{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T15:49:35Z","timestamp":1750780175243,"version":"3.41.0"},"reference-count":78,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2024,7,12]],"date-time":"2024-07-12T00:00:00Z","timestamp":1720742400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100006168","name":"DOE National Nuclear Security Administration","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100006168","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Office of Defense Nuclear Non-proliferation R&D"},{"name":"U.S. Department of Energy National Nuclear Security Administration","award":["DE-AC52-06NA25396"],"award-info":[{"award-number":["DE-AC52-06NA25396"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Model. Comput. Simul."],"published-print":{"date-parts":[[2024,10,31]]},"abstract":"<jats:p>Monitoring of industrial processes is a critical capability in industry and in government to ensure reliability of production cycles, quick emergency response, and national security. Process monitoring allows users to gauge the progress of an organization in an industrial process or predict the degradation or aging of machine parts in processes taking place at a remote location. Similar to many data science applications, we usually only have access to limited raw data, such as satellite imagery, short video clips, event logs, and signatures captured by a small set of sensors. To combat data scarcity, we leverage the knowledge of Subject Matter Experts (SMEs) who are familiar with the actions of interest. SMEs provide expert knowledge of the essential activities required for task completion and the resources necessary to carry out each of these activities. Various process mining techniques have been developed for this type of analysis; typically such approaches combine theoretical process models built based on domain expert insights with ad-hoc integration of available pieces of raw data. Here, we introduce a novel mathematically sound method that integrates theoretical process models (as proposed by SMEs) with interrelated minimal Hidden Markov Models (HMM), built via nonnegative tensor factorization. Our method consolidates: (a) theoretical process models, (b) HMMs, (c) coupled nonnegative matrix-tensor factorizations, and (d) custom model selection. To demonstrate our methodology and its abilities, we apply it on simple synthetic and real-world process models.<\/jats:p>","DOI":"10.1145\/3664813","type":"journal-article","created":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T11:12:44Z","timestamp":1718017964000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Generating Hidden Markov Models from Process Models Through Nonnegative Tensor Factorization"],"prefix":"10.1145","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7707-0838","authenticated-orcid":false,"given":"Erik","family":"Skau","sequence":"first","affiliation":[{"name":"Los Alamos National Laboratory, Los Alamos, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1972-7731","authenticated-orcid":false,"given":"Andrew","family":"Hollis","sequence":"additional","affiliation":[{"name":"North Carolina State University at Raleigh, Raleigh, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2628-1854","authenticated-orcid":false,"given":"Stephan","family":"Eidenbenz","sequence":"additional","affiliation":[{"name":"Los Alamos National Laboratory, Los Alamos, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4029-4723","authenticated-orcid":false,"given":"Kim","family":"Rasmussen","sequence":"additional","affiliation":[{"name":"Los Alamos National Laboratory, Los Alamos, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8636-4603","authenticated-orcid":false,"given":"Boian","family":"Alexandrov","sequence":"additional","affiliation":[{"name":"Los Alamos National Laboratory, Los Alamos, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2024,7,12]]},"reference":[{"key":"e_1_3_1_2_2","unstructured":"Evrim Acar Tamara G. Kolda and Daniel M. Dunlavy. 2011. All-at-once optimization for coupled matrix and tensor factorizations. Retrieved from https:\/\/arXiv:1105.3422"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNSM.2021.3051381"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0101003"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2443"},{"key":"e_1_3_1_6_2","unstructured":"Boian S. Alexandrov Ludmil B. Alexandrov Filip L. Iliev Valentin G. Stanev and Velimir V. Vesselinov. 2020. Source identification by non-negative matrix factorization combined with semi-supervised clustering. U.S. Patent 10 776 718."},{"key":"e_1_3_1_7_2","unstructured":"Boian S. Alexandrov and Kim Orskov Rasmussen. 2021. SmartTensors AI Platform. Los Alamos National Laboratory Technical Report LA-UR-21-25064."},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/sam.11407"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature12477"},{"key":"e_1_3_1_10_2","volume-title":"Unsupervised Abstraction for Reducing the Complexity of Healthcare Process Models","author":"Alharbi Amirah Mohammed","year":"2019","unstructured":"Amirah Mohammed Alharbi. 2019. Unsupervised Abstraction for Reducing the Complexity of Healthcare Process Models. Ph. D. Dissertation. University of Leeds."},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS689"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1089\/106652700750050844"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177697196"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpdc.2023.04.010"},{"key":"e_1_3_1_15_2","article-title":"Bayesian pca","volume":"11","author":"Bishop Christopher","year":"1998","unstructured":"Christopher Bishop. 1998. Bayesian pca. Adv. Neural Info. Process. Syst. 11 (1998).","journal-title":"Adv. Neural Info. Process. Syst."},{"key":"e_1_3_1_16_2","article-title":"An entropic estimator for structure discovery","volume":"11","author":"Brand Matthew","year":"1998","unstructured":"Matthew Brand. 1998. An entropic estimator for structure discovery. Adv. Neural Info. Process. Syst. 11 (1998).","journal-title":"Adv. Neural Info. Process. Syst."},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00216-007-1790-1"},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0308531101"},{"key":"e_1_3_1_19_2","first-page":"477","volume-title":"Proceedings of the International Conference on Business Process Management","author":"Carrera Berny","year":"2014","unstructured":"Berny Carrera and Jae-Yoon Jung. 2014. Constructing probabilistic process models based on hidden Markov models for resource allocation. In Proceedings of the International Conference on Business Process Management. Springer, 477\u2013488."},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1137\/110859063"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1109\/IEMBS.1998.747073"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2132490"},{"key":"e_1_3_1_23_2","article-title":"Applying hidden Markov models to process mining","author":"Silva Gil Aires Da","year":"2009","unstructured":"Gil Aires Da Silva and Diogo R. Ferreira. 2009. Applying hidden Markov models to process mining. Sistemas e Tecnologias de Informa\u00e7\u00e3o. AISTI\/FEUP\/UPF (2009).","journal-title":"Sistemas e Tecnologias de Informa\u00e7\u00e3o. AISTI\/FEUP\/UPF"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1145\/3522594"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.1006\/nimg.1998.0425"},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.1137\/04061101X"},{"key":"e_1_3_1_27_2","first-page":"2068","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Huang Kejun","year":"2018","unstructured":"Kejun Huang, Xiao Fu, and Nicholas Sidiropoulos. 2018. Learning hidden Markov models from pairwise co-occurrences with application to topic modeling. In Proceedings of the International Conference on Machine Learning. PMLR, 2068\u20132077."},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2015.2510969"},{"issue":"11","key":"e_1_3_1_29_2","article-title":"Uncovering novel mutational signatures by de novo extraction with SigProfilerExtractor","volume":"2","author":"Islam S. M. Ashiqul","year":"2022","unstructured":"S. M. Ashiqul Islam, Marcos D\u00edaz-Gay, Yang Wu, Mark Barnes, Raviteja Vangara, Erik N. Bergstrom, Yudou He, Mike Vella, Jingwei Wang, Jon W. Teague et\u00a0al. 2022. Uncovering novel mutational signatures by de novo extraction with SigProfilerExtractor. Cell Genom. 2, 11 (2022).","journal-title":"Cell Genom."},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.1109\/ColCACI.2019.8781973"},{"issue":"11","key":"e_1_3_1_31_2","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1016\/0196-6774(90)90014-6","article-title":"Tensor rank is NP-complete","volume":"4","author":"Johan Hastad","year":"1990","unstructured":"Hastad Johan. 1990. Tensor rank is NP-complete. J. Algor. 4, 11 (1990), 644\u2013654.","journal-title":"J. Algor."},{"key":"e_1_3_1_32_2","unstructured":"Anna Kalenkova Lewis Mitchell and Matthew Roughan. 2022. Performance analysis: Discovering semi-Markov models from event logs. Retrieved from https:\/\/arXiv:2206.14415"},{"key":"e_1_3_1_33_2","first-page":"167","article-title":"Solutions to some functional equations and their applications to characterization of probability distributions","author":"Khatri C. G.","year":"1968","unstructured":"C. G. Khatri and C. Radhakrishna Rao. 1968. Solutions to some functional equations and their applications to characterization of probability distributions. Sankhy\u0101: Indian J. Stat. A (1968), 167\u2013180.","journal-title":"Sankhy\u0101: Indian J. Stat. A"},{"key":"e_1_3_1_34_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-013-0035-4"},{"key":"e_1_3_1_35_2","doi-asserted-by":"publisher","DOI":"10.1137\/07070111X"},{"key":"e_1_3_1_36_2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(77)90069-6"},{"key":"e_1_3_1_37_2","doi-asserted-by":"publisher","DOI":"10.1155\/2008\/764206"},{"key":"e_1_3_1_38_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.dsp.2016.01.003"},{"key":"e_1_3_1_39_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2019.2903736"},{"key":"e_1_3_1_40_2","unstructured":"David J. C MacKay and others. 1994. Bayesian nonlinear modeling for the prediction competition. ASHRAE Transactions 100 2 (1994) 1053\u20131062."},{"issue":"6","key":"e_1_3_1_41_2","article-title":"The Hadamard product","volume":"3","author":"Million Elizabeth","year":"2007","unstructured":"Elizabeth Million. 2007. The Hadamard product. Course Notes 3, 6 (2007).","journal-title":"Course Notes"},{"key":"e_1_3_1_42_2","doi-asserted-by":"publisher","DOI":"10.1137\/S00361445024180"},{"key":"e_1_3_1_43_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0207806"},{"key":"e_1_3_1_44_2","doi-asserted-by":"publisher","DOI":"10.1002\/cem.1223"},{"key":"e_1_3_1_45_2","first-page":"1923","volume-title":"Proceedings of the 17th European Signal Processing Conference","author":"M\u00f8rup Morten","year":"2009","unstructured":"Morten M\u00f8rup and Lars Kai Hansen. 2009. Tuning pruning in sparse non-negative matrix factorization. In Proceedings of the 17th European Signal Processing Conference. IEEE, 1923\u20131927."},{"issue":"2","key":"e_1_3_1_46_2","first-page":"025012","article-title":"A neural network for determination of latent dimensionality in non-negative matrix factorization","volume":"2","author":"Nebgen Benjamin T.","year":"2021","unstructured":"Benjamin T. Nebgen, Raviteja Vangara, Miguel A. Hombrados-Herrera, Svetlana Kuksova, and Boian S. Alexandrov. 2021. A neural network for determination of latent dimensionality in non-negative matrix factorization. Mach. Learn.: Sci. Technol. 2, 2 (2021), 025012.","journal-title":"Mach. Learn.: Sci. Technol."},{"key":"e_1_3_1_47_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2021.06.170"},{"key":"e_1_3_1_48_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2005.130"},{"key":"e_1_3_1_49_2","volume-title":"Proceedings of the Eurographics Conference on Visualization (EuroVis\u201921)","author":"Pulido Jesus","year":"2021","unstructured":"Jesus Pulido, John Patchett, Manish Bhattarai, Boian Alexandrov, and James Ahrens. 2021. Selection of optimal salient time steps by non-negative tucker tensor decomposition. In Proceedings of the Eurographics Conference on Visualization (EuroVis\u201921)."},{"key":"e_1_3_1_50_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2532906"},{"key":"e_1_3_1_51_2","doi-asserted-by":"publisher","DOI":"10.1109\/MASSP.1986.1165342"},{"key":"e_1_3_1_52_2","doi-asserted-by":"publisher","DOI":"10.1109\/5.18626"},{"key":"e_1_3_1_53_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICSITech.2017.8257082"},{"key":"e_1_3_1_54_2","volume-title":"Stochastic Processes","author":"Ross Sheldon M.","year":"1996","unstructured":"Sheldon M. Ross. 1996. Stochastic Processes. Vol. 2. Wiley, New York, NY."},{"key":"e_1_3_1_55_2","doi-asserted-by":"publisher","DOI":"10.1109\/LCOMM.2015.2413407"},{"key":"e_1_3_1_56_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(87)90125-7"},{"key":"e_1_3_1_57_2","article-title":"Akaike information criterion statistics","author":"Sakamoto Yosiyuki","year":"1986","unstructured":"Yosiyuki Sakamoto, Makio Ishiguro, and Genshiro Kitagawa. 1986. Akaike information criterion statistics. In Mathematica and Its Applications, vol. 1. Springer, Dordrecht, The Netherlands, 290 pages.","journal-title":"Mathematica and Its Applications"},{"key":"e_1_3_1_58_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2021.3120656"},{"key":"e_1_3_1_59_2","doi-asserted-by":"publisher","DOI":"10.1109\/WSC.2015.7408405"},{"issue":"4","key":"e_1_3_1_60_2","first-page":"290","article-title":"Hidden Markov model for process mining of parallel business processes","volume":"11","author":"Sarno Riyanarto","year":"2016","unstructured":"Riyanarto Sarno and Kelly R. Sungkono. 2016. Hidden Markov model for process mining of parallel business processes. Int. Rev. Comput. Softw. 11, 4 (2016), 290\u2013300.","journal-title":"Int. Rev. Comput. Softw."},{"key":"e_1_3_1_61_2","doi-asserted-by":"publisher","DOI":"10.1137\/090763202"},{"key":"e_1_3_1_62_2","doi-asserted-by":"publisher","DOI":"10.23919\/Eusipco47968.2020.9287459"},{"key":"e_1_3_1_63_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6377(93)90049-M"},{"key":"e_1_3_1_64_2","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344136"},{"key":"e_1_3_1_65_2","volume-title":"Proceedings of the 10th USENIX Security Symposium (USENIX Security\u201901)","author":"Song Dawn Xiaodong","year":"2001","unstructured":"Dawn Xiaodong Song, David Wagner, and Xuqing Tian. 2001. Timing analysis of keystrokes and timing attacks onSSH. In Proceedings of the 10th USENIX Security Symposium (USENIX Security\u201901)."},{"key":"e_1_3_1_66_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2018.03.006"},{"key":"e_1_3_1_67_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.2014.6854796"},{"key":"e_1_3_1_68_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2012.240"},{"key":"e_1_3_1_69_2","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/aba9ee"},{"key":"e_1_3_1_70_2","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2013.6620636"},{"key":"e_1_3_1_71_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.is.2006.05.003"},{"key":"e_1_3_1_72_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.023248"},{"key":"e_1_3_1_73_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICMLA51294.2020.00060"},{"key":"e_1_3_1_74_2","doi-asserted-by":"publisher","DOI":"10.5555\/1212811"},{"key":"e_1_3_1_75_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.05.039"},{"key":"e_1_3_1_76_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1967.1054010"},{"key":"e_1_3_1_77_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSC.2020.2988760"},{"key":"e_1_3_1_78_2","doi-asserted-by":"publisher","DOI":"10.1109\/JAS.2021.1004308"},{"key":"e_1_3_1_79_2","doi-asserted-by":"publisher","DOI":"10.1109\/HPCC-SmartCity-DSS50907.2020.00163"}],"container-title":["ACM Transactions on Modeling and Computer Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3664813","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3664813","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:17:29Z","timestamp":1750295849000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3664813"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,12]]},"references-count":78,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,10,31]]}},"alternative-id":["10.1145\/3664813"],"URL":"https:\/\/doi.org\/10.1145\/3664813","relation":{},"ISSN":["1049-3301","1558-1195"],"issn-type":[{"type":"print","value":"1049-3301"},{"type":"electronic","value":"1558-1195"}],"subject":[],"published":{"date-parts":[[2024,7,12]]},"assertion":[{"value":"2022-10-21","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-02-04","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-07-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}