Discriminant Neighborhood Analysis Based On Graph Embedding And Its Applications

In recent years, manifold learning has attracted a lot of attention in machine learning and pattern recognition. Generally, manifold learning aims to project the original high-dimensional data into a low-dimensional subspace, and simultaneously preserve the local structure of the original data, which can reveal the inherent low-dimensional manifold in the data.As a representative method in manifold learning, the discriminant neighborhood analysis algorithm based on graph embedding has been successfully applied to face recognition. In this thesis, we focus on discriminant neighborhood analysis based on graph embedding. We find the imbalance problem in the construction of adjacency graph and also propose ways to solve this problem. The main contributions of this thesis are concluded as follows.1. A discriminant neighborhood embedding algorithm based on double adjacency graphs is proposed. Compared to discriminant neighborhood embedding, this algorithm constructs two adjacency graphs: homogeneous and heterogeneous adjacency graphs. Specifically, for each sample, the proposed method establishes the relevance not only to its homogeneous samples, but also to its heterogeneous samples. In doing so, the imbalance problem of adjacent graph can be solved. Experimental results on the face datasets show that the proposed method can improve the separability of data in the low-dimensional space.2. A locality-balanced discriminant neighbor embedding algorithm is presented. Based on our previous work, we introduce the location information between samples to better preserve the neighborhood structure of the samples. Experimental results on the face datasets show that this method has a better recognition rate.3. A similarity-balanced discriminant neighborhood embedding algorithm is proposed. This algorithm constructs new similarity measure functions for intra-class and inter-class data, respectively. New measure functions are respectively used to select homogenous or heterogeneous neighbors, and to measure the location information between samples. Experimental results on the face datasets show the effectiveness of the proposed algorithm.