{"type":"ScholarlyArticle","title":"Two dimensional Large Margin Nearest Neighbor for Matrix Classification","authors":[{"name":"Kun Song","slug":"kun-song","given":"Kun","family":"Song","affiliation":"School of Automation , Northwestern Polytechnical University , Xi'an , 710072 , Shaanxi , P. R. China"},{"name":"Feiping Nie","slug":"feiping-nie","given":"Feiping","family":"Nie","affiliation":"School of Computer Science , Northwestern Polytechnical University , Xi'an , 710072 , P. R. China"},{"name":"Junwei Han","slug":"junwei-han","given":"Junwei","family":"Han","affiliation":"School of Automation , Northwestern Polytechnical University , Xi'an , 710072 , Shaanxi , P. R. China"}],"abstract":"Matrices are common forms of data that are encountered in a wide range of real applications. How to classify this kind of data is an important research topic. In this paper, we propose a novel distance metric learning method named two dimensional large margin nearest neighbor (2DLMNNN), for improving the performance of k nearest neighbor (KNN) classifier in matrix classification. In the proposed method, left and right projection matrices are employed to define the matrix-based Mahalanobis distance, which is used to construct the objective aimed at separating points in different classes by a large margin. The parameters in those two projection matrices are much less than that in its vector-based counterpart, thus our method reduces the risks of overfitting. We also introduce a framework for solving the proposed 2DLMNN. The convergence behavior, initialization, and parameter determination are also analyzed. Compared with vector-based methods, 2DLMNN performs better for matrix data classification. Promising experimental results on several data sets are provided to demonstrate the effectiveness of our method.","doi":"10.24963/ijcai.2017/383","url":"https://ijcai.org/proceedings/2017/383","pdf":"https://ijcai.org/proceedings/2017/0383.pdf","markdown":"https://ijcai.org/proceedings/2017/383.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/383","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Machine Learning S-Z","track":"Main track","number":383,"pages":{"first":2751,"last":2757},"keywords":["Machine Learning: Data Mining","Machine Learning: Machine Learning"],"videos":[],"references":[{"position":1,"raw":"[Belhumeur et al., 1997] Peter N. Belhumeur, João P Hes- panha, and David J. Kriegman. Eigenfaces vs. fisher- faces: Recognition using class specific linear projection. IEEE Transactions on pattern analysis and machine intel- ligence, 19(7):711-720, 1997.","title":"Eigenfaces vs. fisher-faces: Recognition using class specific linear projection","authors":"N Peter, João P Belhumeur, David J Hespanha, Kriegman","year":"1997","venue":"IEEE Transactions on pattern analysis and machine intelligence","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Brockmeier et al., 2013] Austin J Brockmeier, Luis G Sanchez Giraldo, Matthew S Emigh, Jihye Bae, John S Choi, Joseph T Francis, and Jose C Principe. Information- theoretic metric learning: 2-d linear projections of neural data for visualization. In Engineering in Medicine and Biology Society (EMBC), 2013 35th Annual International Conference of the IEEE, pages 5586-5589. IEEE, 2013.","title":"Informationtheoretic metric learning: 2-d linear projections of neural data for visualization","authors":"Austin J Brockmeier, Luis G Sanchez, Giraldo, Matthew S Emigh, Jihye Bae, John S Choi, Joseph T Francis, Jose C Principe","year":"2013","venue":"Engineering in Medicine and Biology Society (EMBC)","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Chang et al., 2016] Xiaojun Chang, Feiping Nie, Sen Wang, Yi Yang, Xiaofang Zhou, and Chengqi Zhang. Compound rank-k projections for bilinear analysis. IEEE transactions on neural networks and learning systems, 27(7):1502-1513, 2016.","title":"Compound rank-k projections for bilinear analysis","authors":"Xiaojun Chang, Feiping Nie, Sen Wang, Yi Yang, Xiaofang Zhou, Chengqi Zhang","year":"2016","venue":"IEEE transactions on neural networks and learning systems","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Hou et al., 2014] Chenping Hou, Feiping Nie, Changshui Zhang, Dongyun Yi, and Yi Wu. Multiple rank multi- linear svm for matrix data classification. Pattern Recog- nition, 47(1):454-469, 2014.","title":"Multiple rank multilinear svm for matrix data classification","authors":"Hou","year":"2014","venue":"Pattern Recognition","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Kohavi and others, 1995] Ron Kohavi et al. A study of cross-validation and bootstrap for accuracy estimation and model selection. In Ijcai, volume 14, pages 1137-1145.","title":"A study of cross-validation and bootstrap for accuracy estimation and model selection","authors":"Ron Kohavi","year":null,"venue":"Ijcai","doi":null,"url":null,"internal_url":"/proceedings/1995/147"},{"position":6,"raw":"[Kong et al., 2005] Hui Kong, Lei Wang, Eam Khwang Teo- h, J-G Wang, and Ronda Venkateswarlu. A framework of 2d fisher discriminant analysis: application to face recognition with small number of training samples. In 2005 IEEE Computer Society Conference on Computer Vi- sion and Pattern Recognition (CVPR'05), volume 2, pages 1083-1088, 2005.","title":"A framework of 2d fisher discriminant analysis: application to face recognition with small number of training samples","authors":"Hui Kong, Lei Wang, Eam Khwang Teoh, J-G Wang, Ronda Venkateswarlu","year":"2005","venue":"IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05)","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Lu et al., 2016a] X Lu, Y Yuan, and X Zheng. Jointly dic- tionary learning for change detection in multispectral im- agery. IEEE Transactions on Cybernetics, 2016.","title":"Jointly dictionary learning for change detection in multispectral imagery","authors":"Lu","year":"2016","venue":"IEEE Transactions on Cybernetics","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Lu et al., 2016b] Xiaoqiang Lu, Xiangtao Zheng, and Xue- long Li. Latent semantic minimal hashing for image re- trieval. IEEE Transactions on Image Processing A Publi- cation of the IEEE Signal Processing Society, 26(1):355- 368, 2016.","title":"Latent semantic minimal hashing for image retrieval","authors":"Lu","year":"2016","venue":"IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Nie and Xianga, 2009] Feiping Nie and Shiming Xianga. Extracting the optimal dimensionality for local tensor dis- criminant analysis. Pattern Recognition, 42(1):105-114, 2009.","title":"Feiping Nie and Shiming Xianga. Extracting the optimal dimensionality for local tensor discriminant analysis","authors":"Xianga Nie","year":"2009","venue":"Pattern Recognition","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Parameswaran and Weinberger, 2010] Shibin; Parameswaran and Q. Weinberger, Kilian. Large margin multi-task metric learning. In Advances in neural information processing systems, pages 1867-1875, 2010.","title":"Large margin multi-task metric learning","authors":"Weinberger ; ] Parameswaran, Q Shibin; Parameswaran, Kilian Weinberger","year":"2010","venue":"Advances in neural information processing systems","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Perrot and A., 2015] M.; Perrot and Habrard A. Regressive virtual metric learning. In Advances in Neural Information Processing Systems, pages 1810-1818. 2015.","title":"Regressive virtual metric learning","authors":"M Perrot, A Habrard","year":"2015","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Rennie and Srebro, 2005] Jasson DM Rennie and Nathan S- rebro. Fast maximum margin matrix factorization for col- laborative prediction. In Proceedings of the 22nd inter- national conference on Machine learning, pages 713-719. ACM, 2005.","title":"Fast maximum margin matrix factorization for collaborative prediction","authors":"Rennie, Srebro ; Jasson, D M Rennie, Nathan Srebro","year":"2005","venue":"Proceedings of the 22nd international conference on Machine learning","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Shakhnarovich et al., 2006] Gregory Shakhnarovich, Piotr Indyk, and Trevor Darrell. Nearest-neighbor methods in learning and vision: theory and practice. 2006.","title":"Nearest-neighbor methods in learning and vision: theory and practice","authors":"Gregory Shakhnarovich, Piotr Indyk, Trevor Darrell","year":"2006","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Shi and Sha, 2014] Bellet A.; Shi, Y. and F. Sha. S- parse compositional metric learning. arXiv preprint, page 1404.4105, 2014.","title":"Sparse compositional metric learning","authors":"A Bellet, Y Shi, F Sha","year":"2014","venue":null,"doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Song et al., 2017] Kun Song, Feiping Nie, Junwei Han, and Xuelong Li. Parameter free large margin nearest neighbor for distance metric learning. AAAI, 2017.","title":"Parameter free large margin nearest neighbor for distance metric learning","authors":"Kun Song, Feiping Nie, Junwei Han, Xuelong Li","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Tomioka et al., 2006] Ryota Tomioka, Kazuyuki Aihara, and Klaus-Robert Müller. Logistic regression for single trial eeg classification. In Advances in neural information processing systems, pages 1377-1384, 2006.","title":"Logistic regression for single trial eeg classification","authors":"Ryota Tomioka, Kazuyuki Aihara, Klaus-Robert Müller","year":"2006","venue":"Advances in neural information processing systems","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Torresani and Lee, 2006] Lorenzo; Torresani and Kuang- chih Lee. Large margin component analysis. In Advances in neural information processing systems, pages 1385- 1392, 2006.","title":"Large margin component analysis","authors":"Lee ; Torresani, ; Lorenzo, Kuangchih Torresani, Lee","year":"2006","venue":"Advances in neural information processing systems","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Weinberger and Saul, 2009] Q.; Weinberger, Kilian and K. Saul, Lawrence. Distance metric learning for large mar- gin nearest neighbor classification. The Journal of Ma- chine Learning Research, 10:207-244, 2009.","title":"Distance metric learning for large margin nearest neighbor classification","authors":"Saul ; Weinberger, ] Q Weinberger, Kilian, K Saul, Lawrence","year":"2009","venue":"The Journal of Machine Learning Research","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Weinberger et al., 2005] Q.; Weinberger, Kilian, John; Blitzer, and K. Saul, Lawrence. Distance metric learn- ing for large margin nearest neighbor classification. In Advances in neural information processing systems, pages 1473-1480, 2005.","title":"Distance metric learning for large margin nearest neighbor classification","authors":"Weinberger","year":"2005","venue":"Advances in neural information processing systems","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Xiang et al., 2008] Shiming Xiang, Feiping Nie, and Changshui Zhang. Learning a mahalanobis distance metric for data clustering and classification. Pattern Recognition, 41(12):3600-3612, 2008.","title":"Learning a mahalanobis distance metric for data clustering and classification","authors":"Shiming Xiang, Feiping Nie, Changshui Zhang","year":"2008","venue":"Pattern Recognition","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Yang and Sukthankar, 2006] R.; Yang, L.; Jin and R. Suk- thankar. An efficient algorithm for local distance metric learning. AAAI, pages 543-548, 2006.","title":"An efficient algorithm for local distance metric learning","authors":"R Yang, L Jin, R Sukthankar","year":"2006","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Yang et al., 2004] Jian Yang, David Zhang, Alejandro F Frangi, and Jing-yu Yang. Two-dimensional pca: a new approach to appearance-based face representation and recognition. IEEE transactions on pattern analysis and machine intelligence, 26(1):131-137, 2004.","title":"Two-dimensional pca: a new approach to appearance-based face representation and recognition","authors":"Jian Yang, David Zhang, Alejandro F Frangi, Jing-Yu Yang","year":"2004","venue":"IEEE transactions on pattern analysis and machine intelligence","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Yang et al., 2013] J. Yang, D. Chu, L. Zhang, Y. Xu, and J. Yang. Sparse representation classifier steered discrim- inative projection with applications to face recognition. IEEE Transactions on Neural Networks and Learning Sys- tems, 24(7):1023-1035, July 2013.","title":"Sparse representation classifier steered discriminative projection with applications to face recognition","authors":"J Yang, D Chu, L Zhang, Y Xu, J Yang","year":"2013","venue":"IEEE Transactions on Neural Networks and Learning Systems","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[You et al., 2004] Jane You, Wai-Kin Kong, David Zhang, and King Hong Cheung. On hierarchical palmprint coding with multiple features for personal identification in large databases. IEEE Transactions on Circuits and Systems for Video Technology, 14(2):234-243, 2004.","title":"On hierarchical palmprint coding with multiple features for personal identification in large databases","authors":"Jane You, Wai-Kin Kong, David Zhang, King Hong Cheung","year":"2004","venue":"IEEE Transactions on Circuits and Systems for Video Technology","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Zhang and Chow, 2012] Zhao Zhang and Tommy WS Chow. Maximum margin multisurface support tensor ma- chines with application to image classification and seg- mentation. Expert Systems with Applications, 39(1):849- 860, 2012.","title":"Maximum margin multisurface support tensor machines with application to image classification and segmentation","authors":"Chow ; ] Zhao Zhang, Tommy Ws Zhang, Chow","year":"2012","venue":"Expert Systems with Applications","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}