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Published in: Pattern Analysis and Applications 2/2015

01-05-2015 | Theoretical Advances

Robust sparse kernel density estimation by inducing randomness

Authors: Fei Chen, Huimin Yu, Jincao Yao, Roland Hu

Published in: Pattern Analysis and Applications | Issue 2/2015

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Abstract

In this paper, a robust sparse kernel density estimation based on the reduced set density estimator is proposed. The key idea is to induce randomness to the plug-in estimation of weighting coefficients. The random fluctuations can inhibit these small nonzero weighting coefficients to cluster in regions of space with greater probability mass. By sequential minimal optimization, these coefficients are merged into a few larger weighting coefficients. Experimental studies show that the proposed model is superior to several related methods both in sparsity and accuracy of the estimation. Moreover, the proposed density estimation is extensively validated on novelty detection and binary classification.

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Appendix
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Literature
1.
go back to reference Tsai A, Yezzi A, Wells W, Tempany C, Tucker D, Fan A, Grimson E, Willsky A (2003) A shape-based approach to the segmentation of medical imagery using level sets. IEEE Trans Med Imaging 22(2):137–154CrossRef Tsai A, Yezzi A, Wells W, Tempany C, Tucker D, Fan A, Grimson E, Willsky A (2003) A shape-based approach to the segmentation of medical imagery using level sets. IEEE Trans Med Imaging 22(2):137–154CrossRef
2.
go back to reference Leventon M, Grimson W, Faugeras O (2000) Statistical shape influence in geodesic active contours. IEEE Int Conf Comput Vis Pattern Recogn 1:316–323 Leventon M, Grimson W, Faugeras O (2000) Statistical shape influence in geodesic active contours. IEEE Int Conf Comput Vis Pattern Recogn 1:316–323
3.
go back to reference Rousson M, Cremers D (2005) Efficient kernel density estimation of shape and intensity priors for level set segmentation. Int Conf Med Image Comput Comput Assist Interv 3750:757–764 Rousson M, Cremers D (2005) Efficient kernel density estimation of shape and intensity priors for level set segmentation. Int Conf Med Image Comput Comput Assist Interv 3750:757–764
4.
go back to reference Comaniciu D, Meer P (2002) Mean shift: a robust approach toward feature space analysis. IEEE Trans Pattern Anal Machine Intell 24:603–619CrossRef Comaniciu D, Meer P (2002) Mean shift: a robust approach toward feature space analysis. IEEE Trans Pattern Anal Machine Intell 24:603–619CrossRef
5.
go back to reference Elgammal A, Duraiswami R, Harwood D, Davis L (2002) Background and foreground modeling using nonparametric kernel density estimation for visual surveillance. Proc IEEE 90:1151–1163CrossRef Elgammal A, Duraiswami R, Harwood D, Davis L (2002) Background and foreground modeling using nonparametric kernel density estimation for visual surveillance. Proc IEEE 90:1151–1163CrossRef
6.
go back to reference Han B, Comaniciu D, Zhu Y, Davis LS (2008) Sequential kernel density approximation and its application to real-time visual tracking. IEEE Trans Pattern Anal Machine Intell 30(7):1186–1197CrossRef Han B, Comaniciu D, Zhu Y, Davis LS (2008) Sequential kernel density approximation and its application to real-time visual tracking. IEEE Trans Pattern Anal Machine Intell 30(7):1186–1197CrossRef
7.
go back to reference Cremers D, Osher S, Soatto S (2006) Kernel density estimation and intrinsic alignment for shape priors in level set segmentation. Int J Comput Vis 69(3):335–351CrossRef Cremers D, Osher S, Soatto S (2006) Kernel density estimation and intrinsic alignment for shape priors in level set segmentation. Int J Comput Vis 69(3):335–351CrossRef
8.
go back to reference Kim J, Scott CD (2010) L2 kernel classification. IEEE Trans Pattern Anal Machine Intell 32(10):1822–1831CrossRef Kim J, Scott CD (2010) L2 kernel classification. IEEE Trans Pattern Anal Machine Intell 32(10):1822–1831CrossRef
9.
go back to reference Silverman BW (1982) Kernel density estimation using the fast Fourier transform. Appl Stat 31:93–99CrossRefMATH Silverman BW (1982) Kernel density estimation using the fast Fourier transform. Appl Stat 31:93–99CrossRefMATH
10.
go back to reference Yang C, Duraiswami R, Gumerov N, Davis L (2003) Improved fast gauss transform and efficient kernel density estimation. IEEE Int Conf Comput vis 1:664–671 Yang C, Duraiswami R, Gumerov N, Davis L (2003) Improved fast gauss transform and efficient kernel density estimation. IEEE Int Conf Comput vis 1:664–671
11.
go back to reference Vapnik V, Mukherjee S (1999) Support vector method for multivariate density estimation. In: Proceedings of NIPS, pp 659–665 Vapnik V, Mukherjee S (1999) Support vector method for multivariate density estimation. In: Proceedings of NIPS, pp 659–665
12.
go back to reference Girolami M, He C (2003) Probability density estimation from optimally condensed data samples. IEEE Trans Pattern Anal Machine Intell 25(10):1253–1264CrossRef Girolami M, He C (2003) Probability density estimation from optimally condensed data samples. IEEE Trans Pattern Anal Machine Intell 25(10):1253–1264CrossRef
13.
go back to reference Chen S, Hong X, Harris CJ (2008) An orthogonal forward regression technique for sparse kernel density estimation. Neurocomputing 71(4):931–943CrossRef Chen S, Hong X, Harris CJ (2008) An orthogonal forward regression technique for sparse kernel density estimation. Neurocomputing 71(4):931–943CrossRef
15.
go back to reference Hong X, Chen S, Harris CJ (2010) Sparse kernel density estimation technique based on zero-norm constraint. In: Proceeding of the IJCNN, pp 3782–3787 Hong X, Chen S, Harris CJ (2010) Sparse kernel density estimation technique based on zero-norm constraint. In: Proceeding of the IJCNN, pp 3782–3787
16.
go back to reference Schölkopf B, Platt J, Shawe-Taylor J, Smola A, Williamson R (2001) Estimating the support of a high-dimensional distribution. Neural Comput 13:1443–1471CrossRefMATH Schölkopf B, Platt J, Shawe-Taylor J, Smola A, Williamson R (2001) Estimating the support of a high-dimensional distribution. Neural Comput 13:1443–1471CrossRefMATH
17.
go back to reference Schölkopf B, Smola AJ (2002) Learning with kernels. MIT Press, Cambridge Schölkopf B, Smola AJ (2002) Learning with kernels. MIT Press, Cambridge
18.
go back to reference Kim J, Scott CD (2008) Robust kernel density estimation. ICASSP, pp 3381–3384 Kim J, Scott CD (2008) Robust kernel density estimation. ICASSP, pp 3381–3384
19.
go back to reference Parsons L, Haque E, Liu H (2004) Subspace clustering for high dimensional data: a review. SIGKDD Explor 6(1):90–105CrossRef Parsons L, Haque E, Liu H (2004) Subspace clustering for high dimensional data: a review. SIGKDD Explor 6(1):90–105CrossRef
21.
go back to reference Sain S (1994) Adaptive kernel density estimation. PhD thesis. Rice University, Houston Sain S (1994) Adaptive kernel density estimation. PhD thesis. Rice University, Houston
22.
go back to reference Silverman BW (1986) Density estimation for statistics and data analysis. Chapman and Hall, LondonCrossRefMATH Silverman BW (1986) Density estimation for statistics and data analysis. Chapman and Hall, LondonCrossRefMATH
23.
go back to reference Bishop CM (1994) Novelty detection and neural network validation. IEEE Proc Vis Image Signal Process 141(4):217–222CrossRef Bishop CM (1994) Novelty detection and neural network validation. IEEE Proc Vis Image Signal Process 141(4):217–222CrossRef
24.
go back to reference Metz C (1978) Basic principles of ROC analysis. Semin Nucl Med 8(4):283–298CrossRef Metz C (1978) Basic principles of ROC analysis. Semin Nucl Med 8(4):283–298CrossRef
25.
go back to reference Chao H, Girolami M (2004) Novelty detection employing an L2 optimal nonparametric density estimator. Pattern Recogn Lett 25(12):1389–1397CrossRef Chao H, Girolami M (2004) Novelty detection employing an L2 optimal nonparametric density estimator. Pattern Recogn Lett 25(12):1389–1397CrossRef
26.
go back to reference Duda RO, Hart PE, Stork DG (2001) Pattern classification, 2nd edn. Wiley-interscience, New YorkMATH Duda RO, Hart PE, Stork DG (2001) Pattern classification, 2nd edn. Wiley-interscience, New YorkMATH
Metadata
Title
Robust sparse kernel density estimation by inducing randomness
Authors
Fei Chen
Huimin Yu
Jincao Yao
Roland Hu
Publication date
01-05-2015
Publisher
Springer London
Published in
Pattern Analysis and Applications / Issue 2/2015
Print ISSN: 1433-7541
Electronic ISSN: 1433-755X
DOI
https://doi.org/10.1007/s10044-013-0330-1

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