DocumentCode :
2716866
Title :
Chebyshev approximations to the histogram χ2 kernel
Author :
Li, Fuxin ; Lebanon, Guy ; Sminchisescu, Cristian
fYear :
2012
fDate :
16-21 June 2012
Firstpage :
2424
Lastpage :
2431
Abstract :
The random Fourier embedding methodology can be used to approximate the performance of non-linear kernel classifiers in linear time on the number of training examples. However, there still exists a non-trivial performance gap between the approximation and the nonlinear models, especially for the exponential χ2 kernel, one of the most powerful models for histograms. Based on analogies with Chebyshev polynomials, we propose an asymptotically convergent analytic series of the χ2 measure. The new series removes the need to use periodic approximations to the χ2 function, as typical in previous methods, and improves the classification accuracy when used in the random Fourier approximation of the exponential χ2 kernel. Besides, out-of-core principal component analysis (PCA) methods are introduced to reduce the dimensionality of the approximation and achieve better performance at the expense of only an additional constant factor to the time complexity. Moreover, when PCA is performed jointly on the training and unlabeled testing data, further performance improvements can be obtained. The proposed approaches are tested on the PASCAL VOC 2010 segmentation and the ImageNet ILSVR-C 2010 datasets, and shown to give statistically significant improvements over alternative approximation methods.
Keywords :
Chebyshev approximation; pattern classification; polynomials; principal component analysis; χ2 function; χ2 measure; Chebyshev approximation; Chebyshev polynomials; asymptotically convergent analytic series; exponential χ2 kernel; histogram χ2 kernel; nonlinear kernel classifiers; periodic approximations; principal component analysis; random Fourier approximation; random Fourier embedding methodology; training examples; Chebyshev approximation; Kernel; Principal component analysis; Radio frequency; Training; Vectors;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Computer Vision and Pattern Recognition (CVPR), 2012 IEEE Conference on
Conference_Location :
Providence, RI
ISSN :
1063-6919
Print_ISBN :
978-1-4673-1226-4
Electronic_ISBN :
1063-6919
Type :
conf
DOI :
10.1109/CVPR.2012.6247956
Filename :
6247956
Link To Document :
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