Node-attributed Spatial Graph Partitioning

Abstract

Given a spatial graph and a set of node attributes, the Node-attributed Spatial Graph Partitioning (NSGP) problem partitions a node-attributed spatial graph into k homogeneous sub-graphs that minimize both the total RMSErank1 and edge-cuts while meeting a size constraint on the sub-graphs. RMSErank1 is the Root Mean Square Error between a matrix and its rank-one decomposition. The NSGP problem is important for many societal applications such as identifying homogeneous communities in a spatial graph and detecting interrelated patterns in traffic accidents. This problem is NP-hard; it is computationally challenging because of the large size of spatial graphs and the constraint that the sub-graphs must be homogeneous, i.e. similar in terms of node attributes. This paper proposes a novel approach for finding a set of homogeneous sub-graphs that can minimize both the total RMSErank1 and edge-cuts while meeting the size constraint. Experiments and a case study using U.S. Census datasets and HP#6 watershed network datasets demonstrate that the proposed approach partitions a spatial graph into a set of homogeneous sub-graphs and reduces the computational cost.