论文信息 - Parallel Approximate Matrix Factorization for Kernel Methods

Parallel Approximate Matrix Factorization for Kernel Methods

The kernel methods play a pivotal role in machine learning algorithms. Unfortunately, working with the kernel methods must deal with an n times n kernel matrix, which is memory intensive. In this paper, we present a parallel, approximate matrix factorization algorithm, which loads only essential data to individual processors to enable parallel processing of data. Our method reduces space requirement for the kernel matrix from O(n2) to O(np/m), where n is the amount of data, p the reduced matrix dimension (p << n), and m the number of processors.

[1] Vladimir Vapnik,et al. The Nature of Statistical Learning , 1995 .

[2] Gene H. Golub,et al. Matrix computations , 1983 .

[3] Katya Scheinberg,et al. Efficient SVM Training Using Low-Rank Kernel Representations , 2002, J. Mach. Learn. Res..

[4] Dominik Brugger,et al. Parallel Support Vector Machines , 2006 .

[5] M. Aizerman,et al. Theoretical Foundations of the Potential Function Method in Pattern Recognition Learning , 1964 .

[6] Sanjay Ghemawat,et al. MapReduce: Simplified Data Processing on Large Clusters , 2004, OSDI.

[7] Sanjay Mehrotra,et al. On the Implementation of a Primal-Dual Interior Point Method , 1992, SIAM J. Optim..

[8] Edward Y. Chang,et al. Incremental approximate matrix factorization for speeding up support vector machines , 2006, KDD '06.

[9] Vladimir N. Vapnik,et al. The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.