Incremental tensor principal component analysis for handwritten digit recognition. (English) Zbl 1407.68426
Summary: To overcome the shortcomings of traditional dimensionality reduction algorithms, incremental tensor principal component analysis (ITPCA) based on updated-SVD technique algorithm is proposed in this paper. This paper proves the relationship between PCA, 2DPCA, MPCA, and the graph embedding framework theoretically and derives the incremental learning procedure to add single sample and multiple samples in detail. The experiments on handwritten digit recognition have demonstrated that ITPCA has achieved better recognition performance than that of vector-based principal component analysis (PCA), incremental principal component analysis (IPCA), and multilinear principal component analysis (MPCA) algorithms. At the same time, ITPCA also has lower time and space complexity.
MSC:
| 68T10 | Pattern recognition, speech recognition |
| 62H25 | Factor analysis and principal components; correspondence analysis |
References:
| [1] | Lu, H.; Plataniotis, K. N.; Venetsanopoulos, A. N., Uncorrelated multilinear discriminant analysis with regularization and aggregation for tensor object recognition, IEEE Transactions on Neural Networks, 20, 1, 103-123 (2009) · doi:10.1109/TNN.2008.2004625 |
| [2] | Liu, C.; He, K.; Zhou, J.-L.; Gao, C.-B.; Nguyen, N. T.; Kim, C.-G.; Janiak, A., Discriminant orthogonal rank-one tensor projections for face recognition, Intelligent Information and Database Systems. Intelligent Information and Database Systems, Lecture Notes in Computer Science, 6592, 203-211 (2011) · doi:10.1007/978-3-642-20042-7_21 |
| [3] | Lu, G.-F.; Lin, Z.; Jin, Z., Face recognition using discriminant locality preserving projections based on maximum margin criterion, Pattern Recognition, 43, 10, 3572-3579 (2010) · Zbl 1209.68469 · doi:10.1016/j.patcog.2010.04.007 |
| [4] | Tao, D.; Li, X.; Wu, X.; Maybank, S. J., General tensor discriminant analysis and Gabor features for gait recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 29, 10, 1700-1715 (2007) · doi:10.1109/TPAMI.2007.1096 |
| [5] | Nie, F.; Xiang, S.; Song, Y.; Zhang, C., Extracting the optimal dimensionality for local tensor discriminant analysis, Pattern Recognition, 42, 1, 105-114 (2009) · Zbl 1159.68545 · doi:10.1016/j.patcog.2008.03.012 |
| [6] | Yu, Z.-Z.; Jia, C.-C.; Pang, W.; Zhang, C.-Y.; Zhong, L.-H., Tensor discriminant analysis with multiscale features for action modeling and categorization, IEEE Signal Processing Letters, 19, 2, 95-98 (2012) · doi:10.1109/LSP.2011.2180018 |
| [7] | Wang, S. J.; Yang, J.; Sun, M. F.; Peng, X. J.; Sun, M. M.; Zhou, C. G., Sparse tensor discriminant color space for face verification, IEEE Transactions on Neural Networks and Learning Systems, 23, 6, 876-888 (2012) · doi:10.1109/TNNLS.2012.2191620 |
| [8] | Minoi, J. L.; Thomaz, C. E.; Gillies, D. F., Tensor-based multivariate statistical discriminant methods for face applications, Proceedings of the International Conference on Statistics in Science, Business, and Engineering (ICSSBE ’12) · doi:10.1109/ICSSBE.2012.6396626 |
| [9] | Tang, N.; Gao, X.; Li, X., Tensor subclass discriminant analysis for radar target classification, Electronics Letters, 48, 8, 455-456 (2012) · doi:10.1049/el.2012.0463 |
| [10] | Lu, H.; Plataniotis, K. N.; Venetsanopoulos, A. N., A survey of multilinear subspace learning for tensor data, Pattern Recognition, 44, 7, 1540-1551 (2011) · Zbl 1210.68083 · doi:10.1016/j.patcog.2011.01.004 |
| [11] | Lu, H.; Plataniotis, K. N.; Venetsanopoulos, A. N., MPCA: multilinear principal component analysis of tensor objects, IEEE Transactions on Neural Networks, 19, 1, 18-39 (2008) · doi:10.1109/TNN.2007.901277 |
| [12] | Yan, S.; Xu, D.; Zhang, B.; Zhang, H.-J.; Yang, Q.; Lin, S., Graph embedding and extensions: a general framework for dimensionality reduction, IEEE Transactions on Pattern Analysis and Machine Intelligence, 29, 1, 40-51 (2007) · doi:10.1109/TPAMI.2007.250598 |
| [13] | Plamondon, R.; Srihari, S. N., On-line and off-line handwriting recognition: a comprehensive survey, IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 1, 63-84 (2000) · doi:10.1109/34.824821 |
| [14] | Johnson, C. M., A survey of current research on online communities of practice, Internet and Higher Education, 4, 1, 45-60 (2001) · doi:10.1016/S1096-7516(01)00047-1 |
| [15] | Hall, P.; Marshall, D.; Martin, R., Merging and splitting eigenspace models, IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 9, 1042-1049 (2000) · doi:10.1109/34.877525 |
| [16] | Sun, J.; Tao, D.; Papadimitriou, S.; Yu, P. S.; Faloutsos, C., Incremental tensor analysis: theory and applications, ACM Transactions on Knowledge Discovery from Data, 2, 3, article 11 (2008) · doi:10.1145/1409620.1409621 |
| [17] | Wen, J.; Gao, X.; Yuan, Y.; Tao, D.; Li, J., Incremental tensor biased discriminant analysis: a new color-based visual tracking method, Neurocomputing, 73, 4-6, 827-839 (2010) · doi:10.1016/j.neucom.2009.10.013 |
| [18] | Wang, J.-G.; Sung, E.; Yau, W.-Y., Incremental two-dimensional linear discriminant analysis with applications to face recognition, Journal of Network and Computer Applications, 33, 3, 314-322 (2010) · doi:10.1016/j.jnca.2009.12.014 |
| [19] | Qiao, X.; Xu, R.; Chen, Y.-W.; Igarashi, T.; Nakao, K.; Kashimoto, A., Generalized N-Dimensional Principal Component Analysis (GND-PCA) based statistical appearance modeling of facial images with multiple modes, IPSJ Transactions on Computer Vision and Applications, 1, 231-241 (2009) · doi:10.2197/ipsjtcva.1.231 |
| [20] | Kong, H.; Li, X.; Wang, L.; Teoh, E. K.; Wang, J.-G.; Venkateswarlu, R., Generalized 2D principal component analysis, Proceedings of the IEEE International Joint Conference on Neural Networks (IJCNN ’05) · doi:10.1109/IJCNN.2005.1555814 |
| [21] | Zhang, D.; Zhou, Z.-H., (2D)2 PCA: two-directional two-dimensional PCA for efficient face representation and recognition, Neurocomputing, 69, 1-3, 224-231 (2005) · doi:10.1016/j.neucom.2005.06.004 |
| [22] | Ye, J., Generalized low rank approximations of matrices, Machine Learning, 61, 1-3, 167-191 (2005) · Zbl 1087.65043 · doi:10.1007/s10994-005-3561-6 |
| [23] | Yang, J.; Zhang, D.; Frangi, A. F.; Yang, J.-Y., 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) · doi:10.1109/TPAMI.2004.1261097 |
| [24] | Yang, J.; Yang, J.-Y., From image vector to matrix: a straightforward image projection technique-IMPCA vs. PCA, Pattern Recognition, 35, 9, 1997-1999 (2002) · Zbl 1006.68865 · doi:10.1016/S0031-3203(02)00040-7 |
| [25] | Kwok, J.; Zhao, H., Incremental eigen decomposition, Proceedings of the International Conference on Artificial Neural Networks (ICANN ’03) |
| [26] | Belhumeur, P. N.; Hespanha, J. P.; Kriegman, D. J., Eigenfaces vs. fisherfaces: recognition using class specific linear projection, IEEE Transactions on Pattern Analysis and Machine Intelligence, 19, 7, 711-720 (1997) · doi:10.1109/34.598228 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
