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Non-Gaussian Component Analysis using Entropy Methods. (arXiv:1807.04936v1 [cs.LG])

来源于:arXiv
Non-Gaussian component analysis (NGCA) is a problem in multidimensional data analysis. Since its formulation in 2006, NGCA has attracted considerable attention in statistics and machine learning. In this problem, we have a random variable $X$ in $n$-dimensional Euclidean space. There is an unknown subspace $U$ of the $n$-dimensional Euclidean space such that the orthogonal projection of $X$ onto $U$ is standard multidimensional Gaussian and the orthogonal projection of $X$ onto $V$, the orthogonal complement of $U$, is non-Gaussian, in the sense that all its one-dimensional marginals are different from the Gaussian in a certain metric defined in terms of moments. The NGCA problem is to approximate the non-Gaussian subspace $V$ given samples of $X$. Vectors in $V$ corresponds to "interesting" directions, whereas vectors in $U$ correspond to the directions where data is very noisy. The most interesting applications of the NGCA model is for the case when the magnitude of the noise is comp 查看全文>>