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In this paper, we propose to quantitatively compare loss functions based onparameterized Tsallis-Havrda-Charvat entropy and classical Shannon entropy forthe training of a deep network in the case of small datasets which are usuallyencountered in medical applications. Shannon cross-entropy is widely used as aloss function for most neural networks applied to the segmentation,classification and detection of images. Shannon entropy is a particular case ofTsallis-Havrda-Charvat entropy. In this work, we compare these two entropiesthrough a medical application for predicting recurrence in patients withhead-neck and lung cancers after treatment. Based on both CT images and patientinformation, a multitask deep neural network is proposed to perform arecurrence prediction task using cross-entropy as a loss function and an imagereconstruction task. Tsallis-Havrda-Charvat cross-entropy is a parameterizedcross entropy with the parameter $\alpha$. Shannon entropy is a particular caseof Tsallis-Havrda-Charvat entropy for $\alpha$ = 1. The influence of thisparameter on the final prediction results is studied. In this paper, theexperiments are conducted on two datasets including in total 580 patients, ofwhom 434 suffered from head-neck cancers and 146 from lung cancers. The resultsshow that Tsallis-Havrda-Charvat entropy can achieve better performance interms of prediction accuracy with some values of $\alpha$.

A Quantitative Comparison between Shannon and Tsallis Havrda Charvat Entropies Applied to Cancer Outcome Prediction