期刊
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
卷 32, 期 4, 页码 1547-1559出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2020.2984958
关键词
Dimensionality reduction; Optimization; Clustering algorithms; Laplace equations; Linear programming; Task analysis; Manifolds; Classification; clustering structure; dimensionality reduction; graph-based; semisupervised learning; unsupervised learning
类别
资金
- National Key Research and Development Program of China [2018AAA0101902]
- National Natural Science Foundation of China [61936014, 61772427, 61751202]
- Fundamental Research Funds for the Central Universities [G2019KY0501]
The article introduces the UPGO framework for dimensionality reduction and clustering, which unifies graph construction and projection learning. It also generalizes the framework to tackle the semisupervised case (SPGO), providing experimental results and theoretical analysis on the effectiveness and convergence of the proposed frameworks.
Graph-based technique is widely used in projection, clustering, and classification tasks. In this article, we propose a novel and solid framework, named unsupervised projection with graph optimization (UPGO), for both dimensionality reduction and clustering. Different from the existing algorithms which treat graph construction and projection learning as two separate steps, UPGO unifies graph construction and projection learning into a general framework. It learns the graph similarity matrix adaptively based on the relationships among the low-dimensional representations. A constraint is introduced to the Laplacian matrix to learn a structured graph which contains the clustering structure, from which the clustering results can be obtained directly without requiring any postprocessing. The structured graph achieves the ideal neighbors assignment, based on which an optimal low-dimensional subspace can be learned. Moreover, we generalize UPGO to tackle the semisupervised case, namely semisupervised projection with graph optimization (SPGO), a framework for both dimensionality reduction and classification. An efficient algorithm is derived to optimize the proposed frameworks. We provide theoretical analysis about convergence analysis, computational complexity, and parameter determination. Experimental results on real-world data sets show the effectiveness of the proposed frameworks compared with the state-of-the-art algorithms. Results also confirm the generality of the proposed frameworks.
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