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Computer Vision and Image Understanding
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Foundations and Trends® in Machine Learning
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AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
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Image and Vision Computing
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Neural Computation
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LSMS/ICSEE'10 Proceedings of the 2010 international conference on Life system modeling and simulation and intelligent computing, and 2010 international conference on Intelligent computing for sustainable energy and environment: Part III
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CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Local Kernel Feature Analysis (LKFA) for object recognition
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NMA'10 Proceedings of the 7th international conference on Numerical methods and applications
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ANNPR'10 Proceedings of the 4th IAPR TC3 conference on Artificial Neural Networks in Pattern Recognition
Computer Vision and Image Understanding
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MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
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Fowlkes et al. [7] recently introduced an approximation to the Normalized Cut (NCut) grouping algorithm [18] based on random subsampling and the Nystr枚m extension. As presented, their method is restricted to the case where W, the weighted adjacency matrix, is positive definite. Although many common measures of image similarity (i.e. kernels) are positive definite, a popular example being Gaussian-weighted distance, there are important cases that are not. In this work, we present a modification to Nystr枚m-NCut that does not require W to be positive definite. The modification only affects the orthogonalization step, and in doing so it necessitates one additional O(m3) operation, where m is the number of random samples used in the approximation. As such it is of interest to know which kernels are positive definite and which are indefinite. In addressing this issue, we further develop connections between NCut and related methods in the kernel machines literature. We provide a proof that the Gaussian-weighted chi-squared kernel is positive definite, which has thus far only been conjectured. We also explore the performance of the approximation algorithm on a variety of grouping cues including contour, color and texture.