2023/03/21 by Duc T. Nguyen, Nguyen, Duc, Anderson Ye Zhang +1
Computer Science · Engineering · #Computer Vision and Pattern Recognition (cs.CV) #Digital Image Processing Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Sparse and Compressive Sensing Techniques #Spectral Theory (math.SP) #Statistics Theory (math.ST) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2303.12051
openalex publication_date 2023/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Permutation synchronization is an important problem in computer science that constitutes the key step of many computer vision tasks. The goal is to recover n latent permutations from their noisy and incomplete pairwise measurements. In recent years, spectral methods have gained increasing popularity thanks to their simplicity and computational efficiency. Spectral methods utilize the leading eigenspace U of the data matrix and its block submatrices U1,U2,…, Un to recover the permutations. In this paper, we propose a novel and statistically optimal spectral algorithm. Unlike the existing methods which use \UjU1^\top\j≥ 2, ours constructs an anchor matrix M by aggregating useful information from all of the block submatrices and estimates the latent permutations through \UjM^\top\j≥ 1. This modification overcomes a crucial limitation of the existing methods caused by the repetitive use of U1 and leads to an improved numerical performance. To establish the optimality of the proposed method, we carry out a fine-grained spectral analysis and obtain a sharp exponential error bound that matches the minimax rate.