Fast, Accurate and Memory-Efficient Partial Permutation Synchronization

TL;DR

The paper introduces MatchFAME, a novel partial permutation synchronization algorithm that is faster, more accurate, and more memory-efficient, suitable for large-scale multi-object matching tasks.

Contribution

It extends the CEMP framework to partial permutations, enabling a nonconvex weighted method that reduces computational complexity and improves accuracy in permutation synchronization.

Findings

Achieves state-of-the-art accuracy on synthetic and real datasets.

Demonstrates lower time and space complexity compared to previous methods.

Proves exact classification of corrupted permutations under certain conditions.

Abstract

Previous partial permutation synchronization (PPS) algorithms, which are commonly used for multi-object matching, often involve computation-intensive and memory-demanding matrix operations. These operations become intractable for large scale structure-from-motion datasets. For pure permutation synchronization, the recent Cycle-Edge Message Passing (CEMP) framework suggests a memory-efficient and fast solution. Here we overcome the restriction of CEMP to compact groups and propose an improved algorithm, CEMP-Partial, for estimating the corruption levels of the observed partial permutations. It allows us to subsequently implement a nonconvex weighted projected power method without the need of spectral initialization. The resulting new PPS algorithm, MatchFAME (Fast, Accurate and Memory-Efficient Matching), only involves sparse matrix operations, and thus enjoys lower time and space complexities in comparison to previous PPS algorithms. We prove that under adversarial corruption, though without additive noise and with certain assumptions, CEMP-Partial is able to exactly classify corrupted and clean partial permutations. We demonstrate the state-of-the-art accuracy, speed and memory efficiency of our method on both synthetic and real datasets.