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Brochet T, Lapuyade-Lahorgue J, Huat A, Thureau S, Pasquier D, Gardin I, Modzelewski R, Gibon D, Thariat J, Grégoire V, Vera P, Ruan S. Correction: Brochet et al. A Quantitative Comparison between Shannon and Tsallis–Havrda–Charvat Entropies Applied to Cancer Outcome Prediction. Entropy 2022, 24, 436. Entropy 2022; 24:e24050685. [PMID: 35626628 PMCID: PMC9142059 DOI: 10.3390/e24050685] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Accepted: 04/29/2022] [Indexed: 11/16/2022]
Abstract
Alexandre Huat, Sébastien Thureau, David Pasquier, Isabelle Gardin, Romain Modzelewski, David Gibon, Juliette Thariat and Vincent Grégoire were not included as authors in the original publication [...]
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Affiliation(s)
- Thibaud Brochet
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
| | - Jérôme Lapuyade-Lahorgue
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
| | - Alexandre Huat
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
- Centre Henri Becquerel, 76038 Rouen, France
- Société Aquilab, 59120 Lille, France;
| | - Sébastien Thureau
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
- Centre Henri Becquerel, 76038 Rouen, France
| | - David Pasquier
- Département de Radiothérapie, Centre Oscar Lambret, 59000 Lille, France;
| | - Isabelle Gardin
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
- Centre Henri Becquerel, 76038 Rouen, France
| | - Romain Modzelewski
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
- Centre Henri Becquerel, 76038 Rouen, France
| | | | - Juliette Thariat
- Département de Radiothérapie, CLCC Francois Baclesse, 14000 Caen, France;
| | - Vincent Grégoire
- Département de Radiothérapie, Centre Léon Berard, 69008 Lyon, France;
| | - Pierre Vera
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
- Centre Henri Becquerel, 76038 Rouen, France
| | - Su Ruan
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
- Correspondence:
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Brochet T, Lapuyade-Lahorgue J, Huat A, Thureau S, Pasquier D, Gardin I, Modzelewski R, Gibon D, Thariat J, Grégoire V, Vera P, Ruan S. A Quantitative Comparison between Shannon and Tsallis–Havrda–Charvat Entropies Applied to Cancer Outcome Prediction. Entropy 2022; 24:e24040436. [PMID: 35455101 PMCID: PMC9031340 DOI: 10.3390/e24040436] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/07/2022] [Revised: 03/18/2022] [Accepted: 03/18/2022] [Indexed: 11/16/2022]
Abstract
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 α. Shannon entropy is a particular case of Tsallis–Havrda–Charvat entropy for α=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–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 α.
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Affiliation(s)
- Thibaud Brochet
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
| | - Jérôme Lapuyade-Lahorgue
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
| | - Alexandre Huat
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
- Centre Henri Becquerel, 76038 Rouen, France
- Société Aquilab, 59120 Lille, France;
| | - Sébastien Thureau
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
- Centre Henri Becquerel, 76038 Rouen, France
| | - David Pasquier
- Département de Radiothérapie, Centre Oscar Lambret, 59000 Lille, France;
| | - Isabelle Gardin
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
- Centre Henri Becquerel, 76038 Rouen, France
| | - Romain Modzelewski
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
- Centre Henri Becquerel, 76038 Rouen, France
| | | | - Juliette Thariat
- Département de Radiothérapie, CLCC Francois Baclesse, 14000 Caen, France;
| | - Vincent Grégoire
- Département de Radiothérapie, Centre Léon Berard, 69008 Lyon, France;
| | - Pierre Vera
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
- Centre Henri Becquerel, 76038 Rouen, France
| | - Su Ruan
- LITIS, Quantif, University of Rouen, 76000 Rouen, France; (T.B.); (J.L.-L.); (A.H.); (S.T.); (I.G.); (R.M.); (P.V.)
- Correspondence:
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