We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Abstract
In this paper, based on the maximum margin criterion (MMC) together with the fuzzy clustering and the tensor theory, a novel matrix based fuzzy maximum margin criterion (MFMMC) is proposed and based upon which a matrix subspace analysis method with fuzzy clustering ability (MSAFC) is derived. Besides, according to the intuitive geometry, a proper method of setting the adjustable parameter\(\gamma \) in the proposed criterion MFMMC is given and its rationale is provided. The proposed method MSAFC can simultaneously realize unsupervised feature extraction and fuzzy clustering for matrix data (e.g. image data). As to the running efficiency of MSAFC, a two-directional orthogonal method of dealing with matrix data without any iteration is developed to improve it. Experimental results on UCI datasets, hand-written digit datasets, face image datasets and gene datasets show the distinctive performance of MSAFC.
This is a preview of subscription content,log in via an institution to check access.
Access this article
Subscribe and save
- Get 10 units per month
- Download Article/Chapter or eBook
- 1 Unit = 1 Article or 1 Chapter
- Cancel anytime
Buy Now
Price includes VAT (Japan)
Instant access to the full article PDF.













Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Notes
Although it is also called as 2D-FLD, it is a two-direction two-dimensional feature extraction method in nature. In order to distinguish it from other single-direction two-dimensional feature extraction methods, we take it as\({\hbox {(2D)}}^{2}{\hbox {LDA}}\) in this paper.
References
Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York
Bian ZQ, Zhang XG (2001) Pattern Recogn. TsingHua University Press, Beijing
Blake CL, Merz CJ (1998) UCI Rrepository of Machine Learning Databases”, Irvine, CA: University of California, Department of Information and Computer Science.http://www.ics.uci.edu/~mlearn/MLRepository.html
Chen SC, Zhu YL, Zhang DQ (2005) Feature extraction approaches based on matrix pattern: MatPCA and MatFLDA. Pattern Recogn Lett 26:1157–1167
Choi JY, Park MS (2009) Theoretical analysis on feature extraction capability of class-augmented PCA. Pattern Recogn 42(2):2353–2362
Chung FL, Wang ST et al (2006) Clustering analysis of gene expression data based on semi-supervised clustering algorithm. Soft Comput 10(5):981–994
Comon P, Jutten C (2010) Handbook of blind source separation, independent component analysis and applications. Academic Press, New York
Cui GQ, Gao W (2005) Face recognition based on two-layer generate virtual data for SVM. Chin J Comput 28(3):368–376
Daizhan Cg, June F, Hongli L (2013) Solving fuzzy relational equations via semi-tensor product. IEEE Trans Fuzzy Syst on-line available now
Fisher RA (1936) The use of multiple measurements in taxonomic problems. Ann Eugenics 7:179–188
Fu Y, Yuan JS, Li Z, Huang TS, Wu Y (2007) Query-driven locally adaptive Fisher faces and expert-model for face recognition. In: Proceedings of the International Conference on Image Processing 2007, pp 141–144
Gao J, Wang ST (2009) Fuzzy maximum scatter difference discriminant criterion based clustering algorithm. J Softw 20(11):2939–2949
Hsieh P, Wang D, Hsu C (2006) A linear feature extraction for multiclass classification problems based on class mean and covariance discriminant information. IEEE Trans Pattern Anal Mach Intell 28(6):223–235
Jain A, Dubes R (1988) Algorithms for clustering data. Prentice Hall, Upper Saddle River
Jing XY, Wong HS, Zhang D (2006) Face recognition based on 2D Fisherface approach. Pattern Recogn 39:707–710
Jolliffe IT (1986) Principal Component Analysis. Springer, New York
Kim YD, Choi S (2007) Color face tensor factorization and slicing for illumination-robust recognition. In: Proceedings of intrenational conference on biometrics, pp 19–28
Kim E, Park M, Kim S, Park M (1998) A transformed input-domain approach to fuzzy modeling. IEEE Trans Fuzzy Syst 6(4):596–604
Kw KC, Pedry W (2005) Face recognition using a fuzzy Fisher classifier. Pattern Recogn 38(10):1717–1732
Lei Z, Chu R, He R, Liao S, Li SZ (2007) Face recognition by discriminant analysis with Gabor tensor representation. In: Proceedings of international conference on biometrics, pp 87–95
Li M, Yuan B (2005) 2D-LDA: a statistical linear discriminant analysis for image matrix. Pattern RecognLett 26:527–532
Li H, Jiang T, Zhang K (2006) Efficient and robust feature extraction by maximum margin criterion. IEEE Trans Neural Netw 17(1):157– 165
Li J, Zhang L, Tao D, Sun H, Zhao D (2009) A prior neurophysiologic knowledge free tensor-based scheme for single trial egg classification. IEEE Trans Neural Syst Rehabilit Eng 17(2):107–115
Li CH, Kuo BC, Lin CT (2011) LDA-based clustering algorithm and its application to an unsupervised feature extraction. IEEE Trans Fuzzy Syst 19(1):152–162
Liu J, Tan XY, Zhang DQ (2007) Comments on efficient and robust feature extraction by maximum margin criterion. IEEE Trans Neural Netw 18(6):1862–1864
Lu HP, Plataniotis KN, Venetsanopoulos AN (2008) MPCA: multilinear principal component analysis of tensor objects. IEEE Trans Neural Netw 19(1):18–39
Lu HP, Plataniotis KN, Venetsanopoulos AN (2009) Uncorrelated multilinear discriminant analysis with regularization and aggregation for tensor object recognition. IEEE Trans Neural Netw 20(1):103– 123
Lu HP, Plataniotis KN, Venetsanopoulos AN (2011) A survey of multilinear subspace learning for tensor data. Pattern Recogn 44(7):1540–1551
Martínez AM, Kak AC (2001) PCA versus LDA. IEEE Trans Pattern Anal Mach Intell 23(2):228–233
Panagakis Y, Kotropoulos C, Arce GR (2010) Non-negative multilinear principal component analysis of auditory temporal modulations for music genre classification. In: IEEE transaction on audio, speech, and language processing 18(3):576–588
Peng J, Zhang P, Riedel N (2008) Discriminant learning analysis. IEEE Trans Syst Man Cybern Part B 38(6):1614–1625
Ren CX, Dai DQ (2010) Incremental learning of bidirectional principal components for face recognition. Pattern Recogn 143(1):318–330
Sirovich L, Kirby M (1987) Low-dimensional procedure for characterization of human faces. J Optical Soc Am 4:519–524
Song FX, Zhang D, Yang JY, Gao XM (2006) Adaptive classication algorithm based on maximum scatter difference discriminant criterion. Acta Automatica Sinica 32(2):541–549
Tao D, Li X, Wu X, Maybank SJ (2007) General tensor discriminant analysis and Gabor features for gait recognition. IEEE Trans Pattern Anal Mach Intell 29(10):1700–1715
Turk M, Pentland A (1991) Eigenfaces for recognition. J Cogn Neurosci 3(1):71–86
Wang JG, Yang WK, Lin YS, Yang JY (2008) Two-directional maximum scatter difference discriminant analysis for face recognition. Neurocomputing 72(1–3):352–358
Wang X, Tang X (2004) A unified framework for subspace face recognition. IEEE Trans Pattern Anal Mach Intell 26(9):1223–1228
Wang Z, Chen SC, Liu J, Zhang DQ (2008) Pattern representation in feature extraction and classification—matrix versus vector. IEEE Trans Neural Netw 19:758–769
Wang F, Wang X (2009) Neighborhood discriminant tensor mapping. Neurocomputing 72(7–9):2035–2039
Wang H, Yan SC, Huang TS, Tang XO (2007) A convengent solution to tensor subspace learning. IN: Proceedings of IJCAI, pp 629–634
Wu KL, Yu K, Yang MS (2005) A novel fuzzy clustering algorithm based on a fuzzy scatter matrix with optimality tests. Pattern Recogn Lett 26(4):639–652
Xiong HL, Swanmy MNS, Ahmad MO (2005) Two-dimensional FLD for face recognition. Pattern Recogn 38:1121–1124
Yan S, Xu D, Yang Q, Zhang L, Tang X, Zhang H (2007) Multilinear discriminant analysis for face recognition. IEEE Trans Image Process 16(1):212–220
Yang WK, Yan H, Wang JG, Yang JY (2008) Face recognition using complete Fuzzy LDA. In: Proceedings of ICPR, pp 1–4
Yang WK, Yan XY, Zhang L, Sun CY (2010) Feature extraction based on fuzzy 2DLDA. Neurocomputing 73(10–12):1556–1561
Yang J, Zhang D, Frangi AF, Yang JY (2004) Two-dimensional PCA: a new approach to appearance-based face representation and recognition. IEEE Trans Pattern Anal Mach Intell 26(1):131–137
Ye JP, Janardan R, Li Q (2004a) GPCA: an efficient dimension reduction scheme for image compression and retrieval. In: Proceedings of the tenth ACM SIGKDD international conference on knowledge discovery and data mining, pp 354–363
Ye JP, Janardan R, Li Q (2004b) Two-dimensional linear discriminant analysis. In: Proceedings of advances in neural information processing systems
Ye JP (2005) Generalized low rank approximations of matrices. Mach Learn 61(1–3):167–191
Ye JH, Liu ZG (2009) Multi-modal face recognition based on local binary pattern and Fisherfaces. Comput Eng 35(11):193–195
Yuen PC, Lai JH (2002) Face representation using independent component analysis. Pattern Recogn 35(6):1247–1257
Zhang DQ, Zhou ZH (2005) (2D)2PCA: two-directional two-dimensional PCA for efficient face representation and recognition. Neurocomputing 69(1–3):224–231
Zheng W, Zou C, Zhao L (2005) Weighted maximum margin discriminant analysis with kernels. Neurocomputing 67:357–362
Acknowledgments
This work was supported in part by the Hong Kong Polytechnic University under Grants 1-ZV5V and G-U724, and by the National Natural Science Foundation of China under Grants 61375001,61170122 and 61272210, and by the Natural Science Foundation of Jiangsu Province under Grants BK2011417BK2011003, JiangSu 333 expert engineering Grant (BRA2011142), and 2011, 2012 &2013 Postgraduate Student’s Creative Research Fund of Jiangsu Province. Also, we are very thankful for the referees whose comments help us greatly improve the quality of the paper.
Author information
Authors and Affiliations
School of Information Engineering, Yancheng Institute of Technology, Yancheng, Jiangsu, China
Jun Gao
School of Digital Media, Jiangnan University, Wuxi, Jiangsu, China
Jun Gao & Shitong Wang
Department of Computing, Hong Kong Polytechnic University, Hong Kong, China
Fulai Chung & Shitong Wang
- Jun Gao
You can also search for this author inPubMed Google Scholar
- Fulai Chung
You can also search for this author inPubMed Google Scholar
- Shitong Wang
You can also search for this author inPubMed Google Scholar
Corresponding author
Correspondence toShitong Wang.
Additional information
Communicated by W. Pedrycz.
Rights and permissions
About this article
Cite this article
Gao, J., Chung, F. & Wang, S. MSAFC: matrix subspace analysis with fuzzy clustering ability.Soft Comput18, 1143–1163 (2014). https://doi.org/10.1007/s00500-013-1134-3
Published:
Issue Date:
Share this article
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt content-sharing initiative