Faster Matrix Completion Using Randomized SVD
This work addresses the computational bottleneck in matrix completion for applications like image inpainting and recommender systems, offering significant speed improvements, though it is incremental as it builds on existing SVT methods.
The paper tackles the problem of accelerating matrix completion by proposing faster randomized singular value decomposition (rSVD) algorithms, such as rSVD-PI and rSVD-BKI, and integrating them with a subspace recycling technique to speed up the singular value thresholding (SVT) method. The results show that the rSVD algorithms are 6X faster than a baseline while maintaining accuracy, and the accelerated SVT algorithm reduces CPU time by 15X for image inpainting and 8X for movie-rating estimation without loss of accuracy.
Matrix completion is a widely used technique for image inpainting and personalized recommender system, etc. In this work, we focus on accelerating the matrix completion using faster randomized singular value decomposition (rSVD). Firstly, two fast randomized algorithms (rSVD-PI and rSVD- BKI) are proposed for handling sparse matrix. They make use of an eigSVD procedure and several accelerating skills. Then, with the rSVD-BKI algorithm and a new subspace recycling technique, we accelerate the singular value thresholding (SVT) method in [1] to realize faster matrix completion. Experiments show that the proposed rSVD algorithms can be 6X faster than the basic rSVD algorithm [2] while keeping same accuracy. For image inpainting and movie-rating estimation problems, the proposed accelerated SVT algorithm consumes 15X and 8X less CPU time than the methods using svds and lansvd respectively, without loss of accuracy.