Ordinal Pattern Tree: A New Representation Method for Brain Network Analysis

Brain networks, describing the functional or structural interactions of brain with graph theory, have been widely used for brain imaging analysis. Currently, several network representation methods have been developed for describing and analyzing brain networks. However, most of these methods ignored the valuable weighted information of the edges in brain networks. In this paper, we propose a new representation method (i.e., ordinal pattern tree) for brain network analysis. Compared with the existing network representation methods, the proposed ordinal pattern tree (OPT) can not only leverage the weighted information of the edges but also express the hierarchical relationships of nodes in brain networks. On OPT, nodes are connected by ordinal edges which are constructed by using the ordinal pattern relationships of weighted edges. We represent brain networks as OPTs and further develop a new graph kernel called optimal transport (OT) based ordinal pattern tree (OT-OPT) kernel to measure the similarity between paired brain networks. In OT-OPT kernel, the OT distances are used to calculate the transport costs between the nodes on the OPTs. Based on these OT distances, we use exponential function to calculate OT-OPT kernel which is proved to be positive definite. To evaluate the effectiveness of the proposed method, we perform classification and regression experiments on ADHD-200, ABIDE and ADNI datasets. The experimental results demonstrate that our proposed method outperforms the state-of-the-art graph methods in the classification and regression tasks.