Abstract
High-order tensors especially matrices are one of the common forms of data in real world. How to classify tensor data is an important research topic. We know that all high-order tensor data can be transformed into matrix data through tucker tensor decomposition and most of them are linear inseparable and the matrices involved are multiple rank. However, up to now most known classifiers for matrix data are linear and a few nonlinear classifiers are only for rank-one matrices. In order to classify linear inseparable multiple rank matrix data, in this paper, a novel nonlinear classifier named as multiple rank multi-linear kernel SVM (MRMLKSVM) is proposed, which is also an extension of MRMLSVM and an improvement of NLS-TSTM. For verifying the effectiveness of the proposed method, a series of comparative experiments are performed on four data sets taken from different databases. Experiment results indicate that MRMLKSVM is an effective and efficient nonlinear classifier.
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References
Vapnik VN (1998) Statistical learning theory. Wiley, New York (1998)
Vapnik V (1995) The nature of statistical learning theory. Springer, New York
Khemchandani JR, Chandra S (2007) Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29(5):905–910
Shao YH, Zhang CH, Wang XB, Deng NY (2011) Improvements on twin support vector machines. IEEE Trans Neural Netw 22(6):962–968
Suykens JAK, Lukas L, Van Dooren P (1999) Least squares support vector machine classifiers: a large scale algorithm. In: Proceedings of European conference circuit theory design pp 839–842
Suykens JAK, Vandewalle J (1999) Least squares support vector machine classifiers. Neural Process Lett 9(3):293–300
Kumar MA, Gopal M (2009) Least squares twin support vector machines for pattern classification. Expert Syst Appl 36(4):7535–7543
Sun L, Mu WS, Qi B, Zhou ZJ (2015) A new privacy-preserving proximal support vector machine for classification of vertically partitioned data. Int J Mac Learn Cybern 6(1):109–118
Chen WJ, Shao YH, Hong N (2014) Laplacian smooth twin support vector machine for semi-supervised classification. Int J Mach Learn Cybern 5(3):459–468
Qiang H, Wu C (2011) Separating theorem of samples in Banach space for support vector machine learning. Int J Mach Learn Cybern 2(1):49–54
Tao D, Li X, Wu X, et al (2007) Supervised tensor learning. Knowl Inf Syst 13(1):1–42
Cai D, He X, Wen JR, Han J, Ma WY (2006) Support tensor machines for text categorization, Department of Computer Science
Hou C, Nie F, Zhang C, Yi D, Wu Y (2014) Multiple rank multi-linear SVM for matrix data classification. Pattern Recognit 47:454–469
Gao X, Fan L, Xu H (2014) NLS-TSTM: a novel and fast nonlinear image classification method. WSEAS Trans Math 13:626–635
Kotsia I, Patras I (2011) Support tucker machines. IEEE Conf Comput Vis Pattern Recognit (CVPR) 6:633–640
Sun J, Tao D, Papadimitriou S, Yu P, Faloutsos C (2008) Incremental tensor analysis: theory and applications. In: Proceedings of ACM transactions on knowledge discovery from data (TKDD) TKDD, 2(3), Article no 11
Khemchandani R, Karpatne A, Chandra S (2013) Proximal support tensor machines. Int J Mach Learn Cybern 4(6):703–712
Zhang X, Gao X, Wang Y (2009) Twin support tensor machines for MCs detection. J Electron (China) 26(3):318–325
Fung G, Mangasarian OL (2007) Proximal support vector machine classifiers. In: Proceedings of seventh international conference on knowledge and data discovery, pp 77–86
Tao D, Li X, Hu W, Maybank SJ, Wu X (2007) General tensor discriminant analysis and gabor features for gait recognition. IEEE Trans Pattern Anal Mach Intell 29(10):1700–1715
Tao D, Li X, Hu W, Maybank SJ, Wu X (2008) Tensor rank one discriminant analysis: a convergent method for discriminative multilinear subspace selection. Neurocomputing 71(1012):1866–1882
Tao D, Song M, Li X, Shen J, Sun J, Wu X, Faloutsos C, Maybank SJ (2008) Bayesian tensor approach for 3-D face modeling. IEEE Trans Circuits Syst Video Technol 18(10):1397–1410
Hou C, Nie F, Yi D, Wu Y (2013) Efficient image classification via multiple rank regression. IEEE Trans Image Process 22(1):340–352
AT&T Labs Cambridge (1994) The Olivetti and Oracle Research Laboratory Database of Faces. http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html
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Gao, X., Fan, L. & Xu, H. Multiple rank multi-linear kernel support vector machine for matrix data classification. Int. J. Mach. Learn. & Cyber. 9, 251–261 (2018). https://doi.org/10.1007/s13042-015-0383-0
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DOI: https://doi.org/10.1007/s13042-015-0383-0
Keywords
- Kernel support vector machine
- Multiple rank matrix
- Matrix kernel function
- Matrix data sets
- Classification