Abstract
This paper presents an approach toward robust and fast Two-Dimensional Linear Discriminant Analysis (2DLDA). 2DLDA is an extension of Linear Discriminant Analysis (LDA) for 2-dimensional objects such as images. Linear transformation matrices are iteratively calculated based on the eigenvectors of asymmetric matrices in 2DLDA. However, repeated calculation of eigenvectors of asymmetric matrices may lead to unstable performance. We propose to use simultaneous diagonalization of scatter matrices so that eigenvectors can be stably calculated. Furthermore, for fast calculation, we propose to use approximate decomposition of a scatter matrix based on its several leading eigenvectors. Preliminary experiments are conducted to investigate the effectiveness of our approach. Results are encouraging, and indicate that our approach can achieve comparative performance with the original 2DLDA with reduced computation time.
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References
Anderson, T.W.: An Introduction to Multivariate Statistical Analysis. Wiley-Interscience (2003)
Ding, C., Ye, J.: Two-dimensional singular value decomposition (2dsvd) for 2d maps and images. In: Proc. of SDM 2005, pp. 32–43 (2005)
Hartigan, J., Wong, M.: Algorithm as136: A k-means clustering algorithm. Journal of Applied Statistics 28, 100–108 (1979)
Harville, D.A.: Matrix Algebra From a Statistican’s Perspective. Splinger (2008)
Strehl, A., Ghosh, J.: Cluster ensembles — a knowledge reuse framework for combining multiple partitions. J. Machine Learning Research 3(3), 583–617 (2002)
Swets, D.L., Weng, J.J.: Using discriminat eigenfeatures for image retrieval. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(8), 831–836 (1996)
von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007)
Voss, J.: Tagging, folksonomy & co – renaissance of manual indexing? In: Proc. 10th International Symposium for Information Science, pp. 234–254 (2007)
Yang, J., Zhang, D., Frangi, A.F., Yu Yang, J.: 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)
Ye, J., Janardan, R., Li, Q.: Two-dimensional linear discriminant analysis. In: Proc. of NIPS 2004, pp. 1569–1576 (2004)
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© 2013 Springer International Publishing Switzerland
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Yoshida, T., Yamada, Y. (2013). Toward Robust and Fast Two-Dimensional Linear Discriminant Analysis. In: Yoshida, T., Kou, G., Skowron, A., Cao, J., Hacid, H., Zhong, N. (eds) Active Media Technology. AMT 2013. Lecture Notes in Computer Science, vol 8210. Springer, Cham. https://doi.org/10.1007/978-3-319-02750-0_13
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DOI: https://doi.org/10.1007/978-3-319-02750-0_13
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02749-4
Online ISBN: 978-3-319-02750-0
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