{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T02:09:15Z","timestamp":1783649355389,"version":"3.55.0"},"reference-count":33,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,3,22]],"date-time":"2022-03-22T00:00:00Z","timestamp":1647907200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we propose to quantitatively compare loss functions based on parameterized Tsallis\u2013Havrda\u2013Charvat entropy and classical Shannon entropy for the training of a deep network in the case of small datasets which are usually encountered in medical applications. Shannon cross-entropy is widely used as a loss function for most neural networks applied to the segmentation, classification and detection of images. Shannon entropy is a particular case of Tsallis\u2013Havrda\u2013Charvat entropy. In this work, we compare these two entropies through a medical application for predicting recurrence in patients with head\u2013neck and lung cancers after treatment. Based on both CT images and patient information, a multitask deep neural network is proposed to perform a recurrence prediction task using cross-entropy as a loss function and an image reconstruction task. Tsallis\u2013Havrda\u2013Charvat cross-entropy is a parameterized cross-entropy with the parameter \u03b1. Shannon entropy is a particular case of Tsallis\u2013Havrda\u2013Charvat entropy for \u03b1=1. The influence of this parameter on the final prediction results is studied. In this paper, the experiments are conducted on two datasets including in total 580 patients, of whom 434 suffered from head\u2013neck cancers and 146 from lung cancers. The results show that Tsallis\u2013Havrda\u2013Charvat entropy can achieve better performance in terms of prediction accuracy with some values of \u03b1.<\/jats:p>","DOI":"10.3390\/e24040436","type":"journal-article","created":{"date-parts":[[2022,3,22]],"date-time":"2022-03-22T14:55:35Z","timestamp":1647960935000},"page":"436","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A Quantitative Comparison between Shannon and Tsallis\u2013Havrda\u2013Charvat Entropies Applied to Cancer Outcome Prediction"],"prefix":"10.3390","volume":"24","author":[{"given":"Thibaud","family":"Brochet","sequence":"first","affiliation":[{"name":"LITIS, Quantif, University of Rouen, 76000 Rouen, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00e9r\u00f4me","family":"Lapuyade-Lahorgue","sequence":"additional","affiliation":[{"name":"LITIS, Quantif, University of Rouen, 76000 Rouen, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexandre","family":"Huat","sequence":"additional","affiliation":[{"name":"LITIS, Quantif, University of Rouen, 76000 Rouen, France"},{"name":"Centre Henri Becquerel, 76038 Rouen, France"},{"name":"Soci\u00e9t\u00e9 Aquilab, 59120 Lille, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5772-2336","authenticated-orcid":false,"given":"S\u00e9bastien","family":"Thureau","sequence":"additional","affiliation":[{"name":"LITIS, Quantif, University of Rouen, 76000 Rouen, France"},{"name":"Centre Henri Becquerel, 76038 Rouen, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6019-7309","authenticated-orcid":false,"given":"David","family":"Pasquier","sequence":"additional","affiliation":[{"name":"D\u00e9partement de Radioth\u00e9rapie, Centre Oscar Lambret, 59000 Lille, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Isabelle","family":"Gardin","sequence":"additional","affiliation":[{"name":"LITIS, Quantif, University of Rouen, 76000 Rouen, France"},{"name":"Centre Henri Becquerel, 76038 Rouen, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Romain","family":"Modzelewski","sequence":"additional","affiliation":[{"name":"LITIS, Quantif, University of Rouen, 76000 Rouen, France"},{"name":"Centre Henri Becquerel, 76038 Rouen, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Gibon","sequence":"additional","affiliation":[{"name":"Soci\u00e9t\u00e9 Aquilab, 59120 Lille, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Juliette","family":"Thariat","sequence":"additional","affiliation":[{"name":"D\u00e9partement de Radioth\u00e9rapie, CLCC Francois Baclesse, 14000 Caen, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vincent","family":"Gr\u00e9goire","sequence":"additional","affiliation":[{"name":"D\u00e9partement de Radioth\u00e9rapie, Centre L\u00e9on Berard, 69008 Lyon, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre","family":"Vera","sequence":"additional","affiliation":[{"name":"LITIS, Quantif, University of Rouen, 76000 Rouen, France"},{"name":"Centre Henri Becquerel, 76038 Rouen, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8785-6917","authenticated-orcid":false,"given":"Su","family":"Ruan","sequence":"additional","affiliation":[{"name":"LITIS, Quantif, University of Rouen, 76000 Rouen, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s40745-020-00253-5","article-title":"A Comprehensive Survey of Loss Functions in Machine Learning","volume":"9","author":"Wang","year":"2020","journal-title":"Ann. 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