Shuffled Linear Regression via Spectral Matching

IF 5.8 2区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC
Hang Liu;Anna Scaglione
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引用次数: 0

Abstract

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.
基于谱匹配的洗牌线性回归
洗刷线性回归(SLR)试图通过线性变换来估计潜在特征,由于测量维度中的未知排列而变得复杂。该问题扩展了传统的最小二乘(LS)和最小绝对收缩和选择算子(LASSO)方法,通过联合估计排列,得到了洗牌LS和洗牌LASSO公式。现有的方法受排列恢复的组合复杂性的限制,通常处理有限测量的小规模情况。相比之下,我们专注于大规模单反相机,特别适合于测量样本丰富的环境。我们提出了一种光谱匹配方法,该方法通过对准测量光谱分量和特征协方差来有效地解决排列问题。严格的理论分析表明,在足够数量的样本下,我们的方法在洗牌LS和洗牌LASSO设置下都能实现准确的估计。此外,我们扩展了我们的方法来解决图像配准任务中的同步姿态和对应估计。在合成数据集和真实图像配准场景上的实验表明,该方法在估计精度和配准性能上都优于现有算法。
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来源期刊
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing 工程技术-工程:电子与电气
CiteScore
11.20
自引率
9.30%
发文量
310
审稿时长
3.0 months
期刊介绍: The IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals. The term “signal” includes, among others, audio, video, speech, image, communication, geophysical, sonar, radar, medical and musical signals. Examples of topics of interest include, but are not limited to, information processing and the theory and application of filtering, coding, transmitting, estimating, detecting, analyzing, recognizing, synthesizing, recording, and reproducing signals.
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