2026-09-20T15:07:08Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/132799 2026-03-24 col_2142_5131 col_2142_8888 com_2142_5130 com_2142_8887 com_2142_234

application/pdf en text Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2027-12-01 The student, Chun Ying Hou, accepted the attached license on 2025-12-04 at 13:44. The student, Chun Ying Hou, submitted this Thesis for approval on 2025-12-10 at 13:35. This Thesis was approved for publication on 2025-12-10 at 18:59. DSpace SAF Submission Ingestion Package generated from Vireo submission #23063 on 2026-02-19 at 20:10:02 Scalable second-order Riemannian optimization for K-means clustering Hou, Chun Ying 2025-12-10 Zhang, Richard Y K-means clustering manifold optimization eng Clustering is a fundamental problem in unsupervised learning. The classical K-means formulation for clustering is a worst-case NP-hard discrete optimization problem. Despite being NP-hard, the SDP relaxation of the discrete formulation is guaranteed to recover the true cluster whenever it is statistically solvable. In this thesis, we propose to solve the relaxed K-means problem as an unconstrained optimization problem on a smooth manifold. The proposed manifold can be parametrized by a product manifold with simple structures, allowing the application of second-order Riemannian algorithms. We show how to efficiently implement the cubic-regularized Riemannian Newton method by exploiting the structure of the Hessian. Numerical results show that our proposed algorithm converges faster while achieving similar accuracy compared with existing methods. 2025-12 Thesis https://hdl.handle.net/2142/132799 Copyright 2025 Chun Ying Hou Electrical & Computer Eng Electrical & Computer Engr University of Illinois Urbana-Champaign M.S. Thesis