The matrix-based Renyi's {\alpha}-order entropy functional was recently introduced using the normalized eigenspectrum of an Hermitian matrix of the projected data in the reproducing kernel Hilbert space (RKHS). However, the current theory in the matrix-based Renyi's {\alpha}-order entropy functional only defines the entropy of a single variable or mutual information between two random variables. In information theory and machine learning communities, one is also frequently interested in multivariate information quantities, such as the multivariate joint entropy and different interactive quantities among multiple variables. In this paper, we first define the matrix-based Renyi's {\alpha}-order joint entropy among multiple variables. We then show how this definition can ease the estimation of various information quantities that measure the interactions among multiple variables, such as interactive information and total correlation. We finally present an application to feature selection to show how our definition provides a simple yet powerful way to estimate a widely-acknowledged intractable quantity from data. A real example on hyperspectral image (HSI) band selection is also provided.

本文介绍了基于矩阵的 Renyi 的 α 阶熵函数及其在多变量信息量例如多变量联合熵和变量之间不同的交互量，交互信息和总相关度的估计方面的应用，还提供了一个实际的高光谱图像（HSI）波段选择的例子。

基于矩阵的 Renyi α 阶熵函数的多元扩展