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

TL;DR

This study compares Shannon and Tsallis-Havrda-Charvat entropies as loss functions in deep neural networks for cancer recurrence prediction, finding that the parameterized Tsallis entropy can improve accuracy on small medical datasets.

Contribution

It introduces a quantitative comparison of Shannon and Tsallis-Havrda-Charvat entropies in deep learning for medical prognosis, highlighting the benefits of the parameterized entropy.

Findings

Tsallis-Havrda-Charvat entropy improves prediction accuracy for certain alpha values.

The parameter alpha influences the effectiveness of the entropy-based loss.

The approach is validated on datasets of 580 cancer patients.

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 $\alpha$. Shannon entropy is a particular case of Tsallis-Havrda-Charvat entropy for $\alpha$ = 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 $\alpha$.