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Metric learning for classification has been intensively studied over the lastdecade. The idea is to learn a metric space induced from a normed vector spaceon which data from different classes are well separated. Different measures ofthe separation thus lead to various designs of the objective function in themetric learning model. One classical metric is the Mahalanobis distance, wherea linear transformation matrix is designed and applied on the original datasetto obtain a new subspace equipped with the Euclidean norm. The kernelizedversion has also been developed, followed by Multiple-Kernel learning models.In this paper, we consider metric learning to be the identification of the bestkernel function with respect to a high class separability in the correspondingmetric space. The contribution is twofold: 1) No pairwise computations arerequired as in most metric learning techniques; 2) Better flexibility and lowercomputational complexity is achieved using the CLAss-Specific (Multiple) Kernel- Metric Learning (CLAS(M)K-ML). The proposed techniques can be considered as apreprocessing step to any kernel method or kernel approximation technique. Anextension to a hierarchical learning structure is also proposed to furtherimprove the classification performance, where on each layer, the CLASMK iscomputed based on a selected "marginal" subset and feature vectors areconstructed by concatenating the features from all previous layers.

Learning Hierarchical Feature Space Using CLAss-specific Subspace Multiple Kernel -- Metric Learning for Classification