Divide-and-Conquer Kronecker Product Decomposition for Memory-Efficient Graph Approximation

Graphs are a widely used data structure for modeling objects in several domains, ranging from social media analytics to molecular biology. Recently, with the surge of big data, finding compact representations of large graphs has become an integral part of large-scale data analysis. To that end, we explore the effectiveness of the Kronecker Product SVD (KPSVD) for scalable sparse graph approximation, in a Divide-and-Conquer fashion. The KPSVD seeks to represent a graph as the sum of the Kronecker Product (KP) of several smaller factor matrices. In our method, we first partition the graph into inter-graph and intra-graph, and then use the Van Loan-Pitsianis (VLP) SVD-based algorithm to find the low-rank KPSVD of each subgraph to approximate the intra-graph. We use both the inter-graph and the intra-graph to find the approximation for the whole graph. We perform experiments on small-scale to large-scale real-world datasets to test the effectiveness of our method in terms of approximation error and spectral clustering results. The experiments demonstrate that our approach can provide better or competitive performance in terms of approximation error and clustering results while saving memory, compared to other state-of-the-art algorithms.