Matrix analysis
Learning the Kernel Matrix with Semi-Definite Programming
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
The em algorithm for kernel matrix completion with auxiliary data
The Journal of Machine Learning Research
Hierarchic Bayesian models for kernel learning
ICML '05 Proceedings of the 22nd international conference on Machine learning
Model-based transductive learning of the kernel matrix
Machine Learning
Expert Systems with Applications: An International Journal
Information Sciences: an International Journal
Graph based semi-supervised learning with sharper edges
ECML'06 Proceedings of the 17th European conference on Machine Learning
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In kernel methods, an interesting recent development seeks to learn a good kernel from empirical data automatically. In this paper, by regarding the transductive learning of the kernel matrix as a missing data problem, we propose a Bayesian hierarchical model for the problem and devise the Tanner-Wong data augmentation algorithm for making inference on the model. The Tanner-Wong algorithm is closely related to Gibbs sampling, and it also bears a strong resemblance to the expectation-maximization (EM) algorithm. For an efficient implementation, we propose a simplified Bayesian hierarchical model and the corresponding Tanner-Wong algorithm. We express the relationship between the kernel on the input space and the kernel on the output space as a symmetric-definite generalized eigenproblem. Based on this eigenproblem, an efficient approach to choosing the base kernel matrices is presented. The effectiveness of our Bayesian model with the Tanner-Wong algorithm is demonstrated through some classification experiments showing promising results.