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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
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