@inproceedings{7108062330ef484e87541eb2ec1ad492,
title = "Independent subspace analysis is unique, given irreducibility",
abstract = "Independent Subspace Analysis (ISA) is a generalization of ICA. It tries to find a basis in which a given random vector can be decomposed into groups of mutually independent random vectors. Since the first introduction of ISA, various algorithms to solve this problem have been introduced, however a general proof of the uniqueness of ISA decompositions remained an open question. In this contribution we address this question and sketch a proof for the separability of ISA. The key condition for separability is to require the subspaces to be not further decomposable (irreducible). Based on a decomposition into irreducible components, we formulate a general model for ISA without restrictions on the group sizes. The validity of the uniqueness result is illustrated on a toy example. Moreover, an extension of ISA to subspace extraction is introduced and its indeterminacies are discussed.",
author = "Gutch, {Harold W.} and Theis, {Fabian J.}",
year = "2007",
doi = "10.1007/978-3-540-74494-8_7",
language = "English",
isbn = "9783540744931",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "49--56",
booktitle = "Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings",
note = "7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007 ; Conference date: 09-09-2007 Through 12-09-2007",
}