Local Embedding Learning via Landmark-Based Dynamic Connections

Abstract

Linear discriminant analysis (LDA) is one of the most effective and popular methods to reduce the dimensionality of data with Gaussian assumption. However, LDA cannot handle non-Gaussian data because the center point is incompetent to represent the distribution of data. Some existing methods based on graph embedding focus on exploring local structures via pairwise relationships of data for addressing the non-Gaussian issue. Due to massive pairwise relationships, the computational complexity is high as well as the locally optimal solution is hard to find. To address these issues, we propose a novel and efficient local embedding learning via landmark-based dynamic connections (LDC) in which we leverage several landmarks to represent different subclusters in the same class and establish the connections between each point and landmark. Furthermore, in order to explore the relationship of landmarks pairwise more precisely, the relationship between each point and their corresponding neighbor landmarks are found in the optimal subspace, rather than the original space, which can avoid the negative influence of the noises. We also propose an efficient iterative algorithm to deal with the proposed ratio minimization problem. Extensive experiments conducted on several real-world datasets have demonstrated the advantages of the proposed method.