Abstract
We apply multilinear principal component analysis to dimension reduction and classification of human volumetric organ data, which are expressed as multiway array data. For the decomposition of multiway array data, tensor-based principal component analysis extracts multilinear structure of the data. We numerically clarify that low-pass filtering after the multidimensional discrete cosine transform efficiently approximates data dimension reduction procedure based on the tensor principal component analysis.
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Maeda, K.: From the subspace methods to the mutual subspace method. In: Cipolla, R., Battiato, S., Farinella, G.M. (eds.) Computer Vision, vol. 285, pp. 135–156. Springer, Heidelberg (2010). doi:10.1007/978-3-642-12848-6_5
Lu, H., Plataniotis, K., Venetsanopoulos, A.: MPCA: multilinear principal component analysis of tensor objects. IEEE Trans. Neural Netw. 19, 18–39 (2008)
Jiang, B., Ma, S., Zhang, S.: Tensor principal component analysis via convex optimization. Math. Program. 150, 423–457 (2014)
Lu, H., Plataniotis, K., Venetsanopoulos, A.: Uncorrelated multilinear principal component analysis for unsupervised multilinear subspace learning. IEEE Trans. Neural Netw. 20, 1820–1836 (2009)
Shen, H., Huang, J.Z.: Sparse principal component analysis via regularized low rank matrix approximation. J. Multivar. Anal. 99, 1015–1034 (2008)
Lai, Z., Xu, Y., Chen, Q., Yang, J., Zhang, D.: Multilinear sparse principal component analysis. IEEE Trans. Neural Netw. Learn. Syst. 25, 1942–1950 (2014)
Panagakis, Y., Kotropoulos, C., Arce, G.R.: Non-negative multilinear principal component analysis of auditory temporal modulations for music genre classification. IEEE Trans. Audio Speech Lang. Process. 18, 576–588 (2010)
Vasilescu, M.A.O., Terzopoulos, D.: Multilinear (Tensor) ICA and dimensionality reduction. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, vol. 4666, pp. 818–826. Springer, Heidelberg (2007). doi:10.1007/978-3-540-74494-8_102
Bro, R.: PARAFAC. Tutorial and applications. Chemometr. Intell. Lab. Syst. 38, 149–171 (1997)
Dean, J., Corrado, G., Monga, R., Chen, K., Devin, M., Mao, M., Ranzato, M., Senior, A., Tucker, P., Yang, K., Le, Q.V., Ng, A.Y.: Large scale distributed deep networks. In: Proceedings of the Conference on Neural Information Processing Systems, pp. 1232–1240 (2012)
Cohen, N., Shashua, A.: Simnets: a generalization of convolutional networks. In: Proceedings NIPS Workshop on Deep Learning (2014)
Hamidi, M., Pearl, J.: Comparison of the cosine and fourier transforms of Markov-1 signals. IEEE Trans Acoust. Speech Sig. Process. 24, 428–429 (1976)
Oja, E.: Subspace Methods of Pattern Recognition. Research Studies Press, Brighton (1983)
Lu, H., Plataniotis, K., Venetsanopoulos, A.: A survey of multilinear subspace learning for tensor data. Pattern Recogn. 44, 1540–1551 (2011)
Cichoki, A., Zdunek, R., Phan, A.H., Amari, S.: Nonnegative Matrix and Tensor Factorizations. Wiley, Hoboken (2009)
Wang, Y., Gong, S.: Tensor discriminant analysis for view-based object recognition. Proc. Int. Conf. Pattern Recogn. 3, 33–36 (2006)
Tao, D., Li, X., Wu, X., Maybank, S.: Elapsed time in human gait recognition: a new approach. Proc. Int. Conf. Acoust. Speech Sig. Process. 2, II (2006). http://ieeexplore.ieee.org/document/1660308/
Hua, G., Viola, P., Drucker, S.: Face recognition using discriminatively trained orthogonal rank one tensor projections. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2007)
Lathauwer, L., Moor, B., Vandewalle, J.: A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21, 1253–1278 (2000)
Lathauwer, L.D., Moor, B.D., Vandewalle, J.: On the best rank-1 and rank-(\(r_1, r_2, r_n\)) approximation of higher-order tensors. SIAM J. Matrix Anal. Appl. 21, 1324–1342 (2000)
Itoh, H., Imiya, A., Sakai, T.: Low-dimensional tensor principle component analysis. Proc. Int. Conf. Comput. Anal. Images Patterns Part I 9256, 223–235 (2015)
Iijima, T.: Theory of pattern recognition. Electron. Commun. Jpn. 1, 123–134 (1963)
Watanabe, S., Pakvasa, N.: Subspace method of pattern recognition. In: Proceedings of the 1st International Joint Conference of Pattern Recognition (1973)
Itoh, H., Sakai, T., Kawamoto, K., Imiya, A.: Topology-preserving dimension-reduction methods for image pattern recognition. In: Kämäräinen, J.-K., Koskela, M. (eds.) SCIA 2013. LNCS, vol. 7944, pp. 195–204. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38886-6_19
Andreopoulos, A., Tsotsos, J.K.: Efficient and generalizable statistical models of shape and appearance for analysis of cardiac MRI. Med. Image Anal. 12, 335–357 (2008)
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Itoh, H., Imiya, A., Sakai, T. (2017). Approximation of N-Way Principal Component Analysis for Organ Data. In: Chen, CS., Lu, J., Ma, KK. (eds) Computer Vision – ACCV 2016 Workshops. ACCV 2016. Lecture Notes in Computer Science(), vol 10118. Springer, Cham. https://doi.org/10.1007/978-3-319-54526-4_2
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