{"doi":"10.1002/hbm.25897","title":"Uncovering shape signatures of <scp>resting‐state</scp> functional connectivity by geometric deep learning on Riemannian manifold","abstract":"Functional neural activities manifest geometric patterns, as evidenced by the evolving network topology of functional connectivities (FC) even in the resting state. In this work, we propose a novel manifold-based geometric neural network for functional brain networks (called \"Geo-Net4Net\" for short) to learn the intrinsic low-dimensional feature representations of resting-state brain networks on the Riemannian manifold. This tool allows us to answer the scientific question of how the spontaneous fluctuation of FC supports behavior and cognition. We deploy a set of positive maps and rectified linear unit (ReLU) layers to uncover the intrinsic low-dimensional feature representations of functional brain networks on the Riemannian manifold taking advantage of the symmetric positive-definite (SPD) form of the correlation matrices. Due to the lack of well-defined ground truth in the resting state, existing learning-based methods are limited to unsupervised methodologies. To go beyond this boundary, we propose to self-supervise the feature representation learning of resting-state functional networks by leveraging the task-based counterparts occurring before and after the underlying resting state. With this extra heuristic, our Geo-Net4Net allows us to establish a more reasonable understanding of resting-state FCs by capturing the geometric patterns (aka. spectral/shape signature) associated with resting states on the Riemannian manifold. We have conducted extensive experiments on both simulated data and task-based functional resonance magnetic imaging (fMRI) data from the Human Connectome Project (HCP) database, where our Geo-Net4Net not only achieves more accurate change detection results than other state-of-the-art counterpart methods but also yields ubiquitous geometric patterns that manifest putative insights into brain function.","journal":"Human Brain Mapping","year":2022,"id":264126,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":12,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9489,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2022-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":921713,"name":"Zhuobin Huang","orcid":"0009-0005-2251-4146","position":1,"is_corresponding":false},{"id":397221,"name":"Hongmin Cai","orcid":"0000-0002-2747-7234","position":2,"is_corresponding":false},{"id":762174,"name":"Robert G. Lyday","orcid":"0000-0002-8031-5867","position":3,"is_corresponding":false},{"id":397223,"name":"Paul J. Laurienti","orcid":"0000-0001-8871-9658","position":4,"is_corresponding":false},{"id":397224,"name":"Guorong Wu","orcid":"0000-0002-0550-6145","position":5,"is_corresponding":false},{"id":921712,"name":"Tingting Dan","orcid":"0000-0001-6936-2649","position":0,"is_corresponding":true}],"reference_count":50,"raw_metadata":null,"created_at":"2026-07-19T00:26:37.567338Z","pmid":"35538672","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}