K中位数聚类、基于模型的压缩感知和地球移动器距离的稀疏恢复
K-Median Clustering, Model-Based Compressive Sensing, and Sparse Recovery for Earth Mover Distance
摘要：
本文首先研究了地球移动距离（EMD）下的稀疏恢复问题。具体地说，我们设计了一个分布在mXn矩阵A上，使得对于任何x，给定Ax，我们可以在EMD距离下恢复x的k-稀疏近似。一种构造产生m = O（k log（n/k））和1 + 1的近似因子，其匹配其他误差度量（例如L_1范数）的最佳可实现的界。我们的算法是通过利用新的连接到其他问题和领域，如流算法的k-中值聚类和基于模型的压缩感知。我们还提供了新的算法和结果，后者的问题。
英文摘要：
We initiate the study of sparse recovery problems under the Earth-Mover Distance (EMD). Specifically, we design a distribution over m x n matrices A such that for any x, given Ax, we can recover a k-sparse approximation to x under the EMD distance. One construction yields m = O(k log(n/k)) and a 1 + epsilon approximation factor, which matches the best achievable bound for other error measures, such as the L_1 norm. Our algorithms are obtained by exploiting novel connections to other problems and areas, such as streaming algorithms for k-median clustering and model-based compressive sensing. We also provide novel algorithms and results for the latter problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
