Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
A new concept for separability problems in blind source separation
Neural Computation
In Search of Non-Gaussian Components of a High-Dimensional Distribution
The Journal of Machine Learning Research
Uniqueness of non-gaussian subspace analysis
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Hierarchical Extraction of Independent Subspaces of Unknown Dimensions
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Second order subspace analysis and simple decompositions
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Contrast functions for independent subspace analysis
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Uniqueness of linear factorizations into independent subspaces
Journal of Multivariate Analysis
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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.