Title :
Efficient band approximation of Gram matrices for large scale kernel methods on GPUs
Author :
Hussein, M.Z.B. ; Abd-Almageed, Wael
Author_Institution :
Dept. of Comput. Sci., Univ. of Maryland, College Park, MD, USA
Abstract :
Kernel-based methods require O(N2) time and space complexities to compute and store non-sparse Gram matrices, which is prohibitively expensive for large scale problems. We introduce a novel method to approximate a Gram matrix with a band matrix. Our method relies on the locality preserving properties of space filling curves, and the special structure of Gram matrices. Our approach has several important merits. First, it computes only those elements of the Gram matrix that lie within the projected band. Second, it is simple to parallelize. Third, using the special band matrix structure makes it space efficient and GPU-friendly. We developed GPU implementations for the Affinity Propagation (AP) clustering algorithm using both our method and the COO sparse representation. Our band approximation is about 5 times more space efficient and faster to construct than COO. AP gains up to 6x speedup using our method without any degradation in its clustering performance.
Keywords :
computational complexity; graphics processing units; matrix algebra; AP clustering algorithm; COO sparse representation; GPU implementation; GPU-friendly; affinity propagation; band approximation; band matrix structure; clustering performance; large scale kernel method; locality preserving properties; nonsparse Gram matrix; space complexity; space filling curve; time complexity; GPU; Gram matrices; affinity propagation; kernel methods; space filling curves; sparse matrices;
Conference_Titel :
High Performance Computing Networking, Storage and Analysis, Proceedings of the Conference on
Conference_Location :
Portland, OR
DOI :
10.1145/1654059.1654091