2021/04/03 by Hossein Moosaei, Ahmad Mousavi, Moosaei, Hossein +5
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Face and Expression Recognition #Machine Learning (cs.LG) #Machine Learning and ELM #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #cs.LG #math.OC
paper · pdf · doi:10.48550/arxiv.2104.01331
arxiv created 2021/04/03 · openalex publication_date 2021/04/03 · arxiv updated 2021/04/06 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28
In binary classification, kernel-free linear or quadratic support vector machines are proposed to avoid dealing with difficulties such as finding appropriate kernel functions or tuning their hyper-parameters. Furthermore, Universum data points, which do not belong to any class, can be exploited to embed prior knowledge into the corresponding models so that the generalization performance is improved. In this paper, we design novel kernel-free Universum quadratic surface support vector machine models. Further, we propose the L1 norm regularized version that is beneficial for detecting potential sparsity patterns in the Hessian of the quadratic surface and reducing to the standard linear models if the data points are (almost) linearly separable. The proposed models are convex such that standard numerical solvers can be utilized for solving them. Nonetheless, we formulate a least squares version of the L1 norm regularized model and next, design an effective tailored algorithm that only requires solving one linear system. Several theoretical properties of these models are then reported/proved as well. We finally conduct numerical experiments on both artificial and public benchmark data sets to demonstrate the feasibility and effectiveness of the proposed models.