Abstract

We propose a new randomized projection method based on entropy optimization of random projection matrices (the ERP method). The concept of compactness indicator of a data matrix, which is stored in projection matrices, is introduced. An ERP algorithm is formulated in the form of a conditional maximization problem for an entropy functional defined on the probability density functions of the projection matrices. A discrete version of this problem is considered, and conditions are obtained for the existence and uniqueness of its positive solution. Procedures are developed for the implementation of entropy-optimal projection matrices by sampling the probability density functions.

中文翻译：

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熵随机投影

摘要

我们提出了一种新的基于随机投影矩阵熵优化的随机投影方法（ERP方法）。介绍了存储在投影矩阵中的数据矩阵的紧密度指示器的概念。针对在投影矩阵的概率密度函数上定义的熵函数，以条件最大化问题的形式制定了ERP算法。考虑该问题的离散形式，并为其正解的存在和唯一性获得条件。通过采样概率密度函数，开发了用于实现熵最佳投影矩阵的程序。