{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-discriminative-stein-kernel-for-spd","title":"Learning Discriminative Stein Kernel for SPD Matrices and Its Applications","arxiv_id":"1407.1974","date":"2014-07-08","proceeding":null,"authors":["Jianjia Zhang","Lei Wang","Luping Zhou","Wanqing Li"],"abstract":"Stein kernel has recently shown promising performance on classifying images\nrepresented by symmetric positive definite (SPD) matrices. It evaluates the\nsimilarity between two SPD matrices through their eigenvalues. In this paper,\nwe argue that directly using the original eigenvalues may be problematic\nbecause: i) Eigenvalue estimation becomes biased when the number of samples is\ninadequate, which may lead to unreliable kernel evaluation; ii) More\nimportantly, eigenvalues only reflect the property of an individual SPD matrix.\nThey are not necessarily optimal for computing Stein kernel when the goal is to\ndiscriminate different sets of SPD matrices. To address the two issues in one\nshot, we propose a discriminative Stein kernel, in which an extra parameter\nvector is defined to adjust the eigenvalues of the input SPD matrices. The\noptimal parameter values are sought by optimizing a proxy of classification\nperformance. To show the generality of the proposed method, three different\nkernel learning criteria that are commonly used in the literature are employed\nrespectively as a proxy. A comprehensive experimental study is conducted on a\nvariety of image classification tasks to compare our proposed discriminative\nStein kernel with the original Stein kernel and other commonly used methods for\nevaluating the similarity between SPD matrices. The experimental results\ndemonstrate that, the discriminative Stein kernel can attain greater\ndiscrimination and better align with classification tasks by altering the\neigenvalues. This makes it produce higher classification performance than the\noriginal Stein kernel and other commonly used methods.","url_abs":"http://arxiv.org/abs/1407.1974v3","url_pdf":"http://arxiv.org/pdf/1407.1974v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-discriminative-stein-kernel-for-spd","repo_url":"https://github.com/seuzjj/DSK","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}