The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning.This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically show that the proposed t-entropy satisfies the prominent axiomatic properties of an entropy measure. We demonstrate an application of the proposed entropy measure for multi-level thresholding of images. We also propose the entropic-loss as a measure of the divergence between two probability distributions, which leads to robust estimators in the context of parametric statistical inference. The consistency and asymptotic breakdown point of the proposed estimator are mathematically analyzed. Finally, we show an application of the t-entropy to feature weighted data clustering.

翻译：Entropy概念在信息理论、统计和机器学习中发挥着关键作用。本文件介绍了一种称为t-entropy的新的昆虫测量方法,它利用了反光函数的相近性。我们分析表明,拟议的t-entropy满足了一种对流测量的突出的不言不语特性。我们展示了对图像多层阈值应用拟议的昆虫测量方法。我们还提议将昆虫损失作为一种测量两种概率分布差异的尺度,这导致在参数统计推断中进行强有力的估测。对拟议的估测师的一致性和无色分解点进行了数学分析。最后,我们展示了对加权数据群集应用t-ropy的方法。