EU Regional School- Sra Seminar
Dr. Suvrit Sra -Matrix Factorization and Approximation Problems
Max Planck Institute for Biological Cybernetics, Tübingen
Modern applications deal with rich and complex data that are often encoded as matrices. The matrix representation not only encourages a better understanding of the data but also often enables efficient data processing. A basic data processing task is that of approximating the input data matrix: for reducing resource requirements, for visualization, or perhaps for discovering structure in the data. For example, consider truncated singular vector decomposition (TSVD), perhaps the most basic matrix approximation, which yields an optimal low-rank approximation to a matrix, reveals structure by decorrelating the data, and even helps visualize the data via its principal components. In this lecture I go beyond the classic TSVD, and discuss some important matrix approximation problems such as: sparsity constrained TSVD, nonnegative matrix factorization, co-clustering, among others. I motivate these matrix approximation problems, while also discussing some important special cases. To make the lecture concrete, I overview algorithms and summarize a broad set of applications. If time permits, I might briefly discuss extension to tensor approximations too.