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

• Published in: IEEE transactions on information theory Vol. 70; no. 1; p. 1
• Main Authors: Tony Cai, T., Ma, Rong
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.01.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive algorithms; Analytical models; Bioinformatics; Data models; Decision theory; Gene sequencing; Genomics; Noise measurement; Optimization; Polynomials; Sorting; Sorting algorithms; Symmetric matrices
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2023.3305538

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.