{"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/a-bi-level-nonlinear-eigenvector-algorithm","title":"A Bi-level Nonlinear Eigenvector Algorithm for Wasserstein Discriminant Analysis","arxiv_id":"2211.11891","date":"2022-11-21","proceeding":null,"authors":["Dong Min Roh","Zhaojun Bai","Ren-cang Li"],"abstract":"Much like the classical Fisher linear discriminant analysis (LDA), the recently proposed Wasserstein discriminant analysis (WDA) is a linear dimensionality reduction method that seeks a projection matrix to maximize the dispersion of different data classes and minimize the dispersion of same data classes via a bi-level optimization. In contrast to LDA, WDA can account for both global and local interconnections between data classes by using the underlying principles of optimal transport. In this paper, a bi-level nonlinear eigenvector algorithm (WDA-nepv) is presented to fully exploit the structures of the bi-level optimization of WDA. The inner level of WDA-nepv for computing the optimal transport matrices is formulated as an eigenvector-dependent nonlinear eigenvalue problem (NEPv), and meanwhile, the outer level for trace ratio optimizations is formulated as another NEPv. Both NEPvs can be computed efficiently under the self-consistent field (SCF) framework. WDA-nepv is derivative-free and surrogate-model-free when compared with existing algorithms. Convergence analysis of the proposed WDA-nepv justifies the utilization of the SCF for solving the bi-level optimization of WDA. Numerical experiments with synthetic and real-life datasets demonstrate the classification accuracy and scalability of WDA-nepv.","url_abs":"https://arxiv.org/abs/2211.11891v2","url_pdf":"https://arxiv.org/pdf/2211.11891v2.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":"a-bi-level-nonlinear-eigenvector-algorithm","repo_url":"https://github.com/gnodking7/wdanepv","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[{"method_slug":"lda","method_name":"LDA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}