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arXiv · 2312.14416

Joint Semi-Symmetric Tensor PCA for Integrating Multi-modal Populations of Networks

Jiaming Liu·Lili Zheng·Zhengwu Zhang·Genevera I. Allen
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Abstract

Multi-modal populations of networks arise in many scenarios including in large-scale multi-modal neuroimaging studies that capture both functional and structural neuroimaging data for thousands of subjects. A major research question in such studies is how functional and structural brain connectivity are related and how they vary across the population. we develop a novel PCA-type framework for integrating multi-modal undirected networks measured on many subjects. Specifically, we arrange these networks as semi-symmetric tensors, where each tensor slice is a symmetric matrix representing a network from an individual subject. We then propose a novel Joint, Integrative Semi-Symmetric Tensor PCA (JisstPCA) model, associated with an efficient iterative algorithm, for jointly finding low-rank representations of two or more networks across the same population of subjects. We establish one-step statistical convergence of our separate low-rank network factors as well as the shared population factors to the true factors, with finite sample statistical error bounds. Through simulation studies and a real data example for integrating multi-subject functional and structural brain connectivity, we illustrate the advantages of our method for finding joint low-rank structures in multi-modal populations of networks.

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BibTeXRIS

Jiaming Liu, Lili Zheng, Zhengwu Zhang, Genevera I. Allen. 2023-12-22. Joint Semi-Symmetric Tensor PCA for Integrating Multi-modal Populations of Networks. https://arxiv.org/abs/2312.14416

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