Keywords
Singular value decomposition
Principal component analysis
How to Cite
Abstract
This project addresses computational methods for obtaining singular values and singular vectors of matrices, focusing on the large-scale setting. Strategies of data compression based on the statistical technique of principal components analysis are our main motivation. At first, Lanczos method, which is a matrix-free strategy to determine a set of eigenpairs of symmetric matrices, was studied and implemented. Then, such fundamentals methods were used to obtain a partial singular value decomposition of data matrices, in order to explore practical problems by means of the principal components analysis. In particular, experimental results were perfomed in image compression.
References
L. Eldén. Matrix Methods in Data Mining and Pattern Recognition. J. Korean Soc. Ind. Appl. Math., Philadelphia, 2007.
C.C. Paige. The Computation of Eigenvalues and Eigenvectors of Very Large Sparse Matrices, PhD thesis, University of London, 1971.
Z. Wang, A. C. Bovik, H. R. Sheikh, E. P. Simoncelli. Image Quality Assessment: From Error Visibility to Structural Similarity. IEEE Trans. Image Process., Vol. 13, No. 4, 2014, 600-612.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright (c) 2019 Revista dos Trabalhos de Iniciação Científica da UNICAMP