A new method for combining features via importance-inhibition analysis （IIA） is described to obtain more effective feature combination in learning question classification. Features are combined based on the inhibiti...A new method for combining features via importance-inhibition analysis （IIA） is described to obtain more effective feature combination in learning question classification. Features are combined based on the inhibition among features as well as the importance of individual features. Experimental results on the Chinese questions set show that, the IIA method shows a gradual increase in average and maximum accuracies at all feature combinations, and achieves great improvement over the importance analysis（IA） method on the whole. Moreover, the IIA method achieves the same highest accuracy as the one by the exhaustive method, and further improves the performance of question classification.展开更多
Partial eigenvalue decomposition(PEVD) and partial singular value decomposition(PSVD) of large sparse matrices are of fundamental importance in a wide range of applications, including latent semantic indexing, spectra...Partial eigenvalue decomposition(PEVD) and partial singular value decomposition(PSVD) of large sparse matrices are of fundamental importance in a wide range of applications, including latent semantic indexing, spectral clustering, and kernel methods for machine learning. The more challenging problems are when a large number of eigenpairs or singular triplets need to be computed. We develop practical and efficient algorithms for these challenging problems. Our algorithms are based on a filter-accelerated block Davidson method.Two types of filters are utilized, one is Chebyshev polynomial filtering, the other is rational-function filtering by solving linear equations. The former utilizes the fastest growth of the Chebyshev polynomial among same degree polynomials; the latter employs the traditional idea of shift-invert, for which we address the important issue of automatic choice of shifts and propose a practical method for solving the shifted linear equations inside the block Davidson method. Our two filters can efficiently generate high-quality basis vectors to augment the projection subspace at each Davidson iteration step, which allows a restart scheme using an active projection subspace of small dimension. This makes our algorithms memory-economical, thus practical for large PEVD/PSVD calculations. We compare our algorithms with representative methods, including ARPACK, PROPACK, the randomized SVD method, and the limited memory SVD method. Extensive numerical tests on representative datasets demonstrate that, in general, our methods have similar or faster convergence speed in terms of CPU time, while requiring much lower memory comparing with other methods. The much lower memory requirement makes our methods more practical for large-scale PEVD/PSVD computations.展开更多
基金The National Natural Science Foundation of China(No.61003112,61170181)the Open Research Fund of State Key Laboratory for Novel Softw are Technology of China(No.KFKT2010B02)the Key Project of Natural Science Research for Anhui Colleges of China(No.KJ2011A048)
文摘A new method for combining features via importance-inhibition analysis （IIA） is described to obtain more effective feature combination in learning question classification. Features are combined based on the inhibition among features as well as the importance of individual features. Experimental results on the Chinese questions set show that, the IIA method shows a gradual increase in average and maximum accuracies at all feature combinations, and achieves great improvement over the importance analysis（IA） method on the whole. Moreover, the IIA method achieves the same highest accuracy as the one by the exhaustive method, and further improves the performance of question classification.
基金supported by National Science Foundation of USA (Grant Nos. DMS1228271 and DMS-1522587)National Natural Science Foundation of China for Creative Research Groups (Grant No. 11321061)+1 种基金the National Basic Research Program of China (Grant No. 2011CB309703)the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences
文摘Partial eigenvalue decomposition(PEVD) and partial singular value decomposition(PSVD) of large sparse matrices are of fundamental importance in a wide range of applications, including latent semantic indexing, spectral clustering, and kernel methods for machine learning. The more challenging problems are when a large number of eigenpairs or singular triplets need to be computed. We develop practical and efficient algorithms for these challenging problems. Our algorithms are based on a filter-accelerated block Davidson method.Two types of filters are utilized, one is Chebyshev polynomial filtering, the other is rational-function filtering by solving linear equations. The former utilizes the fastest growth of the Chebyshev polynomial among same degree polynomials; the latter employs the traditional idea of shift-invert, for which we address the important issue of automatic choice of shifts and propose a practical method for solving the shifted linear equations inside the block Davidson method. Our two filters can efficiently generate high-quality basis vectors to augment the projection subspace at each Davidson iteration step, which allows a restart scheme using an active projection subspace of small dimension. This makes our algorithms memory-economical, thus practical for large PEVD/PSVD calculations. We compare our algorithms with representative methods, including ARPACK, PROPACK, the randomized SVD method, and the limited memory SVD method. Extensive numerical tests on representative datasets demonstrate that, in general, our methods have similar or faster convergence speed in terms of CPU time, while requiring much lower memory comparing with other methods. The much lower memory requirement makes our methods more practical for large-scale PEVD/PSVD computations.
