{"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/max-mahalanobis-linear-discriminant-analysis","title":"Max-Mahalanobis Linear Discriminant Analysis Networks","arxiv_id":"1802.09308","date":"2018-02-26","proceeding":"ICML 2018 7","authors":["Tianyu Pang","Chao Du","Jun Zhu"],"abstract":"A deep neural network (DNN) consists of a nonlinear transformation from an\ninput to a feature representation, followed by a common softmax linear\nclassifier. Though many efforts have been devoted to designing a proper\narchitecture for nonlinear transformation, little investigation has been done\non the classifier part. In this paper, we show that a properly designed\nclassifier can improve robustness to adversarial attacks and lead to better\nprediction results. Specifically, we define a Max-Mahalanobis distribution\n(MMD) and theoretically show that if the input distributes as a MMD, the linear\ndiscriminant analysis (LDA) classifier will have the best robustness to\nadversarial examples. We further propose a novel Max-Mahalanobis linear\ndiscriminant analysis (MM-LDA) network, which explicitly maps a complicated\ndata distribution in the input space to a MMD in the latent feature space and\nthen applies LDA to make predictions. Our results demonstrate that the MM-LDA\nnetworks are significantly more robust to adversarial attacks, and have better\nperformance in class-biased classification.","url_abs":"http://arxiv.org/abs/1802.09308v2","url_pdf":"http://arxiv.org/pdf/1802.09308v2.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":"max-mahalanobis-linear-discriminant-analysis","repo_url":"https://github.com/P2333/Max-Mahalanobis-Training","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"tf","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"max-mahalanobis-linear-discriminant-analysis","repo_url":"https://github.com/futakw/Max-Mahalanobis-CenterLoss_pytorch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"lda","method_name":"LDA"},{"method_slug":"softmax","method_name":"Softmax"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1802.09308","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}