通过变换编码对加权图邻接矩阵进行有损压缩
Lossy compression of weighted graph adjacency matrices by transform coding
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中文总结 AI 辅助
研究加权图邻接矩阵的有损压缩，核心方法是先将无加权图转换为线图，再用图滤波器组变换边权值向量并量化编码，还提出边平滑度衡量压缩难度，实验验证了该方法相较于现有方法的有效性。
中文摘要 AI 辅助
本文提出了一种加权图压缩框架，其中图拓扑无损传输，边权值有损压缩。边权值有损压缩的一个挑战是边之间的潜在关系不明确。为解决此问题，首先将无加权图转换为相应的线图，其节点代表原图的边，边编码它们之间的关系。线图变换使我们能将边权值视为定义在线图上的图信号。先在线图上用图滤波器组变换边权值向量，再对变换后的系数进行量化和熵编码。除了有损压缩方法，还对线图上的边平滑度进行形式化，并表明它可衡量压缩难度，且无需转换为线图就能轻松计算，这有助于了解给定加权图的预期压缩性能。通过在合成数据和真实世界数据上的实验，将该方法与现有矩阵预处理方法比较，验证了其有效性。
英文摘要
In this paper, we propose a compression framework for weighted graphs in which the graph topology is transmitted losslessly and edge weights are compressed lossily. A challenge in the lossy compression of edge weights is that the underlying relationships between edges are ambiguous. To address this issue, we first transform the unweighted graph into the corresponding line graph, whose nodes represent the edges of the original graph and whose edges encode the relationships between them. The line graph transform allows us to regard edge weights as a graph signal defined on the line graph. Instead of transmitting the edge-weight vector, we first transform it with a graph filter bank on the line graph. Then, quantization and entropy coding are performed on the transformed coefficients of the edge weight vector. In addition to the lossy compression method, we formalize edge smoothness on the line graph and show that it serves as a measure of the difficulty of compression. The proposed smoothness measure can be easily calculated without converting to a line graph. This provides insight into the expected compression performance of a given weighted graph. Experiments on synthetic and real-world data validate the effectiveness of the proposed method by comparing it with existing matrix preprocessing methods.
