A low dimensional approach on network characterization

In many applications, one may need to characterize a given network among a large set of base networks, and these networks are large in size and diverse in structure over the search space. In addition, the characterization algorithms are required to have low volatility and with a small circle of uncertainty. For large datasets, these algorithms are computationally intensive and inefficient. However, under the context of network mining, a major concern of some applications is speed. Hence, we are motivated to develop a fast characterization algorithm, which can be used to quickly construct a graph space for analysis purpose. Our approach is to transform a network characterization measure, commonly formulated based on similarity matrices, into simple vector form signatures. We shall show that the N x N similarity matrix can be represented by a dyadic product of two N-dimensional signature vectors; thus the network alignment process, which is usually solved as an assignment problem, can be reduced into a simple alignment problem based on separate signature vectors.