Infinite Max-margin Linear Discriminant Projection Model
WEN Wei①② CAO Xuefei③ CHEN Bo①② HAN Xun① ZHANG Xuefeng①② WANG Penghui① LIU Hongwei①②
①(National Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China) ②(Collaborative Innovation Center of Information Sensing and Understanding at Xidian University, Xi’an 710071, China) ③(School of Cyber and Information Security, Xidian University, Xi’an 710071, China)
Abstract：An infinite Max-Margin Linear Discriminant Projection (iMMLDP) model is developed to deal with the classification problem on multimodal distributed high-dimensional data. Different from global projection, iMMLDP divides the data into a set of local regions via Dirichlet Process (DP) mixture model and meanwhile learns a linear Max-Margin Linear Discriminant Projection (MMLDP) classifier in each local region. By assembling these local classifiers, a flexible nonlinear classifier is constructed. Under this framework, iMMLDP combines dimensionality reduction, clustering and supervised classification in a principled way, therefore, an underlying structure of the data could be uncovered. As a result, the model can handle the classification of data with global nonlinear structure, especially the data with multi-modally distributed structure. With the help of Bayesian nonparametric prior, the model selection problem (e.g. the number of local regions) can be avoided. The proposed model is implemented on synthesized and real-world data, including multi-modally distributed datasets and measured radar high range resolution profile (HRRP) data, to validate its efficiency and effectiveness.
YU Daoyin, WANG Yuexing, CHEN Xiaodong, et al. Visual tracking based on random projection and sparse representation[J]. Journal of Electronics & Information Technology, 2016, 38(7): 1602-1608. doi: 10.11999/JEIT 151064.
[3]
SWETS D and WENG J. Using discriminant eigenfeatures for image retrieval[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1996, 18(8): 831-836. doi: 10.1109/34.531802.
[4]
ETEMAD K and CHELLAPA R. Discriminant analysis for recognition of human face images[J]. Journal of the Optical Society of America A, 1997, 14(8): 1724-1733. doi: 10.1364 /JOSAA.14.001724.
[5]
FISHER R. The use of multiple measurements in taxonomic problems [J]. Annals of Eugenics, 1936, 7(2): 179-188 doi: 10.1111/j.1469-1809.1936.tb02137.
[6]
CHEN B, ZHANG H, ZHANG X, et al. Max-margin discriminant projection via data augmentation[J]. IEEE Transactions on Knowledge and Data Engineering, 2015, 27(7): 1964-1976. doi: 10.1109/TKDE.2015.2397444.
[7]
NIKOLAOS G, VASILEIOS M, and IOANNIS K. Mixture Subclass discriminant analysis[J]. IEEE Signal Processing Letter, 2011, 18(5): 319-322. doi: 10.1109/LSP.2011. 2127474.
[8]
NIKOLAOS G, VASILEIOS M, and IOANNIS K. Mixture subclass discriminant analysis link to restricted Gaussian model and other generalizations[J]. IEEE Transactions on Neural Networks and Learning Systems, 2013, 24(1): 8-21. doi: 10.1109/TNNLS.2012.2216545.
GUO Jichang, ZHANG Fan, and WANG Nan. Image classification based on Fisher constraint and dictionary pair [J]. Journal of Electronics & Information Technology, 2017, 39(2): 270-277. doi: 10.11999/JEIT160329.
[10]
GONEN M. Bayesian supervised dimensionality reduction [J]. IEEE Transactions on Cybernetics, 2013, 4(6): 2179-2189. doi: 10.1109/TCYB.2013.2245321.
[11]
SHAHBABA B and NEAL R. Nonlinear models using Dirichlet process mixtures[J]. The Journal of Machine Learning Research, 2009, 10(4): 1829-1850.
WEN Wei, CAO Xuefei, ZHANG Xuefeng, et al. PolSAR ship detection method based on multiple polarimetric scattering mechanisms[J]. Journal of Electronics & Information Technology, 2017, 39(1): 103-109. doi: 10.11999 /JEIT160204.
[13]
POLSON N G and SCOTT S L. Data augmentation for support vector machines[J]. Bayesian Analysis, 2011, 6(1): 1-24. doi: 10.1214/11-BA601.
[14]
SETHURAMAN J. A constructive definition of Dirichlet priors[J]. Statistica Sinica, 1994, 4(2): 639-650.
[15]
HANNAH L A, BLEI D M, and POWELL W B. Dirichlet process mixtures of generalized linear models[J]. Journal of Machine Learning Research, 2011, 12: 1923-1953.
[16]
RIFKIN R and KLAUTAU A. In defense of one-vs-all classification[J]. Journal of Machine Learning Research, 2004, 5(1): 101-141.
[17]
DU L, LIU H W, BO Z, et al. Radar HRRP statistical recognition: Parametric model and model selection[J]. IEEE Transactions on Signal Processing, 2008, 56 (5): 1931-1943. doi: 10.1109/TSP.2007.912283.
ZHANG Xuefeng, CHEN BO, WANG Penghui, et al. Infinite max-margin Beta process factor analysis model[J]. Journal of Xidian University (Natural Science), 2016, 43(3): 13-18. doi: 10.3969/j.issn.1001-2400.2016.03.003.
[19]
DU L, LIU H W, WANG P H, et al. Noise robust radar HRRP target recognition based on multitask factor analysis with small training data size[J]. IEEE Transactions on Signal Processing, 2012, 60(7): 3546-3559. doi: 10.1109/TSP. 2012.2191965.
target recognition method based on Dirichlet process latent variable support vector machine model[J]. Journal of Electronics & Information Technology, 2015, 37(1): 29-36. doi: 10.11999/JEIT140129.
