NDLI: Optimal Sparse Kernel Learning in the Empirical Kernel Feature Space for Hyperspectral Classification

Content Provider	IEEE Xplore Digital Library
Author	Gurram, P. Heesung Kwon
Copyright Year	2008
Abstract	In this paper, a novel framework for optimal sparse kernel learning for support vector machine (SVM) classifier in a finite-dimensional space called the empirical kernel feature space (EKFS) is presented. In conventional sparse kernel learning techniques, feature selection algorithms are optimal up to linear kernel because the contributions of individual features in the input space to the margin of the classifier can be determined explicitly for a linear kernel. But the use of nonlinear kernels leads to high dimensional, possibly infinite dimensional, Reproducing Kernel Hilbert Spaces (RKHS). Here, feature selection problem is highly combinatorial, and is NP-hard to solve because the number of all the possible combinations of the input features mapped from the input space into the RKHS is often prohibitively large to determine the contributions of subsets of features. To tackle this issue, in the proposed work, feature selection is explicitly and optimally performed in the EKFS instead of in the corresponding RKHS. Unlike the RKHS, the EKFS associated with any positive definite kernel including Gaussian RBF kernel can explicitly be built by using empirical kernel mapping. The feature selection in the EKFS has the same effect as the feature selection in the RKHS since both the EKFS and RKHS associated with same kernel have the same geometrical structure. The features in the EKFS are a kernel representation of each input vector with respect to all the training samples available. Thus, they represent nonlinear similarity measure of each data point with respect to reference samples with known labels. The proposed sparse kernel learning can optimally select multiple subsets of newly mapped features in the EKFS in order to improve the generalization performance of the classifier. The sparse kernel-based learning is tested on several hyperspectral datasets and a performance comparison among different feature selection techniques is presented.
Starting Page	1217
Ending Page	1226
Page Count	10
File Size	1790423
File Format	PDF
ISSN	19391404
Volume Number	7
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Kernel Support vector machines Optimization Vectors Training Quantum cascade lasers Linear programming sparse kernel learning Empirical kernel feature space (EKFS) empirical kernel map optimal feature selection
Content Type	Text
Resource Type	Article
Subject	Atmospheric Science Computers in Earth Sciences

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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