Utility-aware graph dimensionality reduction approach

In recent years graphs with massive nodes and edges have become widely used in various application fields, for example, social networks, web mining, traffic on transport, and more. Several researchers have shown that reducing the dimensions is very important in analyzing extensive graph data. They applied a variety of dimensionality reduction strategies, including linear methods or nonlinear methods. However, it is still not clear to what extent the information is lost or preserved when these techniques are applied to reduce the dimensions of large networks. In this study, we measured the utility of graph dimensionality reduction, and we proved when using the very recently suggested method, which is HDR to reduce dimensional for graph, the utility loss will be small compared with popular linear techniques, such as PCA, LDA, FA, and MDS. We measured the utility based on three essential network metrics: Average Clustering Coefficient (ACC), Average Path Length (APL), and Average Betweenness (ABW). The results showed that HDR achieved a lower rate of utility loss compared to other dimensionality reduction methods. We performed our experiments on the three undirected and unweighted graph datasets.