Fusion of Centroid-Based Clustering With Graph Clustering: An Expectation-Maximization-Based Hybrid Clustering

Abstract

This article extends the expectation-maximization (EM) formulation for the Gaussian mixture model (GMM) with a novel weighted dissimilarity loss. This extension results in the fusion of two different clustering methods, namely, centroid-based clustering and graph clustering in the same framework in order to leverage their advantages. The fusion of centroid-based clustering and graph clustering results in a simple 'soft' asynchronous hybrid clustering method. The proposed algorithm may start as a pure centroid-based clustering algorithm (e.g., k -means), and as the time evolves, it may eventually and gradually turn into a pure graph clustering algorithm [e.g., basic greedy asynchronous distributed interference avoidance (GADIA) (Babadi and Tarokh, 2010)] as the algorithm converges and vice versa. The 'hard' version of the proposed hybrid algorithm includes the standard Hopfield neural networks (and, thus, Bruck's Ln algorithm by (Bruck, 1990) and the Ising model in statistical mechanics), Babadi and Tarokh's basic GADIA in 2010, and the standard k-means (Steinhaus, 1956), (MacQueen, 1967) [i.e., the Lloyd algorithm (Lloyd, 1957, 1982)] as its special cases. We call the 'hard version' of the proposed clustering as 'hybrid-nongreedy asynchronous clustering (H-NAC).' We apply the H-NAC to various clustering problems using well-known benchmark datasets. The computer simulations confirm the superior performance of the H-NAC compared to the k -means clustering, k -GADIA, spectral clustering, and a very recent clustering algorithm structured graph learning (SGL) by Kang et al. (2021), which represents one of the state-of-the-art clustering algorithms.