An application of the principle of maximum information preservation to linear systems
Advances in neural information processing systems 1
Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
A fast fixed-point algorithm for independent component analysis
Neural Computation
Fast and robust fixed-point algorithms for independent component analysis
IEEE Transactions on Neural Networks
A new concept for separability problems in blind source separation
Neural Computation
Separating more sources than sensors using time-frequency distributions
EURASIP Journal on Applied Signal Processing
Method to separate sparse components from signal mixtures
Digital Signal Processing
K-hyperline clustering learning for sparse component analysis
Signal Processing
An improved geometric overcomplete blind source separation algorithm
IWANN '03 Proceedings of the 7th International Work-Conference on Artificial and Natural Neural Networks: Part II: Artificial Neural Nets Problem Solving Methods
Generalizing Geometric ICA to Nonlinear Settings
IWANN '03 Proceedings of the 7th International Work-Conference on Artificial and Natural Neural Networks: Part II: Artificial Neural Nets Problem Solving Methods
An Adaptive Approach to Blind Source Separation Using a Self-Organzing Map and a Neural Gas
IWANN '03 Proceedings of the 7th International Work-Conference on Artificial and Natural Neural Networks: Part II: Artificial Neural Nets Problem Solving Methods
On model identifiability in analytic postnonlinear ICA
Neurocomputing
Adaptive underdetermined ICA for handling an unknown number of sources
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
A new approach to clustering and object detection with independent component analysis
IWINAC'05 Proceedings of the First international work-conference on the Interplay Between Natural and Artificial Computation conference on Artificial Intelligence and Knowledge Engineering Applications: a bioinspired approach - Volume Part II
Clustering of signals using incomplete independent component analysis
IWANN'05 Proceedings of the 8th international conference on Artificial Neural Networks: computational Intelligence and Bioinspired Systems
Region of interest based independent component analysis
ICONIP'06 Proceedings of the 13 international conference on Neural Information Processing - Volume Part I
Uniqueness of linear factorizations into independent subspaces
Journal of Multivariate Analysis
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Geometric algorithms for linear independent component analysis (ICA) have recently received some attention due to their pictorial description and their relative ease of implementation. The geometric approach to ICA was proposed first by Puntonet and Prieto (1995). We will reconsider geometric ICA in a theoretic framework showing that fixed points of geometric ICA fulfill a geometric convergence condition (GCC), which the mixed images of the unit vectors satisfy too. This leads to a conjecture claiming that in the nongaussian unimodal symmetric case, there is only one stable fixed point, implying the uniqueness of geometric ICA after convergence. Guided by the principles of ordinary geometric ICA, we then present a new approach to linear geometric ICA based on histograms observing a considerable improvement in separation quality of different distributions and a sizable reduction in computational cost, by a factor of 100, compared to the ordinary geometric approach. Furthermore, we explore the accuracy of the algorithm depending on the number of samples and the choice of the mixing matrix, and compare geometric algorithms with classical ICA algorithms, namely, Extended Infomax and FastICA. Finally, we discuss the problem of high-dimensional data sets within the realm of geometrical ICA algorithms.