We introduce a new information maximization (infomax) approach for the blind source separation problem. The proposed framework provides an information-theoretic perspective for determinant maximization-based structured matrix factorization methods such as nonnegative and polytopic matrix factorization. For this purpose, we use an alternative joint entropy measure based on the log-determinant of covariance, which we refer to as log-determinant (LD) entropy. The corresponding (LD) mutual information between two vectors reflects a level of their correlation. We pose the infomax BSS criterion as the maximization of the LD-mutual information between the input and output of the separator under the constraint that the output vectors lie in a presumed domain set. In contrast to the ICA infomax approach, the proposed information maximization approach can separate both dependent and independent sources. Furthermore, we can provide a finite sample guarantee for the perfect separation condition in the noiseless case.
翻译:我们为盲源分离问题采用了一种新的信息最大化(infomex)方法。拟议框架为确定基于最大化的结构化矩阵乘数方法提供了一种信息理论视角,例如非负矩阵和多元矩阵乘数。为此,我们使用基于共变的对数确定值的替代联合恒星测量法,我们称之为日志-确定性(LD)对流体。两个矢量之间的对应(LD)相互信息反映了它们之间的关联程度。我们提出Infomex BSS标准,将LD-双向信息作为静态输入和输出之间的最大化,其限制是输出矢量位于假设的域集。与ICA Infomex方法不同的是,拟议的信息最大化方法可以区分依赖性和独立来源。此外,我们可以为无噪音情况下的完美分离条件提供有限的样本保证。