Optimization of Sparse Matrix Kernels for Data Mining

Abstract

Many data mining algorithms rely on eigenvalue computations or it- erative linear solvers in which the running time is dominated by sparse matrix-vector products. Sparse matrix-vector multiplication on mod- ern machines often runs one to two orders of magnitude slower than peak hardware performance, and because of their lack of structure, the worst performance is often observed for matrices from text re- trieval and other data mining applications. In this paper we explore aset of memory hierarchy optimizations forsparse matrix-vector mul- tiplication, concentrating on matrices that arises in text and image retrieval. We also consider algorithms that multiply the sparse ma- trix by a set of vectors, and show that reorganizing the code to take advantage of multiple vectors can significantly speed up the running time. These optimization are supported by a code generation and op- timization system called Sparsity,which automatically tunes sparse matrix-vectormultiplication for a given matrix structure and machine.