Shuffled Linear Regression via Spectral Matching
This addresses the combinatorial complexity in large-scale SLR for applications like image registration, though it is an incremental improvement over existing methods.
The paper tackles the problem of shuffled linear regression (SLR) where unknown permutations complicate feature estimation, proposing a spectral matching method that efficiently resolves permutations by aligning spectral components. Experiments show it outperforms existing algorithms in estimation accuracy and registration performance on synthetic and real-world image datasets.
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute Shrinkage and Selection Operator (LASSO) approaches by jointly estimating the permutation, resulting in shuffled LS and shuffled LASSO formulations. Existing methods, constrained by the combinatorial complexity of permutation recovery, often address small-scale cases with limited measurements. In contrast, we focus on large-scale SLR, particularly suited for environments with abundant measurement samples. We propose a spectral matching method that efficiently resolves permutations by aligning spectral components of the measurement and feature covariances. Rigorous theoretical analyses demonstrate that our method achieves accurate estimates in both shuffled LS and shuffled LASSO settings, given a sufficient number of samples. Furthermore, we extend our approach to address simultaneous pose and correspondence estimation in image registration tasks. Experiments on synthetic datasets and real-world image registration scenarios show that our method outperforms existing algorithms in both estimation accuracy and registration performance.