Shifted Randomized Singular Value Decomposition
This work provides a more efficient method for matrix factorization in data analysis, but it is incremental as it builds directly on an existing algorithm.
The paper tackles the problem of efficiently computing the singular value decomposition (SVD) for shifted data matrices without explicit construction, extending a randomized SVD algorithm to enable low-rank approximation and PCA for off-center data with no loss in accuracy.
We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the original algorithm, the extended algorithm provides for a more efficient way of matrix factorization. The algorithm facilitates the low-rank approximation and principal component analysis (PCA) of off-center data matrices. When applied to different types of data matrices, our experimental results confirm the advantages of the extensions made to the original algorithm.