SKETCHING DISCRETE VALUED SPARSE MATRICES

L. N. Theagarajan
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Abstract

The problem of recovering a sparse matrix X from its sketch AXBT is referred to as the matrix sketching problem. Typically, the sketch is a lower dimensional matrix compared to X, and the sketching matrices A and B are known. Matrix sketching algorithms have been developed in the past to recover matrices from a continuous valued vectorspace (e.g., ℝN×N). However, employing such algorithms to recover discrete valued matrices may not be optimal. In this paper, we propose two novel algorithms that can efficiently recover a discrete valued sparse matrix from its sketch. We consider sparse matrices whose non-zero entries belong to a finite set. First, using the well known orthogonal matching pursuit (OMP), we present a matrix sketching algorithm. Second, we present a low-complexity message passing based recovery algorithm which exploits any sparsity structure that is present in X. Our simulation results verify that the proposed algorithms outperform the state-of-art matrix sketching algorithms in recovering discrete valued sparse matrices.
绘制离散值稀疏矩阵
从稀疏矩阵X的草图AXBT中恢复稀疏矩阵X的问题称为矩阵草图问题。通常,与X相比,草图是一个低维矩阵,并且草图矩阵a和B是已知的。矩阵素描算法已经在过去开发,以恢复矩阵从一个连续的值向量空间(例如,∈N×N)。然而,使用这种算法来恢复离散值矩阵可能不是最优的。在本文中,我们提出了两种新的算法,可以有效地从其草图中恢复离散值稀疏矩阵。我们考虑非零元素属于有限集合的稀疏矩阵。首先,利用正交匹配追踪(OMP)算法,提出了一种矩阵素描算法。其次,我们提出了一种低复杂性的基于消息传递的恢复算法,该算法利用了x中存在的任何稀疏结构。我们的仿真结果验证了所提出的算法在恢复离散值稀疏矩阵方面优于最先进的矩阵素描算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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