A Multi Linear Discriminant Analysis Method Using a Subtraction Criteria

Authors
m rezghi
amin rastegar
10.29252/mmr.3.1.25
Abstract
Linear dimension reduction has been used in different application such as image processing and pattern recognition. All these data folds the original data to vectors and project them to an small dimensions. But in some applications such we may face with data that are not vectors such as image data. Folding the multidimensional data to vectors causes curse of dimensionality and mixed the different feature together. For solving this problem in recent years some multilinear methods have been proposed. beside vector modeling that problem becomes finding the eigenvalues of matrices, in mullinear viewpoint the problem has not such analytical meaning and should be solved by optimization techniques. In this paper by reviewing a new multi linear DATER method, propose a fast method in computation of its solution.
Keywords
dimension reduction
PCA
LDA
Multilinear
MLDA
1. Rezghi M., Abulkasim A., "Noise-free principal component analysis: An efficient dimension reduction technique for high dimensional molecular data, Expert systems with Applications, 41(2014) 7797-7804. 2. Murphy K. P., "Machine Learning: A Probabilistic Perspective", MIT Press (2012). 3. Duda R. O., Hart P. E., Stork D. H., "Pattern Classification (2nd ed.)", Wiley (2006). 4. Binesh N., Rezghi M., "Fuzzy clustering in community detection based on nonnegative matrix factorization with two novel evaluation criteria", Applied Soft Computing, Accepted (2017). 5. Li Q., Schonfeld D., "Multilinear Discriminant Analysis for Higher-order Tensor data Classification", IEEE Transactions on Pattern recognition and Machine Learning, 36 (2014) 2524-2537. 6. Wang J., Barreto A., Wang L., chen Y., Rishe N., Andrianm J., Adjouadi M., "Multilinear principal component analysis for face recognition with fewer features", Neurocomputing, 73, (2010) 1550-1555. 7. Kong S., Wang D., "A Report on Multilinear PCA Plus Multilinear LDA to Deal with Tensorial Data: Visual Classification as An Example", Arxiv (2012). 8. Bishop C., "Pattern Recognition and Machine Learning, Springer (2006). 9. Yan S., Xu D., Yang Q., Zhang L., Tang X., Zhang H. J., "Discriminant analysis with tensor representation, in Proc", IEEE Conference on Computer Vision and Pattern Recognition, vol. I (2005) 526-532. 10. Hao N., kilmer M., Braman K., Hoover R. C., "Facial Recognition Using Tensor-Tensor Decompositions", SIAM Imaging, 6 (2013) 437-463. 11. Yang J., Zhang D., Frangi A. F., Yang J., "Two-dimensional PCA: a new approach to appearance-based face representation and recognition", IEEE Trans- actions on Pattern Analysis and Machine Intelligence (2004) 131-137. 12. Ye J., "Generalized low rank approximations of matrices, Machine Learning,vol. 61, no. 1-3 (2005) 167-191. 13. Ye J., Janardan R., Li Q., "Two-dimensional linear discriminant analysis", in Advances in Neural Information Processing Systems (NIPS) (2004)1569-1576. 14 . Ren C. X., Dai D. Q., "Bilinear Lanczos components for fast dimensionality reduction and feature extraction", Pattern recognition, 43 (2010) 3742-3752. 15. Wu G., Xu W., Leng H., "Inexact and incremental bilinear Lanczos components algorithms for high dimensionality reduction and image reconstruction", Pattern Recognition, 48 (2015) 244-263. 16. Lu H., Plataniotis K. N., Venetsanopoulos A. N., "Multilinear principal component analysis of tensor objects for recognition", in Proc. Int. Conf. on Pattern Recognition (August 2006) 776-779. 17. Ngo T. T., Bellalij M., Saad Y., "The trace ratio optimization problem for dimensionality Reduction", SIAM J. Matrix Anal. and Appl (2010) 2950-2971. 18. Laohakiat S., Phimoltares S., Lurisinsap C., "A clustering algorithm for stream data with LDA-based unsupervised localized dimension reduction, Information science", 381 (2017) 104-123. 19. Raducanu B., Dornaika F., "A supervised non-linear dimensionality reduction approach for manifold learning", Pattern recognition, 45 (2012) 2432-2444.