Blind separation of positive sources by globally convergent gradient search
Neural Computation
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Nonlinear Complex-Valued Extensions of Hebbian Learning: An Essay
Neural Computation
Fixed-point neural independent component analysis algorithms on the orthogonal group
Future Generation Computer Systems
Sparse representations of polyphonic music
Signal Processing - Sparse approximations in signal and image processing
Learning Sparse Overcomplete Codes for Images
Journal of VLSI Signal Processing Systems
Learning Sparse Overcomplete Codes for Images
Journal of VLSI Signal Processing Systems
Learning independent components on the orthogonal group of matrices by retractions
Neural Processing Letters
Descent methods for optimization on homogeneous manifolds
Mathematics and Computers in Simulation
Probabilistic Factorization of Non-negative Data with Entropic Co-occurrence Constraints
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Mutual Information Based Approach for Nonnegative Independent Component Analysis
ICIC '07 Proceedings of the 3rd International Conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence
Gene expression data classification based on non-negative matrix factorization
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Fixed-point neural independent component analysis algorithms on the orthogonal group
Future Generation Computer Systems
Convergence Analysis of Non-Negative Matrix Factorization for BSS Algorithm
Neural Processing Letters
IEEE Transactions on Audio, Speech, and Language Processing
Nonnegative Principal Component Analysis for Cancer Molecular Pattern Discovery
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
A new geometrical BSS approach for non negative sources
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Underdetermined Sparse Blind Source Separation of Nonnegative and Partially Overlapped Data
SIAM Journal on Scientific Computing
Minimum support ICA using order statistics. part II: performance analysis
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Riemannian optimization method on the flag manifold for independent subspace analysis
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
On a sparse component analysis approach to blind source separation
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
An ICA learning algorithm utilizing geodesic approach
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Gradient algorithm for nonnegative independent component analysis
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Monotonic convergence of a nonnegative ICA algorithm on stiefel manifold
ICONIP'06 Proceedings of the 13 international conference on Neural Information Processing - Volume Part I
Journal of Scientific Computing
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We consider the task of solving the independent component analysis (ICA) problem x=As given observations x, with a constraint of nonnegativity of the source random vector s. We refer to this as nonnegative independent component analysis and we consider methods for solving this task. For independent sources with nonzero probability density function (pdf) p(s) down to s=0 it is sufficient to find the orthonormal rotation y=Wz of prewhitened sources z=Vx, which minimizes the mean squared error of the reconstruction of z from the rectified version y+ of y. We suggest some algorithms which perform this, both based on a nonlinear principal component analysis (PCA) approach and on a geodesic search method driven by differential geometry considerations. We demonstrate the operation of these algorithms on an image separation problem, which shows in particular the fast convergence of the rotation and geodesic methods and apply the approach to a musical audio analysis task.