Independent Component Analysis

Oja, Hannu; Nordhausen, Klaus

doi:10.1002/9780470057339.vnn086

Cited by 18 publications

(11 citation statements)

References 28 publications

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“…In independent component analysis, certain fourth moment matrices are used together with the covariance matrix in a similar way to find the transformations to independent components [FOBI by Cardoso (1989) and JADE by Cardoso and Souloumiac (1993)]. See also Oja, Sirkiä and Eriksson (2006).…”

Section: Introductionmentioning

confidence: 99%

Fourth Moments and Independent Component Analysis

Miettinen¹,

Taskinen²,

Nordhausen³

et al. 2015

Statist. Sci.

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Abstract. In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to these independent components. In the engineering literature, there are several traditional estimation procedures based on the use of fourth moments, such as FOBI (fourth order blind identification), JADE (joint approximate diagonalization of eigenmatrices), and FastICA, but the statistical properties of these estimates are not well known. In this paper various independent component functionals based on the fourth moments are discussed in detail, starting with the corresponding optimization problems, deriving the estimating equations and estimation algorithms, and finding asymptotic statistical properties of the estimates. Comparisons of the asymptotic variances of the estimates in wide independent component models show that in most cases JADE and the symmetric version of FastICA perform better than their competitors.

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Section: Introductionmentioning

confidence: 99%

Fourth Moments and Independent Component Analysis

Miettinen¹,

Taskinen²,

Nordhausen³

et al. 2015

Statist. Sci.

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“…This elegant idea, first proposed by Cardoso and Soumouliac (1993), and described in detail in Oja et al (2001), is to replace the maximal variation directions of PCA with maximally non-Gaussian directions. See Peña and Prieto (2001) for a related idea.…”

Section: Data Objects In Image Analysismentioning

confidence: 98%

Overview of object oriented data analysis

Marron

Alonso²

2014

Biometrical J

156

100

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Object oriented data analysis is the statistical analysis of populations of complex objects. In the special case of functional data analysis, these data objects are curves, where a variety of Euclidean approaches, such as principal components analysis, have been very successful. Challenges in modern medical image analysis motivate the statistical analysis of populations of more complex data objects that are elements of mildly non-Euclidean spaces, such as lie groups and symmetric spaces, or of strongly non-Euclidean spaces, such as spaces of tree-structured data objects. These new contexts for object oriented data analysis create several potentially large new interfaces between mathematics and statistics. The notion of object oriented data analysis also impacts data analysis, through providing a framework for discussion of the many choices needed in many modern complex data analyses, especially in interdisciplinary contexts.

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“…Several different methods to perform ICA are proposed in the literature. For general overviews, see for example Hyvärinen, Karhunen, and Oja (2001); Comon and Jutten (2010); Oja and Nordhausen (2012);Yu, Hu, and Xu (2014).…”

Section: Independent Component Analysismentioning

confidence: 99%

Blind Source Separation Based on Joint Diagonalization in R: The Packages JADE and BSSasymp

Miettinen¹,

Nordhausen²,

Taskinen³

2017

J. Stat. Soft.

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Blind source separation (BSS) is a well-known signal processing tool which is used to solve practical data analysis problems in various fields of science. In BSS, we assume that the observed data consists of linear mixtures of latent variables. The mixing system and the distributions of the latent variables are unknown. The aim is to find an estimate of an unmixing matrix which then transforms the observed data back to latent sources. In this paper we present the R packages JADE and BSSasymp. The package JADE offers several BSS methods which are based on joint diagonalization. Package BSSasymp contains functions for computing the asymptotic covariance matrices as well as their data-based estimates for most of the BSS estimators included in package JADE. Several simulated and real datasets are used to illustrate the functions in these two packages.

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Independent Component Analysis

Cited by 18 publications

References 28 publications

Fourth Moments and Independent Component Analysis

Fourth Moments and Independent Component Analysis

Overview of object oriented data analysis

Blind Source Separation Based on Joint Diagonalization in R: The Packages JADE and BSSasymp

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