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 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 $\alpha$.

Deep learning using Havrda-Charvat entropy for classification of pulmonary endomicroscopy

Pulmonary optical endomicroscopy (POE) is an imaging technology in real time. It allows to examine pulmonary alveoli at a microscopic level. Acquired in clinical settings, a POE image sequence can have as much as 25% of the sequence being uninformative frames (i.e. pure-noise and motion artefacts). For future data analysis, these uninformative frames must be first removed from the sequence. Therefore, the objective of our work is to develop an automatic detection method of uninformative images in endomicroscopy images. We propose to take the detection problem as a classification one. Considering advantages of deep learning methods, a classifier based on CNN (Convolutional Neural Network) is designed with a new loss function based on Havrda-Charvat entropy which is a parametrical generalization of the Shannon entropy. We propose to use this formula to get a better hold on all sorts of data since it provides a model more stable than the Shannon entropy. Our method is tested on one POE dataset including 2947 distinct images, is showing better results than using Shannon entropy and behaves better with regard to the problem of overfitting. Keywords: Deep Learning, CNN, Shannon entropy, Havrda-Charvat entropy, Pulmonary optical endomicroscopy.