition of the number of clusters gradually changing from 3 to 4.
• Figure 2: Example of MC for a Gaussian Mixture Model with a mixture size of 2 KY22.
• Figure 3: Plot of data in 2D for the moving overlap dataset at $t=1, 50, 76$.
• Figure 4: Plot of data in 2D for the moving imbalance dataset at $t=1, 55, 76$.
• Figure 5: Estimated values of $k$, $\exp(\mathrm{MC})$, $\exp(\mathrm{MC\text{-}fusion})$, and $\mathrm{Ddim}$ for each time $t$ in the moving overlap dataset. The light blue area represents the transitional period of change, and markers indicate the points where each method raised change alerts.