Abstract
In this chapter, we provide the related work of basic matrix decomposition methods. The first method that we discuss is known as eigenvalue decomposition, which decomposes the initial matrix into a canonical form. The second method is nonnegative matrix factorization (NMF), which factorizes the initial matrix into two smaller matrices with the constraint that each element of the factorized matrices should be nonnegative. The third method is latent semantic indexing (LSI), which applies singular value decomposition (SVD) that uses singular values of the initial matrix to factorize it. The last method is CUR decomposition, which confronts the problem of high density in factorized matrices (a problem that is faced when using the SVD method). This chapter concludes with a description of other state-of-the-art matrix decomposition techniques.
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References
Bensmail, H., Celeux, G.: Regularized gaussian discriminant analysis through eigenvalue decomposition. J. Am. Stat. Assoc. 91(436), 1743–1748 (1996)
Berry, M., Dumais, S., O’Brien, G.: Using linear algebra for intelligent information retrieval. SIAM Rev. 37(4), 573–595 (1994)
Berry, M.W., Browne, M., Langville, A.N., Paul Pauca, V., Plemmons, R.J.: Algorithms and applications for approximate nonnegative matrix factorization. Comput. Stat. Data Anal. 52(1), 155–173 (2007)
Beyer, K.S., Goldstein, J., Ramakrishnan, R., Shaft, U.: When is “nearest neighbor” meaningful? In: ICDT, Lecture Notes in Computer Science, vol. 1540, pp. 217–235. Springer (1999)
Dhillon, I.S., Sra, S.: Generalized nonnegative matrix approximations with bregman divergences. In: NIPS, pp. 283–290 (2005)
Dhillon, I.S., Sra, S.: Generalized nonnegative matrix approximations with bregman divergences. In: Neural Information Processing Systems, pp. 283–290 (2005)
Drineas, P., Kannan, R., Mahoney, M.W.: Fast monte carlo algorithms for matrices III: computing a compressed approximate matrix decomposition. SIAM J. Comput. 36(1), 184–206 (2006)
Furnas, G., Deerwester, S., Dumais, S., et al.: Information retrieval using a singular value decomposition model of latent semantic structure. In: Proceedings of ACM SIGIR Conference, pp. 465–480 (1988)
Gabriel, H.-H., Spiliopoulou, M., Nanopoulos, A.: Eigenvector-based clustering using aggregated similarity matrices. In: Proceedings of the 2010 ACM Symposium on Applied Computing, pp. 1083–1087. ACM (2010)
Goldberg, K., Roeder, T., Gupta, T., Perkins, C.: Eigentaste: a constant time collaborative filtering algorithm. Inf. Retrieval 4(2), 133–151 (2001)
Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. Johns Hopkins University Press, Baltimore, MD, USA (1996)
Hofmann, T.: Latent semantic models for collaborative filtering. ACM Trans. Inf. Syst. 22(1), 89–115 (2004)
Lee, D.D., Seung, H.S.: Learning the parts of objects by nonnegative matrix factorization. Nature 401, 788–791 (1999)
Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: NIPS, pp. 556–562 (2000)
Lin, C.-J.: On the convergence of multiplicative update algorithms for nonnegative matrix factorization. IEEE Trans. Neural Netw. 18(6), 1589–1596 (2007)
Mahoney, M.W., Maggioni, M., Drineas, P.: Tensor-cur decompositions for tensor-based data. SIAM J. Matrix Anal. Appl. 30(3), 957–987 (2008)
Mirza, B.J.: Jumping connections: a graph-theoretic model for recommender systems. Technical report, Master’s thesis, Virginia Tech (2001)
Moler, C.B., Stewart, G.W.: An algorithm for generalized matrix eigenvalue problems. SIAM J. Numer. Anal. 10(2), 241–256 (1973)
Pudil, P., Novovičová, J.: Novel methods for feature subset selection with respect to problem knowledge. In: Feature Extraction. Construction and Selection. Springer International Series in Engineering and Computer Science, vol. 453, pp. 101–116. Springer, US (1998)
Anand Rajaraman and Jeffrey David Ullman: Mining of Massive Datasets. Cambridge University Press, New York, NY, USA (2011)
Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)
Sarwar, B., Karypis, G., Konstan, J., Riedl, J.: Analysis of recommendation algorithms for e-commerce. In: Proceedings of ACM Electronic Commerce Conference, pp. 158–167 (2000)
Sarwar, B., Karypis, G., Konstan, J., Riedl, J.: Application of dimensionality reduction in recommender system-a case study. In: ACM WebKDD Workshop (2000)
Sarwar, B., Karypis, G., Konstan, J., Riedl, J.: Incremental singular value decomposition algorithms for higly scalable recommender systems. In: Proceedings of Computer and Information Technology (2002)
Shaw, B., Jebara, T.: Structure preserving embedding. In: Proceedings of the 26th Annual International Conference on Machine Learning, ICML’09, New York, NY, USA, pp. 937–944. ACM (2009)
Strang, G.: Linear Algebra and Its Applications. Thomson Brooks/Cole (2006)
Symeonidis, P.: Content-based dimensionality reduction for recommender systems. In: Proceedings of the 31st Conference of the German Classification Society (GfKl’2007), Freiburg (2007)
Symeonidis, P., Nanopoulos, A., Papadopoulos, A., Manolopoulos, Y.: Collaborative filtering based on users trends. In: Proceedings of the 30th Conference of the German Classification Society (GfKl’2006), Berlin (2006)
Symeonidis, P., Nanopoulos, A., Papadopoulos, A., Manolopoulos, Y.: Scalable collaborative filtering based on latent semantic indexing. In: Proceedings of the 21st AAAI Workshop on Intelligent Techniques for Web Personalization (ITWP), pp. 1–9, Boston, MA (2006)
Symeonidis, P., Nanopoulos, A., Papadopoulos, A., Manolopoulos, Y.: Collaborative recommender systems: combining effectiveness and efficiency. Expert Syst. Appl. 34(4), 2995–3013 (2008)
Wikipedia: Non-negative matrix factorization—wikipedia, the free encyclopedia, 2015. Accessed 13 Sept 2015
Wilkinson, J.H., Wilkinson, J.H., Wilkinson, J.H.: The Algebraic Eigenvalue Problem, vol. 87. Clarendon Press Oxford (1965)
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Symeonidis, P., Zioupos, A. (2016). Related Work on Matrix Factorization. In: Matrix and Tensor Factorization Techniques for Recommender Systems. SpringerBriefs in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-41357-0_2
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