Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Multiple kernel learning, conic duality, and the SMO algorithm
ICML '04 Proceedings of the twenty-first international conference on Machine learning
A Modified Finite Newton Method for Fast Solution of Large Scale Linear SVMs
The Journal of Machine Learning Research
SIAM Journal on Matrix Analysis and Applications
Training linear SVMs in linear time
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Training a Support Vector Machine in the Primal
Neural Computation
Large Scale Multiple Kernel Learning
The Journal of Machine Learning Research
Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples
The Journal of Machine Learning Research
Pegasos: Primal Estimated sub-GrAdient SOlver for SVM
Proceedings of the 24th international conference on Machine learning
An RKHS for multi-view learning and manifold co-regularization
Proceedings of the 25th international conference on Machine learning
Global optimization for a class of fractional programming problems
Journal of Global Optimization
SVMs modeling for highly imbalanced classification
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on human computing
Machine Learning
A Quasi-Newton Approach to Nonsmooth Convex Optimization Problems in Machine Learning
The Journal of Machine Learning Research
Variable Sparsity Kernel Learning
The Journal of Machine Learning Research
LIBSVM: A library for support vector machines
ACM Transactions on Intelligent Systems and Technology (TIST)
lp-Norm Multiple Kernel Learning
The Journal of Machine Learning Research
Laplacian Support Vector Machines Trained in the Primal
The Journal of Machine Learning Research
Multiple Kernel Learning Algorithms
The Journal of Machine Learning Research
Efficient Sparse Generalized Multiple Kernel Learning
IEEE Transactions on Neural Networks
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Some multiple kernel learning (MKL) models are usually solved by utilizing the alternating optimization method where one alternately solves SVMs in the dual and updates kernel weights. Since the dual and primal optimization can achieve the same aim, it is valuable in exploring how to perform Lp norm MKL in the primal. In this paper, we propose an Lp norm multiple kernel learning algorithm in the primal where we resort to the alternating optimization method: one cycle for solving SVMs in the primal by using the preconditioned conjugate gradient method and other cycle for learning the kernel weights. It is interesting to note that the kernel weights in our method can obtain analytical solutions. Most importantly, the proposed method is well suited for the manifold regularization framework in the primal since solving LapSVMs in the primal is much more effective than solving LapSVMs in the dual. In addition, we also carry out theoretical analysis for multiple kernel learning in the primal in terms of the empirical Rademacher complexity. It is found that optimizing the empirical Rademacher complexity may obtain a type of kernel weights. The experiments on some datasets are carried out to demonstrate the feasibility and effectiveness of the proposed method.