| Summary: | 碩士 === 國立臺灣大學 === 應用數學科學研究所 === 105 === Dimension reduction and feature extraction are the important techniques in the big-data era to reduce the dimension of data and the computational cost for further data analysis. Low-rank singular value decomposition (low-rank SVD) is the key part of these techniques. In order to compute low-rank SVD faster, some researchers propose to use randomized subspace sketching algorithm to get an approximation result (rSVD). In this research, we propose an idea for integrating the results from randomized algorithm to get a more accurate approximation, which is called integrated singular value decomposition (iSVD). We analyze iSVD and the integration methods by theoretical analysis and numerical experiment. The integration scheme is a constraint optimization problem with unique local maximizer up to orthogonal transformation. Line search type method, Kolmogorov-Nagumo type average method and reduction type method are introduced and analyzed for their theoretical background and computational complexity. The similarity and difference between iSVD and rSVD with same sketching number are also explained and analyzed. The numerical experiment shows that the line search method in iSVD converges faster than the one in rSVD for our test examples. Also, using the integrated subspace from reduction as the initial value of line search method can reduce the iteration number to converge.
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