{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T04:43:08Z","timestamp":1760848988105,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T00:00:00Z","timestamp":1760572800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R35GM152245","U19AG056169"],"award-info":[{"award-number":["R35GM152245","U19AG056169"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1944247"],"award-info":[{"award-number":["1944247"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014989","name":"Chan Zuckerberg Initiative","doi-asserted-by":"publisher","award":["253558"],"award-info":[{"award-number":["253558"]}],"id":[{"id":"10.13039\/100014989","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["BDCC"],"abstract":"<jats:p>Temporal network diffusion models play a crucial role in healthcare, information technology, and machine learning, enabling the analysis of dynamic event-based processes such as disease spread, information propagation, and behavioral diffusion. This study addresses the challenge of reconstructing temporal network diffusion events in real time under conditions of missing and evolving data. A novel non-parametric reconstruction method by simple weights differentiationis proposed to enhance source detection robustness with provable improved error bounds. The approach introduces adaptive cost adjustments, dynamically reducing high-risk source penalties and enabling bounded detours to mitigate errors introduced by missing edges. Theoretical analysis establishes enhanced upper bounds on false positives caused by detouring, while a stepwise evaluation of dynamic costs minimizes redundant solutions, resulting in robust Steiner tree reconstructions. Empirical validation on three real-world datasets demonstrates a 5% improvement in Matthews correlation coefficient (MCC), a twofold reduction in redundant sources, and a 50% decrease in source variance. These results confirm the effectiveness of the proposed method in accurately reconstructing temporal network diffusion while improving stability and reliability in both offline and online settings.<\/jats:p>","DOI":"10.3390\/bdcc9100262","type":"journal-article","created":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T16:33:22Z","timestamp":1760632402000},"page":"262","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Source Robust Non-Parametric Reconstruction of Epidemic-like Event-Based Network Diffusion Processes Under Online Data"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6530-2489","authenticated-orcid":false,"given":"Jiajia","family":"Xie","sequence":"first","affiliation":[{"name":"Laboratory for Pathology Dynamics, Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA 30332, USA"},{"name":"Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"}]},{"given":"Chen","family":"Lin","sequence":"additional","affiliation":[{"name":"Laboratory for Pathology Dynamics, Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA 30332, USA"},{"name":"Machine Learning Center, Georgia Institute of Technology, Atlanta, GA 30332, USA"}]},{"given":"Xinyu","family":"Guo","sequence":"additional","affiliation":[{"name":"Laboratory for Pathology Dynamics, Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA 30332, USA"},{"name":"Machine Learning Center, Georgia Institute of Technology, Atlanta, GA 30332, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5472-6355","authenticated-orcid":false,"given":"Cassie S.","family":"Mitchell","sequence":"additional","affiliation":[{"name":"Laboratory for Pathology Dynamics, Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA 30332, USA"},{"name":"Machine Learning Center, Georgia Institute of Technology, Atlanta, GA 30332, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.4269\/ajtmh.20-0812","article-title":"COVID-19\u2013related infodemic and its impact on public health: A global social media analysis","volume":"103","author":"Islam","year":"2020","journal-title":"Am. J. Trop. Med. Hygen."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Li, Z., Xia, L., Hua, H., Zhang, S., Wang, S., and Huang, C. (2025, January 10\u201314). DiffGraph: Heterogeneous Graph Diffusion Model. Proceedings of the Eighteenth ACM International Conference on Web Search and Data Mining, Hannover, Germany.","DOI":"10.1145\/3701551.3703590"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Xiao, H., Rozenshtein, P., Tatti, N., and Gionis, A. (2018). Reconstructing a cascade from temporal observations. Proceedings of the 2018 SIAM International Conference on Data Mining, SIAM.","DOI":"10.1137\/1.9781611975321.75"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Xiao, H., Aslay, C., and Gionis, A. (2018, January 17\u201320). Robust cascade reconstruction by steiner tree sampling. Proceedings of the 2018 IEEE International Conference on Data Mining (ICDM), Singapore.","DOI":"10.1109\/ICDM.2018.00079"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Rozenshtein, P., Gionis, A., Prakash, B.A., and Vreeken, J. (2016, January 13\u201317). Reconstructing an epidemic over time. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/2939672.2939865"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Jang, H., Pai, S., Adhikari, B., and Pemmaraju, S.V. (2021, January 7\u201310). Risk-aware temporal cascade reconstruction to detect asymptomatic cases: For the cdc mind healthcare network. Proceedings of the 2021 IEEE International Conference on Data Mining (ICDM), Auckland, New Zealand.","DOI":"10.1109\/ICDM51629.2021.00034"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Jang, H., Fu, A., Cui, J., Kamruzzaman, M., Prakash, B.A., Vullikanti, A., Adhikari, B., and Pemmaraju, S.V. (2023, January 7\u201314). Detecting sources of healthcare associated infections. Proceedings of the AAAI Conference on Artificial Intelligence, Washington, DC, USA.","DOI":"10.1609\/aaai.v37i4.25554"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Mishra, R., Heavey, J., Kaur, G., Adiga, A., and Vullikanti, A. (2023, January 7\u201314). Reconstructing an epidemic outbreak using steiner connectivity. Proceedings of the AAAI Conference on Artificial Intelligence, Washington, DC, USA.","DOI":"10.1609\/aaai.v37i10.26372"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"E653","DOI":"10.1503\/cmaj.200922","article-title":"Digital contact tracing for COVID-19","volume":"192","author":"Kleinman","year":"2020","journal-title":"CMAJ"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"395","DOI":"10.7326\/M20-5834","article-title":"Ethical framework for assessing manual and digital contact tracing for COVID-19","volume":"174","author":"Lo","year":"2021","journal-title":"Ann. Intern. Med."},{"key":"ref_11","first-page":"2021","article-title":"WiFi mobility models for COVID-19 enable less burdensome and more localized interventions for university campuses","volume":"16","author":"Swain","year":"2021","journal-title":"medRxiv"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"100307","DOI":"10.1016\/j.cosrev.2020.100307","article-title":"Applicability of mobile contact tracing in fighting pandemic (COVID-19): Issues, challenges and solutions","volume":"38","author":"Dar","year":"2020","journal-title":"Comput. Sci. Rev."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1038\/s41586-020-2923-3","article-title":"Mobility network models of COVID-19 explain inequities and inform reopening","volume":"589","author":"Chang","year":"2021","journal-title":"Nature"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1016\/S2213-2600(20)30453-7","article-title":"False-positive COVID-19 results: Hidden problems and costs","volume":"8","author":"Surkova","year":"2020","journal-title":"Lancet Respir. Med."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2369","DOI":"10.1007\/s11469-020-00331-y","article-title":"Fear of COVID-19 and positivity: Mediating role of intolerance of uncertainty, depression, anxiety, and stress","volume":"19","author":"Korkmaz","year":"2021","journal-title":"Int. J. Ment. Health Addict."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Rocha, L.E., Liljeros, F., and Holme, P. (2011). Simulated epidemics in an empirical spatiotemporal network of 50,185 sexual contacts. PLoS Comput. Biol., 7.","DOI":"10.1371\/journal.pcbi.1001109"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1006\/jagm.1999.1042","article-title":"Approximation algorithms for directed Steiner problems","volume":"33","author":"Charikar","year":"1999","journal-title":"J. Algorithms"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Osthus, D., Daughton, A.R., and Priedhorsky, R. (2019). Even a good influenza forecasting model can benefit from internet-based nowcasts, but those benefits are limited. PLoS Comput. Biol., 15.","DOI":"10.1371\/journal.pcbi.1006599"},{"key":"ref_19","unstructured":"Kamarthi, H., Rodr\u00edguez, A., and Prakash, B.A. (2021). Back2Future: Leveraging Backfill Dynamics for Improving Real-time Predictions in Future. arXiv."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Kim, M., and Leskovec, J. (2011). The Network Completion Problem: Inferring Missing Nodes and Edges in Networks. Proceedings of the 2011 SIAM International Conference on Data Mining (SDM), SIAM.","DOI":"10.1137\/1.9781611972818.5"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1109\/TETC.2023.3282539","article-title":"Graph embedding techniques for predicting missing links in biological networks: An empirical evaluation","volume":"12","author":"Teji","year":"2023","journal-title":"IEEE Trans. Emerg. Top. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"104392","DOI":"10.1016\/j.jprot.2021.104392","article-title":"PROTREC: A probability-based approach for recovering missing proteins based on biological networks","volume":"250","author":"Kong","year":"2022","journal-title":"J. Proteom."},{"key":"ref_23","unstructured":"Hao, Q., Diwan, N., Yuan, Y., Apruzzese, G., Conti, M., and Wang, G. (2024, January 14\u201316). It doesn\u2019t look like anything to me: Using diffusion model to subvert visual phishing detectors. Proceedings of the 33rd USENIX Security Symposium (USENIX Security 24), Philadelphia, PA, USA."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wang, T., Zhuo, L., Chen, Y., Fu, X., Zeng, X., and Zou, Q. (2024). ECD-CDGI: An efficient energy-constrained diffusion model for cancer driver gene identification. PLoS Comput. Biol., 20.","DOI":"10.1371\/journal.pcbi.1012400"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Xie, J., Tandon, R., and Mitchell, C.S. (2025). Network Diffusion-Constrained Variational Generative Models for Investigating the Molecular Dynamics of Brain Connectomes Under Neurodegeneration. Int. J. Mol. Sci., 26.","DOI":"10.3390\/ijms26031062"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1136\/jech-2020-214051","article-title":"Efficacy of contact tracing for the containment of the 2019 novel coronavirus (COVID-19)","volume":"74","author":"Keeling","year":"2020","journal-title":"J. Epidemiol. Community Health"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5163","DOI":"10.1109\/TIT.2011.2158885","article-title":"Rumors in a network: Who\u2019s the culprit?","volume":"57","author":"Shah","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/s10115-013-0671-5","article-title":"Efficiently spotting the starting points of an epidemic in a large graph","volume":"38","author":"Prakash","year":"2014","journal-title":"Knowl. Inf. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Sundareisan, S., Vreeken, J., and Prakash, B.A. (2015). Hidden hazards: Finding missing nodes in large graph epidemics. Proceedings of the 2015 SIAM International Conference on Data Mining, SIAM.","DOI":"10.1137\/1.9781611974010.47"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Makar, M., Guttag, J., and Wiens, J. (2018, January 2\u20137). Learning the probability of activation in the presence of latent spreaders. Proceedings of the AAAI Conference on Artificial Intelligence, New Orleans, LA, USA.","DOI":"10.1609\/aaai.v32i1.11305"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Wang, J., Jiang, J., and Zhao, L. (2022, January 25\u201329). An invertible graph diffusion neural network for source localization. Proceedings of the ACM Web Conference 2022, Lyon, France.","DOI":"10.1145\/3485447.3512155"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Ling, C., Jiang, J., Wang, J., and Liang, Z. (2022, January 14\u201318). Source localization of graph diffusion via variational autoencoders for graph inverse problems. Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, Washington, DC, USA.","DOI":"10.1145\/3534678.3539288"},{"key":"ref_33","unstructured":"He, Q., Bao, Y., Fang, H., Lin, Y., and Sun, H. (March, January 25). Hhan: Comprehensive infectious disease source tracing via heterogeneous hypergraph neural network. Proceedings of the AAAI Conference on Artificial Intelligence, Philadelphia, PA, USA."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Cheng, L., Zhu, P., Tang, K., Gao, C., and Wang, Z. (2024, January 20\u201327). GIN-SD: Source detection in graphs with incomplete nodes via positional encoding and attentive fusion. Proceedings of the AAAI Conference on Artificial Intelligence, Vancouver, BC, Canada.","DOI":"10.1609\/aaai.v38i1.27755"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1561\/2400000013","article-title":"Introduction to online convex optimization","volume":"2","author":"Hazan","year":"2016","journal-title":"Found. Trends\u00ae Optim."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1140\/epjds\/s13688-021-00302-w","article-title":"Using wearable proximity sensors to characterize social contact patterns in a village of rural Malawi","volume":"10","author":"Ozella","year":"2021","journal-title":"EPJ Data Sci."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Rossi, R.A., and Ahmed, N.K. (2015, January 25\u201330). The Network Data Repository with Interactive Graph Analytics and Visualization. Proceedings of the AAAI Conference on Artificial Intelligence, Austin, TX, USA.","DOI":"10.1609\/aaai.v29i1.9277"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1109\/TKDE.2017.2776282","article-title":"Propagation-based temporal network summarization","volume":"30","author":"Adhikari","year":"2017","journal-title":"IEEE Trans. Knowl. Data Eng."}],"container-title":["Big Data and Cognitive Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2504-2289\/9\/10\/262\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T04:10:39Z","timestamp":1760847039000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2504-2289\/9\/10\/262"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,16]]},"references-count":38,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["bdcc9100262"],"URL":"https:\/\/doi.org\/10.3390\/bdcc9100262","relation":{},"ISSN":["2504-2289"],"issn-type":[{"type":"electronic","value":"2504-2289"}],"subject":[],"published":{"date-parts":[[2025,10,16]]}}}