Abstract
Spectral clustering is one of the most popular and important clustering methods in pattern recognition, machine learning, and data mining. However, its high computational complexity limits it in applications involving truly large-scale datasets. For a clustering problem with n samples, it needs to compute the eigenvectors of the graph Laplacian with O(n3) time complexity. To address this problem, we propose a novel method called anchor-based spectral clustering (ASC) by employing anchor points of data. Specifically, m (m ≪ n) anchor points are selected from the dataset, which can basically maintain the intrinsic (manifold) structure of the original data. Then a mapping matrix between the original data and the anchors is constructed. More importantly, it is proved that this data-anchor mapping matrix essentially preserves the clustering structure of the data. Based on this mapping matrix, it is easy to approximate the spectral embedding of the original data. The proposed method scales linearly relative to the size of the data but with low degradation of the clustering performance. The proposed method, ASC, is compared to the classical spectral clustering and two state-of-the-art accelerating methods, i.e., power iteration clustering and landmark-based spectral clustering, on 10 real-world applications under three evaluation metrics. Experimental results show that ASC is consistently faster than the classical spectral clustering with comparable clustering performance, and at least comparable with or better than the state-of-the-art methods on both effectiveness and efficiency.
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Project supported by the National Natural Science Foundation of China (Nos. 61271405, 61403353, 41576011, and U1706218), the PhD Program Foundation of the Ministry of Education of China (No. 20120132110018), the International Science & Technology Cooperation Program of China (No. 2014DFA10410), the Science and Technology Program of Qingdao, China (No. 17-3-3-20-nsh), and the Fundamental Research Funds for the Central Universities, China
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Zhang, Q., Zhong, Gq. & Dong, Jy. An anchor-based spectral clustering method. Frontiers Inf Technol Electronic Eng 19, 1385–1396 (2018). https://doi.org/10.1631/FITEE.1700262
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DOI: https://doi.org/10.1631/FITEE.1700262