The nature of statistical learning theory
The nature of statistical learning theory
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Fast training of support vector machines using sequential minimal optimization
Advances in kernel methods
Sparse Greedy Matrix Approximation for Machine Learning
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
The Effect of the Input Density Distribution on Kernel-based Classifiers
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
Implementation of Kernel Methods on the GPU
DICTA '05 Proceedings of the Digital Image Computing on Techniques and Applications
An Experimental Study on Pedestrian Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scan primitives for GPU computing
Proceedings of the 22nd ACM SIGGRAPH/EUROGRAPHICS symposium on Graphics hardware
Alternative Algorithm for Hilbert's Space-Filling Curve
IEEE Transactions on Computers
Scalable Parallel Programming with CUDA
Queue - GPU Computing
Fast scan algorithms on graphics processors
Proceedings of the 22nd annual international conference on Supercomputing
Fast support vector machine training and classification on graphics processors
Proceedings of the 25th international conference on Machine learning
Sparse matrix computations on manycore GPU's
Proceedings of the 45th annual Design Automation Conference
A Fast Similarity Join Algorithm Using Graphics Processing Units
ICDE '08 Proceedings of the 2008 IEEE 24th International Conference on Data Engineering
Approximating a gram matrix for improved kernel-based learning
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Face recognition using kernel direct discriminant analysis algorithms
IEEE Transactions on Neural Networks
Optimization of N-queens solvers on graphics processors
APPT'11 Proceedings of the 9th international conference on Advanced parallel processing technologies
Dense affinity propagation on clusters of GPUs
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
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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.