| Title | : | Low-Rank Representation and Affinity Propagation based Approaches to Semi-Supervised Metric Learning |
| Speaker | : | Ujjal Kr Dutta (IITM) |
| Details | : | Mon, 23 Oct, 2017 3:30 PM @ A M Turing Hall |
| Abstract: | : | The problem of learning a distance metric can be considered as a problem of learning a mapping function on the input feature space such that the learnt distance between a pair of examples in the input feature space can be expressed as the Euclidean distance between the examples in the mapped feature space. An equivalent problem is learning a parametric matrix associated with the mapping function. Laplacian Regularized Metric Learning (LRML) involves learning a distance metric that satisfies the given sets of pairwise similarity and dissimilarity constraints and preserves the topological structure of the given data via a Laplacian regularizer. The Laplacian matrix is dependent on the affinity matrix that is computed using the local neighborhood relationships among examples in the input feature space. It is proposed to obtain the affinity matrix using the adjacency relationships in a graph constructed by computing a low-rank representation of the given data. Such an affinity matrix can capture better the global structure of the data such as clusters, subspaces and manifolds. In the proposed method, the affinity matrix is obtained by solving a convex optimization problem that involves constraining the entire data. The proposed distance metric learning method is called as LRML with Non-negative (LRML-N) low-rank and sparse graph. It is further extended by including the available pairwise constraints in the graph construction phase as well, leading to LRML-N with Similarity and Dissimilarity (LRML-NSD) constraints. Furthermore, a general framework for affinity propagation based semi-supervised metric learning is proposed by constraining the learnt metric to be close to a prior metric while preserving the topological structure of the data. A closed-form solution for the proposed framework is derived. Different choices for the prior metric lead to different approaches to semi-supervised metric learning. It is also shown that the proposed framework can be used to apply a weakly-supervised metric learning approach to the semi-supervised setting. Effectiveness of the proposed approaches to distance metric learning is studied on benchmark datasets. |
