A Review on Various Matrix Factorizaton Techniques

Authors

  • Mishra R Computer Science and Engineering Shri Ram Group of Institution Jabalpur, M.P., India
  • Choudhary S Computer Science and Engineering Shri Ram Group of Institution Jabalpur, M.P., India

Keywords:

Matrix Factorization, Non Negative Matrix Factorization, Singular Value Decomposition

Abstract

In this work, we give the related work of fundamental matrix decomposition techniques. The primary strategy that we talk about is known as Eigen value decomposition, which breaks down the underlying matrix into an authoritative shape. The second strategy is nonnegative matrix factorization (NMF), which factorizes the underlying grid into two littler matrixes with the imperative that every component of the factorized matrix ought to be nonnegative. The third strategy is singular value decomposition (SVD) that utilizations particular estimations of the underlying network to factorize it. The last technique is CUR decomposition, which faces the issue of high thickness in factorized matrixes (an issue that is confronted when utilizing the SVD strategy). This work concludes with a description of other state-of-the-art matrix decomposition technique.

References

[1] Pudil, P., Novoviˇ cová, 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).

[2] Anand Rajaraman and Jeffrey David Ullman: Mining of Massive Datasets. Cambridge University Press, New York, NY, USA (2011).

[3] Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000).

[4] Bensmail, H., Celeux, G.: Regularized gaussian discriminant analysis through eigenvalue decomposition. J. Am. Stat. Assoc. 91(436), 1743–1748 (1996).

[5] 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).

[6] Mahoney, M.W., Maggioni, M., Drineas, P.: Tensor-cur decompositions for tensor-based data. SIAM J. Matrix Anal. Appl. 30(3), 957–987 (2008).

[7] Anand Rajaraman and Jeffrey David Ullman: Mining of Massive Datasets. Cambridge University Press, New York, NY, USA (2011).

Downloads

Published

2025-11-25

How to Cite

[1]
R. Mishra and S. Choudhary, “A Review on Various Matrix Factorizaton Techniques”, Int. J. Comp. Sci. Eng., vol. 7, no. 10, pp. 13–15, Nov. 2025.