Abstract
This paper describes a new classification method based on modeling data by embedding diffusions into orthonormal decompositions of graph-based data representations. The training data is represented by an adjacency matrix calculated using either the correlation or the covariance of the training set. The application of the modified Gram-Schmidt orthonormal decomposition alternating with diffusion and data reduction stages, is applied recursively at each scale level. The diffusion process is strengthening the representation pattern of representative features. Meanwhile, noise is removed together with non-essential detail during the data reduction stage. The proposed methodology is shown to be robust when applied to face recognition considering low image resolution and corruption by various types of noise.
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References
Belhumeur, P., Hespanha, J., Kriegman, D.: Eigenfaces vs. fisherfaces: Recognition using class specific linear projection. IEEE Trans. on Pattern Analysis and Machine Intelligence 19(7), 711–720 (1997)
Cai, D., He, X., Han, J., Zhang, H.J.: Orthogonal laplacianfaces for face recognition. IEEE Trans. on Image Processing 15(11), 3608–3614 (2006)
Coifman, R.R., Lafon, S.: Diffusion maps. Applied Comput. Harmon. Anal. 21(1), 5–30 (2006)
Draper, B., Baek, K., Bartlett, M., Beveridge, R.: Recognizing faces with PCA and ICA. Computer Vision and Image Understanding 91(1–2), 115–137 (2003)
Essafi, S., Langs, G., Paragios, N.: Hierarchical 3d diffusion wavelet shape priors. In: Proc. of IEEE Int. Conf. on Computer Vision, pp. 1717–1724 (2009)
Gudivada, S., Bors, A.G.: Face recognition using ortho-diffusion bases. In: Proc. 20th European Signal Processing Conference, pp. 1578–1582 (2012)
Gudivada, S., Bors, A.G.: Ortho-diffusion decompositions of graph-based representation of images. Pattern Recognition (2015)
He, X., Yan, S., Hu, Y., Niyogi, P., Zhang, H.J.: Face recognition using laplacianfaces. IEEE Trans. on Pattern Analysis and Machine Intelligence 27(3), 328–340 (2005)
Lu, J., Dorsey, J., Rushmeier, H.: Dominant texture and diffusion distance manifolds. Proc. Eurographics Computer Graphics Forum 28(2), 667–676 (2009)
Luxburg, U.: A tutorial on spectral clustering. J. of Statistics and Computing 17(4), 395–416 (2007)
Magioni, M., Mahadevan, S.: Fast direct policy evaluation using multiscale analysis of markov diffusion processes. In: Proc. of the 23rd International Conference on Machine Learning, pp. 601–608 (2005)
Singer, A., Coifman, R.R.: Non-linear independent component analysis with diffusion maps. Applied and Computational Harmonic Analysis 25(1), 226–239 (2008)
Trefethen, L.N., Bau, D.: Numerical Linear Algebra. SIAM (1997)
Turk, M., Pentland, A.: Eigenfaces for recognition. J. Cognitive Neuroscience 3(1), 71–86 (1991)
Wang, C., Mahadevan, S.: Multiscale dimensionality reduction based on diffusion wavelets. Tech. rep., Univ. of Massachusetts (2009)
Wartak, S., Bors, A.G.: Optical flow estimation using diffusion distances. In: Proc. Int. Conf on Pattern Recognition, pp. 189–192 (2010)
Wild, M.: Nonlinear approximation of spatiotemporal data using diffusion wavelets. In: Kropatsch, W.G., Kampel, M., Hanbury, A. (eds.) CAIP 2007. LNCS, vol. 4673, pp. 886–894. Springer, Heidelberg (2007)
Yan, S., Yu, D., Yang, Q., Zhang, L., Tang, X., Zhang, H.: Multilinear discriminant analysis for face recognition. IEEE Trans on Image Processing 16(1), 212–220 (2007)
Zhang, B.C., Shan, S.G., Chen, X., Gao, W.: Histogram of gabor phase patterns: A novel object representation approach for face recognition. IEEE Trans. on Image Processing 16(1), 504–516 (2007)
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Gudivada, S., Bors, A.G. (2015). Robust Learning from Ortho-Diffusion Decompositions. In: Azzopardi, G., Petkov, N. (eds) Computer Analysis of Images and Patterns. CAIP 2015. Lecture Notes in Computer Science(), vol 9256. Springer, Cham. https://doi.org/10.1007/978-3-319-23192-1_46
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DOI: https://doi.org/10.1007/978-3-319-23192-1_46
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