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A Quantitative Comparison between Shannon and Tsallis–Havrda–Charvat Entropies Applied to Cancer Outcome Prediction
In this paper, we propose to quantitatively compare loss functions based on parameterized Tsallis–Havrda–Charvat 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 wide...
Autores principales: | , , , , , , , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9031340/ https://www.ncbi.nlm.nih.gov/pubmed/35455101 http://dx.doi.org/10.3390/e24040436 |
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author | Brochet, Thibaud Lapuyade-Lahorgue, Jérôme Huat, Alexandre Thureau, Sébastien Pasquier, David Gardin, Isabelle Modzelewski, Romain Gibon, David Thariat, Juliette Grégoire, Vincent Vera, Pierre Ruan, Su |
author_facet | Brochet, Thibaud Lapuyade-Lahorgue, Jérôme Huat, Alexandre Thureau, Sébastien Pasquier, David Gardin, Isabelle Modzelewski, Romain Gibon, David Thariat, Juliette Grégoire, Vincent Vera, Pierre Ruan, Su |
author_sort | Brochet, Thibaud |
collection | PubMed |
description | In this paper, we propose to quantitatively compare loss functions based on parameterized Tsallis–Havrda–Charvat 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–Havrda–Charvat entropy. In this work, we compare these two entropies through a medical application for predicting recurrence in patients with head–neck 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–Havrda–Charvat cross-entropy is a parameterized cross-entropy with the parameter [Formula: see text] . Shannon entropy is a particular case of Tsallis–Havrda–Charvat entropy for [Formula: see text] . 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–neck cancers and 146 from lung cancers. The results show that Tsallis–Havrda–Charvat entropy can achieve better performance in terms of prediction accuracy with some values of [Formula: see text] . |
format | Online Article Text |
id | pubmed-9031340 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-90313402022-04-23 A Quantitative Comparison between Shannon and Tsallis–Havrda–Charvat Entropies Applied to Cancer Outcome Prediction Brochet, Thibaud Lapuyade-Lahorgue, Jérôme Huat, Alexandre Thureau, Sébastien Pasquier, David Gardin, Isabelle Modzelewski, Romain Gibon, David Thariat, Juliette Grégoire, Vincent Vera, Pierre Ruan, Su Entropy (Basel) Article In this paper, we propose to quantitatively compare loss functions based on parameterized Tsallis–Havrda–Charvat 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–Havrda–Charvat entropy. In this work, we compare these two entropies through a medical application for predicting recurrence in patients with head–neck 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–Havrda–Charvat cross-entropy is a parameterized cross-entropy with the parameter [Formula: see text] . Shannon entropy is a particular case of Tsallis–Havrda–Charvat entropy for [Formula: see text] . 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–neck cancers and 146 from lung cancers. The results show that Tsallis–Havrda–Charvat entropy can achieve better performance in terms of prediction accuracy with some values of [Formula: see text] . MDPI 2022-03-22 /pmc/articles/PMC9031340/ /pubmed/35455101 http://dx.doi.org/10.3390/e24040436 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Brochet, Thibaud Lapuyade-Lahorgue, Jérôme Huat, Alexandre Thureau, Sébastien Pasquier, David Gardin, Isabelle Modzelewski, Romain Gibon, David Thariat, Juliette Grégoire, Vincent Vera, Pierre Ruan, Su A Quantitative Comparison between Shannon and Tsallis–Havrda–Charvat Entropies Applied to Cancer Outcome Prediction |
title | A Quantitative Comparison between Shannon and Tsallis–Havrda–Charvat Entropies Applied to Cancer Outcome Prediction |
title_full | A Quantitative Comparison between Shannon and Tsallis–Havrda–Charvat Entropies Applied to Cancer Outcome Prediction |
title_fullStr | A Quantitative Comparison between Shannon and Tsallis–Havrda–Charvat Entropies Applied to Cancer Outcome Prediction |
title_full_unstemmed | A Quantitative Comparison between Shannon and Tsallis–Havrda–Charvat Entropies Applied to Cancer Outcome Prediction |
title_short | A Quantitative Comparison between Shannon and Tsallis–Havrda–Charvat Entropies Applied to Cancer Outcome Prediction |
title_sort | quantitative comparison between shannon and tsallis–havrda–charvat entropies applied to cancer outcome prediction |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9031340/ https://www.ncbi.nlm.nih.gov/pubmed/35455101 http://dx.doi.org/10.3390/e24040436 |
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