噪声无序矩阵的矩阵重排：最优性与计算高效算法
Matrix Reordering for Noisy Disordered Matrices: Optimality and Computationally Efficient Algorithms
AI总结：
本文研究噪声无序单调Toeplitz模型下的矩阵重排问题，建立统计极限，证明谱排序次优，并提出具有性能保证的多项式时间自适应排序算法，在单细胞RNA测序数据上表现优于现有方法。
摘要：
受单细胞生物学和宏基因组学应用的驱动，我们研究了基于噪声无序单调Toeplitz矩阵模型的矩阵重排问题。我们在决策理论框架下建立了该问题的基本统计极限，并证明约束最小二乘估计器能达到最优速率。然而，由于其计算复杂度较高，我们分析了一种流行的多项式时间算法——谱排序（spectral seriation），并证明它是次优的。为解决这一问题，我们提出了一种新颖的多项式时间自适应排序算法，并保证了性能提升。对两个真实单细胞RNA测序数据集的模拟和分析表明，我们的算法优于现有方法。
英文摘要：
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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