Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Kernel partial least squares regression in reproducing kernel hilbert space
The Journal of Machine Learning Research
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Convex Optimization
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Dimensionality Reduction for Supervised Learning with Reproducing Kernel Hilbert Spaces
The Journal of Machine Learning Research
Introduction to Computational Genomics: A Case Studies Approach
Introduction to Computational Genomics: A Case Studies Approach
Large Scale Multiple Kernel Learning
The Journal of Machine Learning Research
A dependence maximization view of clustering
Proceedings of the 24th international conference on Machine learning
Supervised feature selection via dependence estimation
Proceedings of the 24th international conference on Machine learning
Predicting Structured Data (Neural Information Processing)
Predicting Structured Data (Neural Information Processing)
Heterogeneous data fusion for alzheimer's disease study
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
A subspace kernel for nonlinear feature extraction
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Measuring statistical dependence with hilbert-schmidt norms
ALT'05 Proceedings of the 16th international conference on Algorithmic Learning Theory
Semi-supervised Discriminant Analysis Based on Dependence Estimation
ADMA '09 Proceedings of the 5th International Conference on Advanced Data Mining and Applications
Multilabel dimensionality reduction via dependence maximization
ACM Transactions on Knowledge Discovery from Data (TKDD)
SPF-GMKL: generalized multiple kernel learning with a million kernels
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
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Kernel methods have been applied successfully in many data mining tasks. Subspace kernel learning was recently proposed to discover an effective low-dimensional subspace of a kernel feature space for improved classification. In this paper, we propose to construct a subspace kernel using the Hilbert-Schmidt Independence Criterion (HSIC). We show that the optimal subspace kernel can be obtained efficiently by solving an eigenvalue problem. One limitation of the existing subspace kernel learning formulations is that the kernel learning and classification are independent and the subspace kernel may not be optimally adapted for classification. To overcome this limitation, we propose a joint optimization framework, in which we learn the subspace kernel and subsequent classifiers simultaneously. In addition, we propose a novel learning formulation that extracts an uncorrelated subspace kernel to reduce the redundant information in a subspace kernel. Following the idea from multiple kernel learning, we extend the proposed formulations to the case when multiple kernels are available and need to be combined. We show that the integration of subspace kernels can be formulated as a semidefinite program (SDP) which is computationally expensive. To improve the efficiency of the SDP formulation, we propose an equivalent semi-infinite linear program (SILP) formulation which can be solved efficiently by the column generation technique. Experimental results on a collection of benchmark data sets demonstrate the effectiveness of the proposed algorithms.