2024/05/27 by Sheng Yang, Yang, Sheng, Peihan Liu +3
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Machine Learning (cs.LG) #Medical Image Segmentation Techniques #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2405.17198
openalex publication_date 2024/05/27 · openalex created_date 2024/05/29 · openalex updated_date 2026/07/28
Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant challenges. In particular, extending support vector machines to hyperbolic spaces is in general a constrained non-convex optimization problem. Previous and popular attempts to solve hyperbolic SVMs, primarily using projected gradient descent, are generally sensitive to hyperparameters and initializations, often leading to suboptimal solutions. In this work, by first rewriting the problem into a polynomial optimization, we apply semidefinite relaxation and sparse moment-sum-of-squares relaxation to effectively approximate the optima. From extensive empirical experiments, these methods are shown to perform better than the projected gradient descent approach.