Syed Mujahid N
Department of Systems Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia.
Entropy (Basel). 2018 Feb 27;20(3):150. doi: 10.3390/e20030150.
Data or signal separation is one of the critical areas of data analysis. In this work, the problem of non-negative data separation is considered. The problem can be briefly described as follows: given X ∈ R m × N , find A ∈ R m × n and S ∈ R + n × N such that X = A S . Specifically, the problem with sparse locally dominant sources is addressed in this work. Although the problem is well studied in the literature, a test to validate the locally dominant assumption is not yet available. In addition to that, the typical approaches available in the literature sequentially extract the elements of the mixing matrix. In this work, a mathematical modeling-based approach is presented that can simultaneously validate the assumption, and separate the given mixture data. In addition to that, a correntropy-based measure is proposed to reduce the model size. The approach presented in this paper is suitable for big data separation. Numerical experiments are conducted to illustrate the performance and validity of the proposed approach.
数据或信号分离是数据分析的关键领域之一。在这项工作中，考虑了非负数据分离问题。该问题可简要描述如下：给定(X\in\mathbb{R}^{m\times N})，找到(A\in\mathbb{R}^{m\times n})和(S\in\mathbb{R}_{+}^{n\times N})，使得(X = AS)。具体而言，这项工作解决了具有稀疏局部主导源的问题。尽管该问题在文献中已有充分研究，但尚未有验证局部主导假设的测试方法。除此之外，文献中现有的典型方法是依次提取混合矩阵的元素。在这项工作中，提出了一种基于数学建模的方法，该方法可以同时验证假设并分离给定的混合数据。此外，还提出了一种基于核相关熵的度量来减小模型规模。本文提出的方法适用于大数据分离。进行了数值实验以说明所提方法的性能和有效性。
