Matrix Reordering for Noisy Disordered Matrices: Optimality and Computationally Efficient Algorithms
This work solves matrix reordering problems in computational biology applications like single-cell biology and metagenomics, offering a computationally efficient algorithm with proven improvements.
The paper tackles the problem of matrix reordering for noisy disordered matrices, establishing the fundamental statistical limit and showing that a constrained least squares estimator achieves optimal rates, but is computationally complex. To address this, they propose a novel polynomial-time adaptive sorting algorithm that outperforms existing methods, as demonstrated on real single-cell RNA sequencing datasets.
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.