邻接矩阵的图滤波器组有损压缩
Lossy Compression of Adjacency Matrices by Graph Filter Banks
AI总结：
提出基于图滤波器组的加权邻接矩阵有损压缩框架，无损保留拓扑信息，有损压缩边权重，实验验证其有效性。
摘要：
本文提出了一种基于图滤波器组的加权图邻接矩阵压缩框架。邻接矩阵是图的一种广泛使用的数学表示，在信号处理、机器学习和数据挖掘的各种应用中都有使用。在许多感兴趣的问题中，这些邻接矩阵可能很大，因此高效的压缩方法至关重要。本文提出了一种加权邻接矩阵的有损压缩方法，其中二值邻接信息被无损编码（因此图的拓扑信息得以保留），而边权重则被有损压缩。对于边权重压缩，目标图被转换为线图，其节点对应于原图的边，原边权重被视为线图上的图信号。然后，我们使用图滤波器组对线图上的边权重进行变换，以获得稀疏表示。在合成数据上的实验通过将所提方法与现有的有损矩阵压缩方法进行比较，验证了其有效性。
英文摘要：
This paper proposes a compression framework for adjacency matrices of weighted graphs based on graph filter banks. Adjacency matrices are widely used mathematical representations of graphs and are used in various applications in signal processing, machine learning, and data mining. In many problems of interest, these adjacency matrices can be large, so efficient compression methods are crucial. In this paper, we propose a lossy compression of weighted adjacency matrices, where the binary adjacency information is encoded losslessly (so the topological information of the graph is preserved) while the edge weights are compressed lossily. For the edge weight compression, the target graph is converted into a line graph, whose nodes correspond to the edges of the original graph, and where the original edge weights are regarded as a graph signal on the line graph. We then transform the edge weights on the line graph with a graph filter bank for sparse representation. Experiments on synthetic data validate the effectiveness of the proposed method by comparing it with existing lossy matrix compression methods.
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。
