A1 Refereed original research article in a scientific journal
The squared symmetric FastICA estimator
Authors: Miettinen J, Nordhausen K, Oja H, Taskinen S, Virta J
Publisher: ELSEVIER SCIENCE BV
Publication year: 2017
Journal: Signal Processing
Journal name in source: SIGNAL PROCESSING
Journal acronym: SIGNAL PROCESS
Volume: 131
First page : 402
Last page: 411
Number of pages: 10
ISSN: 0165-1684
eISSN: 1879-2677
DOI: https://doi.org/10.1016/j.sigpro.2016.08.028(external)
Abstract
In this paper we study the theoretical properties of the deflation-based FastICA method, the original symmetric FastICA method, and a modified symmetric FastICA method, here called the squared symmetric FastICA. This modification is obtained by replacing the absolute values in the FastICA objective function by their squares. In the deflation-based case this replacement has no effect on the estimate since the maximization problem stays the same. However, in the symmetric case we obtain a different estimate which has been mentioned in the literature, but its theoretical properties have not been studied at all. In the paper we review the classic deflation-based and symmetric FastICA approaches and contrast these with the squared symmetric version of FastICA in a unified way. We find the estimating equations and derive the asymptotical properties of the squared symmetric FastICA estimator with an arbitrary choice of nonlinearity. This allows the main contribution of the paper, i.e., efficiency comparison of the estimates in a wide variety of situations using asymptotic variances of the unmixing matrix estimates. (C) 2016 Elsevier B.V. All rights reserved.
In this paper we study the theoretical properties of the deflation-based FastICA method, the original symmetric FastICA method, and a modified symmetric FastICA method, here called the squared symmetric FastICA. This modification is obtained by replacing the absolute values in the FastICA objective function by their squares. In the deflation-based case this replacement has no effect on the estimate since the maximization problem stays the same. However, in the symmetric case we obtain a different estimate which has been mentioned in the literature, but its theoretical properties have not been studied at all. In the paper we review the classic deflation-based and symmetric FastICA approaches and contrast these with the squared symmetric version of FastICA in a unified way. We find the estimating equations and derive the asymptotical properties of the squared symmetric FastICA estimator with an arbitrary choice of nonlinearity. This allows the main contribution of the paper, i.e., efficiency comparison of the estimates in a wide variety of situations using asymptotic variances of the unmixing matrix estimates. (C) 2016 Elsevier B.V. All rights reserved.
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