Randomization or Condensation? LinearCost Matrix Sketching Via Cascaded Compression Sampling
published: Oct. 9, 2017, recorded: August 2017, views: 4
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Matrix sketching is aimed at finding compact representations of a matrix while simultaneously preserving most of its properties, which is a fundamental building block in modern scientific computing. Randomized algorithms represent state-of-the-art and have attracted huge interest from the fields of machine learning, data mining, and theoretic computer science. However, it still requires the use of the entire input matrix in producing desired factorizations, which can be a major computational and memory bottleneck in truly large problems. In this paper, we uncover an interesting theoretic connection between matrix low-rank decomposition and lossy signal compression, based on which a cascaded compression sampling framework is devised to approximate an m-by-n matrix in only O(m+n) time and space. Indeed, the proposed method accesses only a small number of matrix rows and columns, which significantly improves the memory footprint. Meanwhile, by sequentially teaming two rounds of approximation procedures and upgrading the sampling strategy from a uniform probability to more sophisticated, encoding-orientated sampling, significant algorithmic boosting is achieved to uncover more granular structures in the data. Empirical results on a wide spectrum of real-world, large-scale matrices show that by taking only linear time and space, the accuracy of our method rivals those state-of-the-art randomized algorithms consuming a quadratic, O(mn), amount of resources.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !