Transductive Kernel Matrix Learningwith Hierarchic Bayesian Model, Application to Hyperspectral Images

In recent years, kernel methods have demonstrated their performance in hyperspectral imaging. Among the reasons their ability to handle large input spaces is essential. However for this type of applications a critical problem is the choice of the kernel which must combine spectral and spatial information [1] and of course achieve good generalization performance. The kernel design stage is generally defined as the optimization of a distance metric when the kernel is chosen in a particular subspace. The alignment criterion between a parametrized kernel and a target kernel [2, 3] belongs to this family. However this solution does not embed the kernel learning problem in a particular kernel-based algorithms such as the support vector machine (SVM). This is not the case of [4] where both problems of kernel learning and SVM estimation are jointly solved in a transductive setting using semidefinite programming. The Bayesian formalism is another powerful framework for kernel learning. In [5] a hierarchical model is used to achieve a transductive learning of the kernel matrix. In the Bayesian learning context, relevance vector machine (RVM) is the natural choice to tackle jointly the Kernel learning and estimation of the classification algorithm parameters. A solution to this problem is proposed in [6] where linear composite kernel learning and RVM regression coefficients estimation are performed using a global hierarchic Bayesian model. This contributions proposes a general formalism for joint transductive learning of the kernel matrix and regression coefficients estimation in a Bayesian context.