Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 34, Issue 11, Pages 9481-9492Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2022.3203014
Keywords
Learning systems; Principal component analysis; Optics; Image color analysis; Data models; Computational complexity; Transforms; Landmark-based dynamic connections (LDC); local embedding learning; non-Gaussian data; supervised dimensionality reduction
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This article proposes a local embedding learning method using landmark-based dynamic connections to address the dimensionality reduction problem in non-Gaussian data. The method leverages landmarks to represent different subclusters and establishes connections to handle the local structure of the data. Experiments have demonstrated the advantages of this method.
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.
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