Tracy-Widom Guided Dimension Reduction Space Selection for Orthogonal Matrix Factorization-based Clustering
Zhang, Xiaorong Xiao, Yun Peng, Xiaopeng Hu, Ruonan Chang, Xiaojun Xing, Tianzhang
Zhang, Xiaorong
Xiao, Yun
Peng, Xiaopeng
Hu, Ruonan
Chang, Xiaojun
Xing, Tianzhang
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Computer Vision
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Journal article
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English
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Abstract
Matrix factorization is an efficient dimension reduction technique for large-scale datasets clustering. Most matrix factorization algorithms determine the dimension reduction space (specifically, the number of dimensions of the reduced data space) by traversing the entire space or rely on prior knowledge. This often results in high computational cost or potential performance degradation. To address these challenges, we propose an efficient Tracy-Widom law-based dimension reduction space selection algorithm (TW algorithm), which can be plugged into any orthogonal matrix factorization-based clustering algorithm to automatically select the dimension reduction space. The proposed algorithm transforms the problem of determining the dimension reduction space into a comparison between sorted eigenvalues and critical values, which simplifies the solution process. To determine the critical values distinguishing signal-related eigenvalues from noise, we theoretically prove that the maximum eigenvalue of a Gaussian random matrix after orthogonal matrix factorization still follows the Tracy-Widom distribution, which ensures that the Tracy-Widom law remains valid for the reduced matrix. Due to the invariance of the non-zero eigenvalues of the matrix before and after orthogonal matrix factorization, we creatively propose to use the eigenvalues of the original data to infer the dimension reduction space. We further propose two specific frameworks respectively for single-view clustering matrix factorization (TW-SVCMF) and multi-view clustering matrix factorization (TW-MVCMF) in combination with the TW algorithm. Extensive experiments on four single-view datasets and five multi-view datasets demonstrate the effectiveness of the proposed TW algorithm. The average accuracy is improved by 3.58% on the five multi-view datasets compared to the original algorithms without the TW algorithm. In addition, it achieves an average runtime reduction of 60% compared to traversal-based algorithms.
Citation
X. Zhang, Y. Xiao, X. Peng, R. Hu, X. Chang, T. Xing, "Tracy-Widom Guided Dimension Reduction Space Selection for Orthogonal Matrix Factorization-based Clustering," Expert Systems with Applications, vol. 320, pp. 131984-131984, 2026, https://doi.org/10.1016/j.eswa.2026.131984.
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Expert Systems with Applications
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Keywords
40 Engineering, 46 Information and Computing Sciences, 4603 Computer Vision and Multimedia Computation
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Elsevier