Distributions are ubiquitous, with applications extending far beyond probability and statistics into nearly all scientific disciplines. In the field of machine learning, finite probability distributions form the softmax output layers in Convolutional Neural Networks (CNNs) and Large Language Models (LLMs), where they represent class probabilities in image classification and token probabilities in language generation. However, when dealing with very large distributions, this incurs significant storage and computational costs. In our previous work, we introduced generalizations of Shannon entropy derived from f-divergences, using majorization as a reference framework for comparing homogeneity. Here, we extend these entropies as tools for dimensionality reduction while integrating them into the concept of Shannon’s information channel.