DGVAC: Disentangled Gaussian-vMF alignment for deep clustering

The core challenge of unsupervised deep clustering lies in learning representations that can simultaneously discriminate between different categories and remain robust to intra-class variations. However, existing variational autoencoder (VAE)-based generative models are often limited by representation entanglement: they struggle to disentangle discrete class identity from continuous stylistic factors, which leads to degraded clustering performance. To address this fundamental problem, we propose a disentangled variational framework explicitly designed for clustering alignment. Specifically, the latent space is decomposed into two heterogeneous subspaces: a Euclidean subspace modeled by a Gaussian prior to capture continuous, cluster-irrelevant intra-class variations, and a unit hyperspherical subspace modeled by a von Mises-Fisher (vMF) prior, whose directional nature explicitly encodes core categorical semantics. To robustly learn the clustering-oriented subspace, we introduce a probabilistic alignment strategy that integrates the classical Product-of-Experts (PoE) mechanism into a modern self-supervised par adigm. By fusing multiple augmented views at the probabilistic level, this approach derives a joint posterior distribution that is more resilient to strong perturbations, thereby enabling stable latent representations for downstream clustering. Building upon this, we further develop a staged optimization scheme for the Evidence Lower Bound (ELBO), which is rigorously decomposed into four synergistic components-reconstruction, clustering, categorical regularization, and Gaussian regularization-to ensure stable disentangled training while jointly optimizing the clustering objective in an end-to-end manner. Extensive experiments on multiple benchmark datasets demonstrate that our method consistently improves clustering accuracy and generative quality, validating its effectiveness in enhancing deep clustering through disentangled representation learning. The source code of our model is publicly accessible at https://github.com/jsnkos/DGVAE.