Integrating Global and Local Structures in Semi-supervised Discriminant Analysis

In this paper, in terms of pairwise constraints which specify whether a pair of instances belong to the same class (must-link constraints) or different classes (cannot-link constraints), we propose a novel semi-supervised discriminant analysis algorithm which integrates both global and local structures. Specifically, our objective is to learn a smooth as well as discriminative subspace. In order to achieve it, we jointly use both the instances in the cannot-link constraints to maximize the separability between different classes while applying those in the must-link constraints to minimize the distance between the same class and the integration of global and local structures of the data to make nearby instances in the original space close to each other in the embedding space. Experimental results on a collection of real-world data sets demonstrated the effectiveness of the proposed algorithm.