Ultra-Scalable Spectral Clustering and Ensemble Clustering

• Published in: IEEE transactions on knowledge and data engineering Vol. 32; no. 6; pp. 1212 - 1226
• Main Authors: Huang, Dong, Wang, Chang-Dong, Wu, Jian-Sheng, Lai, Jian-Huang, Kwoh, Chee-Keong
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Approximation algorithms; Bipartite graph; Clustering; Clustering algorithms; Complexity theory; Data clustering; Datasets; ensemble clustering; Graph theory; large-scale clustering; large-scale datasets; nonlinearly separable datasets; Robustness; Scalability; Sparse matrices; Spectra; spectral clustering
• ISSN: 1041-4347; 1558-2191
• DOI: 10.1109/TKDE.2019.2903410

This paper focuses on scalability and robustness of spectral clustering for extremely large-scale datasets with limited resources. Two novel algorithms are proposed, namely, ultra-scalable spectral clustering (U-SPEC) and ultra-scalable ensemble clustering (U-SENC). In U-SPEC, a hybrid representative selection strategy and a fast approximation method for <inline-formula><tex-math notation="LaTeX">K</tex-math> <mml:math><mml:mi>K</mml:mi></mml:math><inline-graphic xlink:href="wang-ieq1-2903410.gif"/> </inline-formula>-nearest representatives are proposed for the construction of a sparse affinity sub-matrix. By interpreting the sparse sub-matrix as a bipartite graph, the transfer cut is then utilized to efficiently partition the graph and obtain the clustering result. In U-SENC, multiple U-SPEC clusterers are further integrated into an ensemble clustering framework to enhance the robustness of U-SPEC while maintaining high efficiency. Based on the ensemble generation via multiple U-SEPC's, a new bipartite graph is constructed between objects and base clusters and then efficiently partitioned to achieve the consensus clustering result. It is noteworthy that both U-SPEC and U-SENC have nearly linear time and space complexity, and are capable of robustly and efficiently partitioning 10-million-level nonlinearly-separable datasets on a PC with 64 GB memory. Experiments on various large-scale datasets have demonstrated the scalability and robustness of our algorithms. The MATLAB code and experimental data are available at https://www.researchgate.net/publication/330760669 .