Independent component analysis: recent advances

By Aapo Hyvärinen. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2013

435 citations recorded by the source corpus.

Independent component analysis is a probabilistic method for learning a linear transform of a random vector. The goal is to find components that are maximally independent and non-Gaussian (non-normal). Its fundamental difference to classical multi-variate statistical methods is in the assumption of non-Gaussianity, which enables the identification of original, underlying components, in contrast to classical methods. The basic theory of independent component analysis was mainly developed in the 1990s and summarized, for example, in our monograph in 2001. Here, we provide an overview of some recent developments in the theory since the year 2000. The main topics are: analysis of causal relations, testing independent components, analysing multiple datasets (three-way data), modelling dependencies between the components and improved methods for estimating the basic model.

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Citations in the corpus

Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “The field of 2-way CA is maturing and has generated efficient algorithms for 2-way component analysis, especially for sparse/functional PCA/SVD, ICA, NMF and SCA [11, 58, 129, 299].”
Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis (2014, background): “Multi-faceted data can be naturally stacked into a tensor; for instance, in wire-5 less communications the so-called signal diversity (temporal, spatial, spectral, . . . ) corresponds to the order of the tensor [18].”