Matrix Reordering for Noisy Disordered Matrices: Optimality and Computationally Efficient Algorithms

• URL: http://arxiv.org/abs/2201.06438v2
• Date: Sun, 13 Aug 2023 13:54:10 GMT
• Title: Matrix Reordering for Noisy Disordered Matrices: Optimality and Computationally Efficient Algorithms
• Authors: T. Tony Cai and Rong Ma
• Abstract summary: Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrixing based on a noisy monotone Toeplitz matrix model. We establish fundamental statistical limit for this problem in a decision-theoretic framework and demonstrate that a constrained least squares rate. To address this, we propose a novel-time adaptive sorting algorithm with guaranteed performance improvement.
• Score: 9.245687221460654
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrix reordering based on a noisy disordered monotone Toeplitz matrix model. We establish the fundamental statistical limit for this problem in a decision-theoretic framework and demonstrate that a constrained least squares estimator achieves the optimal rate. However, due to its computational complexity, we analyze a popular polynomial-time algorithm, spectral seriation, and show that it is suboptimal. To address this, we propose a novel polynomial-time adaptive sorting algorithm with guaranteed performance improvement. Simulations and analyses of two real single-cell RNA sequencing datasets demonstrate the superiority of our algorithm over existing methods.

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