| Title | : | Distance Metric Learning based Kernels for Pattern Classification |
| Speaker | : | Shajee Mohan B S (IITM) |
| Details | : | Tue, 11 Jul, 2017 3:00 PM @ Alan M Turing Hall |
| Abstract: | : | The commonly used approaches to distance metric learning (DML) involve learning a parametric matrix of the squared Mahalanobis distance between a pair of examples using the sets of constraints derived from the labelled training examples. In these approaches, the parametric matrix is associated with a linear transformation and a single matrix is learnt using the data of all the classes in a multi-class pattern classification task. We propose the class-specific Mahalanobis DML approach that involves learning a different parametric matrix for each of the classes. A nonlinear transformation can be associated with the parametric matrix by formulating the Mahalanobis DML problem as a problem of learning the kernel gram matrix of a Mercer kernel. For the DML based kernel matrix learning, an optimal kernel gram matrix is learnt from the gram matrix of a base kernel, such as Gaussian kernel, by solving an optimization problem that minimizes the logdet divergence between the two gram matrices. We propose the class-specific DML based kernel to be used in multi-class pattern classification using support vector machines (SVMs). We explore the use of DML based kernels in the kernel principal component analysis method for nonlinear dimension reduction to obtain a discriminatory representation. We propose an approach to extend the DML framework to the multi-label pattern classification task. In this approach, the sets of constraints are formed using the Hamming distance between the relevant label set vectors of a pair of multi-label training examples. The metric learnt using the proposed approach is used in the multi-label K nearest neighbors method and the ranking SVM method for multi-label pattern classification. Finally, an approach to learn a DML based kernel using the labelled and unlabelled examples in the self-training method for semi-supervised learning for multi-class pattern classification using SVMs is proposed. Effectiveness of the proposed approaches is demonstrated through the results of experimental studies on benchmark datasets. |
