Locally Permuted Low Rank Column-wise Sensing

2025/09/11 by Ahmed Ali Abbasi, Abbasi, Ahmed Ali, Namrata Vaswani +1
Engineering · Chemical Engineering · #Advanced Fiber Optic Sensors #Analytical Chemistry and Sensors #Indoor and Outdoor Localization Technologies

paper · pdf · doi:10.48550/arxiv.2509.09820

Abstract

We precisely formulate, and provide a solution for, the Low Rank Columnwise Sensing (LRCS) problem when some of the observed data is scrambled/permuted/unlabeled. This problem, which we refer to as permuted LRCS, lies at the intersection of two distinct topics of recent research: unlabeled sensing and low rank column-wise (matrix) sensing. We introduce a novel generalization of the recently developed Alternating Gradient Descent and Minimization (AltGDMin) algorithm to solve this problem. We also develop an alternating minimization (AltMin) solution. We show, using simulation experiments, that both converge but PermutedAltGDmin is much faster than Permuted-AltMin.

Citations

• Unlabeled Compressed Sensing from Multiple Measurement Vectors
• Efficient Federated Low Rank Matrix Completion
• Low-rank Matrix Recovery With Unknown Correspondence
• Fast and Sample-Efficient Federated Low Rank Matrix Recovery from column-wise Linear and Quadratic Projections
• Unlabeled Principal Component Analysis and Matrix Completion
• Sample-Efficient Low Rank Phase Retrieval
• A Two-Stage Approach to Multivariate Linear Regression with Sparsely Mismatched Data
• The Benefits of Diversity: Permutation Recovery in Unlabeled Sensing from Multiple Measurement Vectors
• Linear Regression with Sparsely Permuted Data
• Denoising Linear Models with Permuted Data
• Unlabeled Sensing with Random Linear Measurements

Related

• Noisy Low Rank Column-wise Sensing
• Alternating minimization algorithm with initialization analysis for r-local and k-sparse unlabeled sensing
• A Fast Algorithm for Low Rank + Sparse column-wise Compressive Sensing
• Randomly Initialized Alternating Least Squares: Fast Convergence for Matrix Sensing
• An Improved Sample Complexity for Rank-1 Matrix Sensing