Hypothesis Testing for Two Sample Comparison of Network Data

Abstract

Network data is a major object data type that has been widely collected or derived from common sources such as brain imaging. Such data contains numeric, topological, and geometrical information, and may be necessarily considered in certain non-Euclidean space for appropriate statistical analysis. The development of statistical methodologies for network data is challenging and currently at its infancy; for instance, the non-Euclidean counterpart of basic two-sample tests for network data is scarce in literature. In this study, a novel framework is presented for two independent sample comparison of networks. Specifically, an approximation distance metric to quotient Euclidean distance is proposed, and then combined with network spectral distance to quantify the local and global dissimilarity of networks simultaneously. A permutational non-Euclidean analysis of variance is adapted to the proposed distance metric for the comparison of two independent groups of networks. Comprehensive simulation studies and real applications are conducted to demonstrate the superior performance of our method over other alternatives. The asymptotic properties of the proposed test are investigated and its high-dimensional extension is discussed as well.

Tighter Bound Estimation for Efficient Biquadratic Optimization Over Unit Spheres

“…Here, X can be the Laplace matrix or the Toeplitz matrix in graph signals and image processing [22,23]. If X and Z are both the connectivity matrices in brain image analysis, or unidirectional networks, then the attributes A will be a nonnegative fourth-order PS-tensor [24,25]. A can also be considered as the representation of a real bilinear function A(X, Y ) : S m×m × S n×n → R,…”