Discrete Orthogonal Moments-Based Deep Clustering: A Racah Polynomials and Cauchy Distribution Approach

Abstract

Deep embedded clustering (DEC) has emerged as a powerful paradigm for unsupervised representation learning in high-dimensional data. This paper introduces a novel DEC framework that integrates a fully connected autoencoder with separable discrete orthogonal moments (SDOMs) derived from Racah polynomials. Specifically, the x-axis leverages Racah moments, while the y-axis employs a choice between Racah, Tchebichef, Krawtchouck, or Hahn moments, enabling rich spatial feature extraction. To enhance computational efficiency, we propose using only half of the moment orders, which have been empirically shown to retain discriminative power while reducing dimensionality. Furthermore, we replace the traditional Student t-distribution with a Cauchy distribution in the clustering layer, offering improved robustness to outliers. Experiments on MNIST, Fashion-MNIST, and USPS demonstrate superior performance over state-of-the-art methods in clustering accuracy, normalized mutual information (NMI), and adjusted Rand index (ARI). Theoretical insights, ablation studies, and limitations are thoroughly discussed, indicating that hybrid moment configurations and a Cauchy-based clustering objective hold considerable promise for robust deep clustering.