PhD Oral Exam - Zhiwen Luo, Information and Systems Engineering

When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.

Abstract

Clustering complex visual, bioinformatics, and geometric sensing data with deep generative models requires latent representations whose geometry matches the structure to be discovered. However, many variational deep generative models rely on Euclidean Gaussian priors, which can mismatch normalized embeddings, weaken clustering structure, and contribute to posterior collapse. This thesis develops geometry-aware latent representations for variational deep generative clustering of complex high-dimensional data. It first introduces the Watson distribution into variational autoencoders (VAEs) for axial data, producing hyperspherical latent representations that encode antipodal equivalence while establishing Kummer-aware Watson variational terms and Watson-specific reparameterized sampling. It then extends this Watson-based hyperspherical representation learner to a Watson mixture prior in VAEs, internalizing mixture structure and enabling variational hyperspherical deep generative clustering for axial data. The third contribution moves from the Watson axial case to more general L2-normalized hyperspherical latent spaces, developing disentangled hyperspherical VAEs with von Mises-Fisher (vMF) mixture priors, contrastive alignment, uniformity, assignment consistency, and entropy-based cluster number selection. The fourth contribution introduces Bayesian nonparametric deep generative clustering with infinite vMF mixture priors, jointly learning hyperspherical representations, cluster assignments, and unknown cluster numbers through recursive plastic-stable optimization. Finally, the thesis develops hierarchical nonparametric Bayesian clustering by integrating hierarchical Pitman-Yor vMF mixture priors with contrastive refinement, supporting imbalanced and long-tailed cluster structures. Across these studies, clustering is not a post-hoc operation but a structure-discovery objective coupled with latent-geometry representation learning in deep generative models. The thesis shows that geometry-matched priors, variational inference, and geometric regularization produce more stable, informative, and cluster-discriminative latent spaces.