Spectral ensemble clustering with doubly stochastic co-association matrix

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Although co-association (CA) matrix-based spectral ensemble clustering (SEC) has achieved significant success, it faces two persistent challenges: (1) CA matrix-based SEC may result in imbalanced cluster outcomes, and (2) SEC encounters difficulties due to the high time and space complexity resulting from the quadratic scaling of the CA matrix with the number of data points. To tackle these issues, we propose a doubly stochastic co-association (DSCA) matrix construction method. We have theoretically demonstrated that DSCA matrix-based SEC can achieve a more balanced cluster outcome compared to CA matrix-based SEC. Leveraging the DSCA matrix, we introduce two novel methods: Fast SEC (FSEC) and Approximate SEC (ASEC). FSEC efficiently solves the normalized cut on the DSCA matrix as it is symmetric and doubly stochastic. In ASEC, we employ random samples rather than the entire big dataset for ensemble clustering. After obtaining the ensemble clustering result of benchmark random sample, the approximate ensemble clustering result for all data points is derived using our newly proposed probability nearest neighbors (PNN) algorithm. Experimental results on both real-world and synthetic datasets are evaluated in terms of accuracy (ACC), normalized mutual information (NMI), purity, F1-score, and adjusted rand index (ARI) and confirm the scalability and effectiveness of the proposed FSEC and ASEC.