Jihong Shen | Searcharxiv

arXiv2026

A two-steps tensor eigenvector centrality for nodes and hyperedges in hypergraphs

Hypergraphs have been a powerful tool to represent higher-order interactions, where hyperedges can connect an arbitrary number of nodes. Quantifying the relative importance of nodes and hyperedges in hypergraphs is a fundamental problem in network analysis. In this paper, we propose a new tensor-based centrality measure for general hypergraphs. We use a third-order tensor to represent the relationship between nodes and hyperedges. The tensor's positive Perron vector is defined as the centrality vector of the hypergraph. The existence and uniqueness of this centrality vector are guaranteed by the Perron-Frobenius theorem for tensors. This new centrality measure captures a higher-order mutual reinforcement mechanism: a node's importance is determined by the importance of its incident hyperedges and the other nodes within these hyperedges; symmetrically, a hyperedge's importance is determined by the importance of its constituent nodes and the other hyperedges containing these nodes. We further provide a combinatorial interpretation by proving that the centrality vector represents the limit geometric capacity of two-steps expansion trees. We illustrate the centrality measure on real-world hypergraph datasets.

cs.SI↗

arXiv2021

Interpreting Depression From Question-wise Long-term Video Recording of SDS Evaluation

Self-Rating Depression Scale (SDS) questionnaire has frequently been used for efficient depression preliminary screening. However, the uncontrollable self-administered measure can be easily affected by insouciantly or deceptively answering, and producing the different results with the clinician-administered Hamilton Depression Rating Scale (HDRS) and the final diagnosis. Clinically, facial expression (FE) and actions play a vital role in clinician-administered evaluation, while FE and action are underexplored for self-administered evaluations. In this work, we collect a novel dataset of 200 subjects to evidence the validity of self-rating questionnaires with their corresponding question-wise video recording. To automatically interpret depression from the SDS evaluation and the paired video, we propose an end-to-end hierarchical framework for the long-term variable-length video, which is also conditioned on the questionnaire results and the answering time. Specifically, we resort to a hierarchical model which utilizes a 3D CNN for local temporal pattern exploration and a redundancy-aware self-attention (RAS) scheme for question-wise global feature aggregation. Targeting for the redundant long-term FE video processing, our RAS is able to effectively exploit the correlations of each video clip within a question set to emphasize the discriminative information and eliminate the redundancy based on feature pair-wise affinity. Then, the question-wise video feature is concatenated with the questionnaire scores for final depression detection. Our thorough evaluations also show the validity of fusing SDS evaluation and its video recording, and the superiority of our framework to the conventional state-of-the-art temporal modeling methods.

cs.CV↗