{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T20:28:57Z","timestamp":1787171337705,"version":"3.56.0"},"reference-count":76,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,8,8]],"date-time":"2026-08-08T00:00:00Z","timestamp":1786147200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/100020655","name":"European Health and Digital Executive Agency","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100020655","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Foundation for Science and Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005855","name":"Universidade Nova de Lisboa","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100005855","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Neurocomputing"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.neucom.2026.134773","type":"journal-article","created":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T15:45:03Z","timestamp":1786376703000},"page":"134773","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Gaussian mixture modeling layer and its application to end-to-end generative high-dimensional clustering"],"prefix":"10.1016","volume":"703","author":[{"given":"Alexandre","family":"Marques","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4862-8177","authenticated-orcid":false,"given":"Roberto","family":"Henriques","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mauro","family":"Castelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.neucom.2026.134773_bib0005","series-title":"Proceedings of the 14th International Conference on Artificial Intelligence and Statistics (AISTATS)","article-title":"An analysis of single layer networks in unsupervised feature learning","author":"Adam Coates","year":"2011"},{"key":"10.1016\/j.neucom.2026.134773_bib0010","series-title":"Neural Networks for Pattern Recognition","author":"Bishop","year":"1995"},{"key":"10.1016\/j.neucom.2026.134773_bib0015","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/BF00332918","article-title":"Auto-association by multilayer perceptrons and singular value decomposition","volume":"59","author":"Bourlard","year":"1988","journal-title":"Biol. Cybern."},{"key":"10.1016\/j.neucom.2026.134773_bib0020","series-title":"Proceedings of the 20th SIGNLL Conference on Computational Natural Language Learning","first-page":"10","article-title":"Generating sentences from a continuous space","author":"Bowman","year":"2016"},{"key":"10.1016\/j.neucom.2026.134773_bib0025","series-title":"Machine Learning and Knowledge Discovery in Databases","first-page":"108","article-title":"Simple, scalable, and stable variational deep clustering","author":"Cao","year":"2021"},{"key":"10.1016\/j.neucom.2026.134773_bib0030","series-title":"Computer Vision \u2013 ECCV 2018: 15th European Conference, Munich, Germany, September 8\u201314, 2018, Proceedings, Part XIV","first-page":"139","article-title":"Deep clustering for unsupervised learning of visual features","author":"Caron","year":"2018"},{"key":"10.1016\/j.neucom.2026.134773_bib0035","series-title":"Advances in Neural Information Processing Systems","first-page":"9912","article-title":"Unsupervised learning of visual features by contrasting cluster assignments","author":"Caron","year":"2020"},{"key":"10.1016\/j.neucom.2026.134773_bib0040","series-title":"2021 IEEE\/CVF International Conference on Computer Vision (ICCV)","first-page":"9630","article-title":"Emerging properties in self-supervised vision transformers","author":"Caron","year":"2021"},{"key":"10.1016\/j.neucom.2026.134773_bib0045","author":"Celarek"},{"key":"10.1016\/j.neucom.2026.134773_bib0050","series-title":"Proceedings of the 37th International Conference on Machine Learning (ICML)","first-page":"1597","article-title":"A simple framework for contrastive learning of visual representations","author":"Chen","year":"2020"},{"key":"10.1016\/j.neucom.2026.134773_bib0055","series-title":"Proceedings of the 30th International Conference on Neural Information Processing Systems","first-page":"2180","article-title":"InfoGAN: interpretable representation learning by information maximizing generative adversarial nets","author":"Chen","year":"2016"},{"key":"10.1016\/j.neucom.2026.134773_bib0060","author":"Datta"},{"key":"10.1016\/j.neucom.2026.134773_bib0065","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood from incomplete data via the EM algorithm","volume":"39","author":"Dempster","year":"2018","journal-title":"J. R. Stat. Soc.: B (Methodol.)"},{"key":"10.1016\/j.neucom.2026.134773_bib0070","series-title":"2009 IEEE Conference on Computer Vision and Pattern Recognition","first-page":"248","article-title":"ImageNet: a large-scale hierarchical image database","author":"Deng","year":"2009"},{"key":"10.1016\/j.neucom.2026.134773_bib0075","author":"Dilokthanakul"},{"key":"10.1016\/j.neucom.2026.134773_bib0080","series-title":"2017 IEEE International Conference on Computer Vision (ICCV)","first-page":"5747","article-title":"Deep clustering via joint convolutional autoencoder embedding and relative entropy minimization","author":"Dizaji","year":"2017"},{"key":"10.1016\/j.neucom.2026.134773_bib0085","series-title":"NeurIPS","article-title":"Is simple better?: Revisiting simple generative models for unsupervised clustering","author":"Figueroa","year":"2017"},{"key":"10.1016\/j.neucom.2026.134773_bib0090","author":"Graves"},{"key":"10.1016\/j.neucom.2026.134773_bib0095","author":"Grill"},{"key":"10.1016\/j.neucom.2026.134773_bib0100","article-title":"Gaussian mixture model and deep neural network based vehicle detection and classification","volume":"7","author":"Harsha","year":"2016","journal-title":"Int. J. Adv. Comput. Sci. Appl."},{"key":"10.1016\/j.neucom.2026.134773_bib0105","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1214\/aos\/1176346577","article-title":"The dip test of unimodality","volume":"13","author":"Hartigan","year":"1985","journal-title":"Ann. Stat."},{"key":"10.1016\/j.neucom.2026.134773_bib0110","first-page":"320","article-title":"Computation of the dip statistic to test for unimodality","volume":"34","author":"Hartigan","year":"2018","journal-title":"J. R. Stat. Soc. C Appl. Stat."},{"key":"10.1016\/j.neucom.2026.134773_bib0115","series-title":"Proceedings of the 7th International Conference on Neural Information Processing Systems","first-page":"3","article-title":"Autoencoders, minimum description length and helmholtz free energy","author":"Hinton","year":"1993"},{"key":"10.1016\/j.neucom.2026.134773_bib0120","series-title":"Proceedings of the 34th International Conference on Machine Learning - Volume 70","first-page":"1558","article-title":"Learning discrete representations via information maximizing self-augmented training","author":"Hu","year":"2017"},{"key":"10.1016\/j.neucom.2026.134773_bib0125","series-title":"Hidden Markov Models for Speech Recognition","author":"Huang","year":"1990"},{"key":"10.1016\/j.neucom.2026.134773_bib0130","series-title":"Proceedings of the IEEE\/CVF International Conference on Computer Vision (ICCV)","article-title":"Invariant information clustering for unsupervised image classification and segmentation","author":"Ji","year":"2019"},{"key":"10.1016\/j.neucom.2026.134773_bib0135","series-title":"Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering","first-page":"1965","author":"Jiang","year":"2017"},{"key":"10.1016\/j.neucom.2026.134773_bib0140","doi-asserted-by":"crossref","first-page":"1404","DOI":"10.1109\/TASSP.1985.1164727","article-title":"Mixture autoregressive hidden Markov models for speech signals","volume":"33","author":"Juang","year":"1985","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"10.1016\/j.neucom.2026.134773_bib0145","first-page":"71","article-title":"III. contributions to the mathematical theory of evolution","volume":"185","author":"Karl","year":"1894","journal-title":"Philos. Trans. R. Soc. Lond. (A.)"},{"key":"10.1016\/j.neucom.2026.134773_bib0150","series-title":"International Conference on Learning Representations","article-title":"Adam: a method for stochastic optimization","author":"Kingma","year":"2014"},{"key":"10.1016\/j.neucom.2026.134773_bib0155","article-title":"Semi-supervised learning with deep generative models","volume":"4","author":"Kingma","year":"2014","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.134773_bib0160","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1561\/2200000056","article-title":"An introduction to variational autoencoders","volume":"12","author":"Kingma","year":"2019","journal-title":"Found. Trends\u00ae Mach. Learn."},{"key":"10.1016\/j.neucom.2026.134773_bib0165","series-title":"Learning Multiple Layers of Features From Tiny Images","author":"Krizhevsky","year":"2009"},{"key":"10.1016\/j.neucom.2026.134773_bib0170","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1002\/nav.3800020109","article-title":"The Hungarian method for the assignment problem","volume":"2","author":"Kuhn","year":"1955","journal-title":"Nav. Res. Logist. Q."},{"key":"10.1016\/j.neucom.2026.134773_bib0175","author":"LeCun"},{"key":"10.1016\/j.neucom.2026.134773_bib0180","article-title":"Modeles connexionnistes de l\u2019apprentissage","volume":"2","author":"Lecun","year":"1987","journal-title":"Intellectica spec. issue apprentiss. mach."},{"key":"10.1016\/j.neucom.2026.134773_bib0185","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1109\/TMM.2012.2229969","article-title":"Continuous birdsong recognition using Gaussian mixture modeling of image shape features","volume":"15","author":"Lee","year":"2013","journal-title":"IEEE Trans. Multimed."},{"key":"10.1016\/j.neucom.2026.134773_bib0190","author":"Leiber"},{"key":"10.1016\/j.neucom.2026.134773_bib0195","series-title":"Publisher Copyright: \u00a9 2021 ICLR 2021 - 9th International Conference on Learning Representations. All Rights Reserved.; 9th International Conference on Learning Representations, ICLR 2021; Conference Date: 03-05-2021 Through 07-05-2021","article-title":"Prototypical contrastive learning of unsupervised representations","author":"Li","year":"2021"},{"key":"10.1016\/j.neucom.2026.134773_bib0200","series-title":"Proceedings of the 36th International Conference on Neural Information Processing Systems","article-title":"GMMSeg: Gaussian mixture based generative semantic segmentation models","author":"Liang","year":"2022"},{"key":"10.1016\/j.neucom.2026.134773_bib0205","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1109\/TIT.1982.1056544","article-title":"Maximum likelihood estimation for multivariate observations of Markov sources","volume":"28","author":"Liporace","year":"2006","journal-title":"IEEE Trans. Inf. Theor."},{"key":"10.1016\/j.neucom.2026.134773_bib0210","series-title":"CAIBDA 2022; 2nd International Conference on Artificial Intelligence, Big Data and Algorithms","first-page":"1","article-title":"Super convergence cosine annealing with warm-up learning rate","author":"Liu","year":"2022"},{"key":"10.1016\/j.neucom.2026.134773_bib0215","author":"Lu"},{"key":"10.1016\/j.neucom.2026.134773_bib0220","doi-asserted-by":"crossref","DOI":"10.3934\/mbe.2022484","article-title":"Achieving deep clustering through the use of variational autoencoders and similarity-based loss","volume":"19","author":"Ma","year":"2022","journal-title":"Math. Biosci. Eng."},{"key":"10.1016\/j.neucom.2026.134773_bib0225","series-title":"Finite Mixture Models","author":"McLachlan","year":"2000"},{"key":"10.1016\/j.neucom.2026.134773_bib0230","doi-asserted-by":"crossref","first-page":"39501","DOI":"10.1109\/ACCESS.2018.2855437","article-title":"A survey of clustering with deep learning: from the perspective of network architecture","volume":"6","author":"Min","year":"2018","journal-title":"IEEE Access"},{"key":"10.1016\/j.neucom.2026.134773_bib0235","series-title":"AAAI Conference on Artificial Intelligence","article-title":"ClusterGAN: latent space clustering in generative adversarial networks","author":"Mukherjee","year":"2018"},{"key":"10.1016\/j.neucom.2026.134773_bib0240","author":"van den Oord"},{"key":"10.1016\/j.neucom.2026.134773_bib0245","series-title":"Advances in Neural Information Processing Systems","article-title":"Factoring variations in natural images with deep Gaussian mixture models","author":"Van den Oord","year":"2014"},{"key":"10.1016\/j.neucom.2026.134773_bib0250","author":"Oquab"},{"key":"10.1016\/j.neucom.2026.134773_bib0255","series-title":"2020 International Joint Conference on Neural Networks (IJCNN)","first-page":"1","article-title":"Variational clustering: leveraging variational autoencoders for image clustering","author":"Prasad","year":"2020"},{"key":"10.1016\/j.neucom.2026.134773_bib0260","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1137\/1026034","article-title":"Mixture densities, maximum likelihood and the EM algorithm","volume":"26","author":"Redner","year":"1984","journal-title":"SIAM Rev."},{"key":"10.1016\/j.neucom.2026.134773_bib0265","doi-asserted-by":"crossref","first-page":"5858","DOI":"10.1109\/TNNLS.2024.3403155","article-title":"Deep clustering: a comprehensive survey","volume":"36","author":"Ren","year":"2025","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"10.1016\/j.neucom.2026.134773_bib0270","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1109\/89.365379","article-title":"Robust text-independent speaker identification using Gaussian mixture speaker models","volume":"3","author":"Reynolds","year":"1995","journal-title":"IEEE Trans. Speech Audio Process."},{"key":"10.1016\/j.neucom.2026.134773_bib0275","series-title":"Proceedings of the 31st International Conference on Machine Learning","first-page":"1278","article-title":"Stochastic backpropagation and approximate inference in deep generative models","author":"Rezende","year":"2014"},{"key":"10.1016\/j.neucom.2026.134773_bib0280","author":"Roy"},{"key":"10.1016\/j.neucom.2026.134773_bib0285","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s11263-015-0816-y","article-title":"ImageNet large scale visual recognition challenge","volume":"115","author":"Russakovsky","year":"2015","journal-title":"Int. J. Comput. Vis."},{"key":"10.1016\/j.neucom.2026.134773_bib0290","series-title":"International Conference on Machine Learning, Optimization, and Data Science","first-page":"339","article-title":"Deep Gaussian mixture model for unsupervised image segmentation","author":"Schwab","year":"2024"},{"key":"10.1016\/j.neucom.2026.134773_bib0295","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"10.1016\/j.neucom.2026.134773_bib0300","series-title":"Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications","first-page":"117","article-title":"Auto-encoder based data clustering","author":"Song","year":"2013"},{"key":"10.1016\/j.neucom.2026.134773_bib0305","author":"S\u00f8nderby"},{"key":"10.1016\/j.neucom.2026.134773_bib0310","series-title":"Statistical Analysis of Finite Mixture Distributions","author":"Titterington","year":"1985"},{"key":"10.1016\/j.neucom.2026.134773_bib0315","series-title":"On the Use of Gaussian Mixture Model Framework to Improve Speaker Adaptation of Deep Neural Network Acoustic Models","first-page":"3788","author":"Tomashenko","year":"2016"},{"key":"10.1016\/j.neucom.2026.134773_bib0320","series-title":"The Elements of Statistical Learning","author":"Trevor Hastie","year":"2009"},{"key":"10.1016\/j.neucom.2026.134773_bib0325","series-title":"Asymptotic Statistics","author":"Vaart","year":"1998"},{"key":"10.1016\/j.neucom.2026.134773_bib0330","series-title":"Computer Vision \u2013 ECCV 2020","first-page":"268","article-title":"SCAN: learning to classify images without labels","author":"Van Gansbeke","year":"2020"},{"key":"10.1016\/j.neucom.2026.134773_bib0335","series-title":"2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","first-page":"4270","article-title":"A Gaussian mixture model layer jointly optimized with discriminative features within a deep neural network architecture","author":"Variani","year":"2015"},{"key":"10.1016\/j.neucom.2026.134773_bib0340","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.neucom.2020.12.082","article-title":"Unsupervised deep clustering via adaptive GMM modeling and optimization","volume":"433","author":"Wang","year":"2021","journal-title":"Neurocomputing"},{"key":"10.1016\/j.neucom.2026.134773_bib0345","doi-asserted-by":"crossref","DOI":"10.1016\/j.neucom.2024.127761","article-title":"An overview on deep clustering","volume":"590","author":"Wei","year":"2024","journal-title":"Neurocomputing"},{"key":"10.1016\/j.neucom.2026.134773_bib0350","author":"Xiao"},{"key":"10.1016\/j.neucom.2026.134773_bib0355","author":"Xie"},{"key":"10.1016\/j.neucom.2026.134773_bib0360","series-title":"14th Annual Conference of the International Speech Communication Association, InterSpeech 2013","article-title":"A scalable approach to using DNN-derived features in GMM-HMM based acoustic modeling for LVCSR","author":"Yan","year":"2013"},{"key":"10.1016\/j.neucom.2026.134773_bib0365","series-title":"Proceedings of the 34th International Conference on Machine Learning - Volume 70","first-page":"3861","article-title":"Towards K-means-friendly spaces: simultaneous deep learning and clustering","author":"Yang","year":"2017"},{"key":"10.1016\/j.neucom.2026.134773_bib0370","series-title":"2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)","first-page":"5147","article-title":"Joint unsupervised learning of deep representations and image clusters","author":"Yang","year":"2016"},{"key":"10.1016\/j.neucom.2026.134773_bib0375","doi-asserted-by":"crossref","DOI":"10.1016\/j.compeleceng.2020.106603","article-title":"A Gaussian mixture based hidden Markov model for motion recognition with 3D vision device","volume":"83","author":"Zhang","year":"2020","journal-title":"Comput. & Electr. Eng."},{"key":"10.1016\/j.neucom.2026.134773_bib0380","author":"Zhou"}],"container-title":["Neurocomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0925231226021715?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0925231226021715?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T20:15:17Z","timestamp":1787170517000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0925231226021715"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":76,"alternative-id":["S0925231226021715"],"URL":"https:\/\/doi.org\/10.1016\/j.neucom.2026.134773","relation":{},"ISSN":["0925-2312"],"issn-type":[{"value":"0925-2312","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Gaussian mixture modeling layer and its application to end-to-end generative high-dimensional clustering","name":"articletitle","label":"Article Title"},{"value":"Neurocomputing","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.neucom.2026.134773","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"134773"}}