{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T16:54:55Z","timestamp":1775667295594,"version":"3.50.1"},"reference-count":36,"publisher":"Public Library of Science (PLoS)","issue":"11","license":[{"start":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T00:00:00Z","timestamp":1762300800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100013409","name":"Sistema General de Regal\u00c3\u00adas de Colombia","doi-asserted-by":"publisher","award":["BPIN 2019000100-060"],"award-info":[{"award-number":["BPIN 2019000100-060"]}],"id":[{"id":"10.13039\/501100013409","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002753","name":"Universidad Nacional de Colombia","doi-asserted-by":"publisher","award":["Minciencias: 110192092354"],"award-info":[{"award-number":["Minciencias: 110192092354"]}],"id":[{"id":"10.13039\/501100002753","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"\n Classification methods based on deep learning require selecting between fully-supervised or weakly-supervised approaches, each presenting limitations in uncertainty quantification and interpretability. A framework unifying both supervision modes while maintaining quantifiable interpretation metrics remains unexplored. We introduce WiSDoM (Weakly-Supervised Density Matrices), which uses kernel matrices to model probability distributions of input data and their labels. The framework integrates: (1) differentiable kernel density matrices enabling stochastic gradient descent optimization, (2) local-global attention mechanisms for multi-scale feature weighting, (3) data-driven prototype generation through kernel space sampling, and (4) ordinal regression through density matrix operations. WiSDoM was validated through supervised patch classification (\n \n \n \n \n \n \u03ba<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n = 0.896) and weakly-supervised whole-slide classification (\n \n \n \n \n \n \u03ba<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n = 0.930) on histopathology images. WiSDoM generates three quantifiable outputs: posterior probability distributions, variance-based uncertainty maps, and phenotype prototypes. Through validation in a Gleason grading task at a patch and whole-slide level using histopathology images, WiSDoM demonstrated consistent performance across supervision modes (\n \n \n \n \n \n \u03ba<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n > 0.89) and prototype interpretability (0.88 expert agreement). These results show that kernel density matrices can serve as a foundation for classification models requiring both prediction interpretability and uncertainty quantification across supervision modes.\n <\/jats:p>","DOI":"10.1371\/journal.pone.0335826","type":"journal-article","created":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T18:38:24Z","timestamp":1762367904000},"page":"e0335826","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":1,"title":["Interpretable weakly-supervised learning through kernel density matrices: A digital pathology use case"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4154-0519","authenticated-orcid":true,"given":"Sebastian","family":"Medina","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eduardo","family":"Romero","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angel","family":"Cruz-Roa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9009-7288","authenticated-orcid":true,"given":"Fabio A.","family":"Gonz\u00e1lez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,11,5]]},"reference":[{"key":"pone.0335826.ref001","doi-asserted-by":"crossref","first-page":"105111","DOI":"10.1016\/j.compbiomed.2021.105111","article-title":"Transparency of deep neural networks for medical image analysis: a review of interpretability methods","volume":"140","author":"Z Salahuddin","year":"2022","journal-title":"Comput Biol Med."},{"key":"pone.0335826.ref002","unstructured":"Shao Z, Bian H, Chen Y, Wang Y, Zhang J, Ji X. TransMIL: transformer based correlated multiple instance learning for whole slide image classification. In: Advances in Neural Information Processing Systems. 2021. p. 2136\u201347."},{"key":"pone.0335826.ref003","unstructured":"Javed S, Juyal D, Padigela H, Taylor-Weiner A, Yu L, Prakash A. Additive MIL: intrinsically interpretable multiple instance learning for pathology. In: Advances in Neural Information Processing Systems. 2022. p. 20689\u2013702."},{"issue":"6","key":"pone.0335826.ref004","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1038\/s41551-020-00682-w","article-title":"Data-efficient and weakly supervised computational pathology on whole-slide images","volume":"5","author":"MY Lu","year":"2021","journal-title":"Nat Biomed Eng."},{"key":"pone.0335826.ref005","unstructured":"Gonz\u00e1lez FA, Ramos-Poll\u00e1n R, Gallego-Mejia JA. Kernel density matrices for probabilistic deep learning. 2023."},{"key":"pone.0335826.ref006","doi-asserted-by":"crossref","first-page":"105472","DOI":"10.1016\/j.compbiomed.2022.105472","article-title":"Grading diabetic retinopathy and prostate cancer diagnostic images with deep quantum ordinal regression","volume":"145","author":"S Toledo-Cort\u00e9s","year":"2022","journal-title":"Comput Biol Med."},{"issue":"12","key":"pone.0335826.ref007","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1038\/s44222-023-00096-8","article-title":"Artificial intelligence for digital and computational pathology","volume":"1","author":"AH Song","year":"2023","journal-title":"Nat Rev Bioeng."},{"issue":"11","key":"pone.0335826.ref008","doi-asserted-by":"crossref","first-page":"1596","DOI":"10.1038\/s41374-019-0275-0","article-title":"Deep learning assisted mitotic counting for breast cancer","volume":"99","author":"MCA Balkenhol","year":"2019","journal-title":"Lab Invest."},{"issue":"9","key":"pone.0335826.ref009","doi-asserted-by":"crossref","first-page":"1686","DOI":"10.1016\/j.ajpath.2019.05.007","article-title":"Pathology image analysis using segmentation deep learning algorithms","volume":"189","author":"S Wang","year":"2019","journal-title":"Am J Pathol."},{"issue":"1","key":"pone.0335826.ref010","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1038\/s41698-021-00174-3","article-title":"Computer extracted gland features from H&E predicts prostate cancer recurrence comparably to a genomic companion diagnostic test: a large multi-site study","volume":"5","author":"P Leo","year":"2021","journal-title":"NPJ Precis Oncol."},{"issue":"1","key":"pone.0335826.ref011","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1038\/s43856-023-00428-0","article-title":"Computational pathology identifies immune-mediated collagen disruption to predict clinical outcomes in gynecologic malignancies","volume":"4","author":"A Aggarwal","year":"2024","journal-title":"Commun Med (Lond)."},{"issue":"3","key":"pone.0335826.ref012","article-title":"Predicting biochemical recurrence in prostate cancer patients post-radical prostatectomy: a computational pathology approach using glandular and immune architecture features","volume":"104","author":"S Medina","year":"2024","journal-title":"Laboratory Investigation."},{"issue":"4","key":"pone.0335826.ref013","doi-asserted-by":"crossref","first-page":"722","DOI":"10.1016\/j.euf.2021.04.016","article-title":"Computationally derived cribriform area index from prostate cancer hematoxylin and eosin images is associated with biochemical recurrence following radical prostatectomy and is most prognostic in gleason grade group 2","volume":"7","author":"P Leo","year":"2021","journal-title":"Eur Urol Focus."},{"issue":"8","key":"pone.0335826.ref014","doi-asserted-by":"crossref","DOI":"10.1056\/EVIDoa2300023","article-title":"Artificial intelligence predictive model for hormone therapy use in prostate cancer","volume":"2","author":"DE Spratt","year":"2023","journal-title":"NEJM Evid."},{"key":"pone.0335826.ref015","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1200\/JCO.2025.43.16_suppl.1560","article-title":"Computational pathology to predict docetaxel benefit in patients with metastatic hormone-sensitive prostate cancer from the CHAARTED trial (ECOG-ACRIN E3805)","volume":"43","author":"SR Medina","year":"2025","journal-title":"JCO."},{"key":"pone.0335826.ref016","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.1200\/JCO.2025.43.16_suppl.1557","article-title":"Computational pathology to predict docetaxel benefit for high-risk localized prostate cancer in NRG\/RTOG 0521 (NCT00288080)","volume":"43","author":"SR Medina","year":"2025","journal-title":"JCO."},{"issue":"8","key":"pone.0335826.ref017","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1038\/s41591-019-0508-1","article-title":"Clinical-grade computational pathology using weakly supervised deep learning on whole slide images","volume":"25","author":"G Campanella","year":"2019","journal-title":"Nat Med."},{"issue":"2","key":"pone.0335826.ref018","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/S1470-2045(19)30739-9","article-title":"Automated deep-learning system for Gleason grading of prostate cancer using biopsies: a diagnostic study","volume":"21","author":"W Bulten","year":"2020","journal-title":"Lancet Oncol."},{"key":"pone.0335826.ref019","doi-asserted-by":"crossref","unstructured":"Xu G, Song Z, Sun Z, Ku C, Yang Z, Liu C. CAMEL: a weakly supervised learning framework for histopathology image segmentation. In: Proceedings of the IEEE\/CVF International Conference on Computer Vision (ICCV). 2019. p. 10682\u201391.","DOI":"10.1109\/ICCV.2019.01078"},{"issue":"3","key":"pone.0335826.ref020","first-page":"209","article-title":"Global cancer statistics 2020 : GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries","volume":"71","author":"H Sung","year":"2021","journal-title":"CA Cancer J Clin."},{"issue":"1","key":"pone.0335826.ref021","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/S0022-5347(17)59889-4","article-title":"Prediction of prognosis for prostatic adenocarcinoma by combined histological grading and clinical staging","volume":"111","author":"DF Gleason","year":"1974","journal-title":"J Urol."},{"issue":"2","key":"pone.0335826.ref022","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1097\/PAS.0000000000000530","article-title":"The 2014 International Society of Urological Pathology (ISUP) Consensus Conference on Gleason Grading of Prostatic Carcinoma: Definition of Grading Patterns and Proposal for a New Grading System","volume":"40","author":"JI Epstein","year":"2016","journal-title":"Am J Surg Pathol."},{"issue":"6","key":"pone.0335826.ref023","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1080\/21681805.2016.1206619","article-title":"Interobserver variability in Gleason histological grading of prostate cancer","volume":"50","author":"TA Ozkan","year":"2016","journal-title":"Scand J Urol."},{"issue":"10","key":"pone.0335826.ref024","doi-asserted-by":"crossref","first-page":"2058","DOI":"10.1038\/s41379-020-0551-y","article-title":"Novel artificial intelligence system increases the detection of prostate cancer in whole slide images of core needle biopsies","volume":"33","author":"P Raciti","year":"2020","journal-title":"Mod Pathol."},{"issue":"5","key":"pone.0335826.ref025","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1016\/j.eururo.2016.11.031","article-title":"Validation of a contemporary five-tiered gleason grade grouping using population-based data","volume":"71","author":"J He","year":"2017","journal-title":"Eur Urol."},{"issue":"6","key":"pone.0335826.ref026","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1046\/j.1464-410X.2002.02669.x","article-title":"Prognostic value of the Gleason score in prostate cancer","volume":"89","author":"L Egevad","year":"2002","journal-title":"BJU Int."},{"key":"pone.0335826.ref027","unstructured":"Gonz\u00e1lez FA, Ramos-Poll\u00e1n R, Gallego-Mejia JA. Quantum Kernel mixtures for probabilistic deep learning. 2023."},{"key":"pone.0335826.ref028","unstructured":"Rao Y, Zhao W, Liu B, Lu J, Zhou J, Hsieh CJ. DynamicViT: efficient vision transformers with dynamic token sparsification. 2021."},{"key":"pone.0335826.ref029","doi-asserted-by":"crossref","unstructured":"Liu Z, Mao H, Wu CY, Feichtenhofer C, Darrell T, Xie S. A ConvNet for the 2020 s. 2022.","DOI":"10.1109\/CVPR52688.2022.01167"},{"key":"pone.0335826.ref030","unstructured":"Kingma DP, Ba J. Adam: a method for stochastic optimization. 2017."},{"issue":"1","key":"pone.0335826.ref031","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1038\/s41591-021-01620-2","article-title":"Artificial intelligence for diagnosis and Gleason grading of prostate cancer: the PANDA challenge","volume":"28","author":"W Bulten","year":"2022","journal-title":"Nat Med."},{"key":"pone.0335826.ref032","unstructured":"Tan M, Le QV. EfficientNet: rethinking model scaling for convolutional neural networks; 2019."},{"issue":"3","key":"pone.0335826.ref033","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1038\/s41591-024-02857-3","article-title":"Towards a general-purpose foundation model for computational pathology","volume":"30","author":"RJ Chen","year":"2024","journal-title":"Nat Med."},{"key":"pone.0335826.ref034","unstructured":"Shao Z, Bian H, Chen Y, Wang Y, Zhang J, Ji X. TransMIL: transformer based correlated multiple instance learning for whole slide image classification. In: Advances in Neural Information Processing Systems. 2021. p. 2136\u201347."},{"key":"pone.0335826.ref035","unstructured":"Shao D, Chen RJ, Song AH, Runevic J, Lu MY, Ding T. Do multiple instance learning models transfer? 2025."},{"key":"pone.0335826.ref036","unstructured":"Pohjonen J, Ariotta V. HistoPrep: Preprocessing large medical images for machine learning made easy! 2022. https:\/\/github.com\/Pohjonen\/HistoPrep"}],"container-title":["PLOS One"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0335826","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T18:38:29Z","timestamp":1762367909000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0335826"}},"subtitle":[],"editor":[{"given":"Anita Mitico","family":"Tanaka-Azevedo","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,11,5]]},"references-count":36,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11,5]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0335826","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,5]]}}}