Natural gradient works efficiently in learning
Neural Computation
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Quasi-Geodesic Neural Learning Algorithms Over the Orthogonal Group: A Tutorial
The Journal of Machine Learning Research
Algorithms for nonnegative independent component analysis
IEEE Transactions on Neural Networks
Undercomplete Blind Subspace Deconvolution
The Journal of Machine Learning Research
Natural Conjugate Gradient on Complex Flag Manifolds for Complex Independent Subspace Analysis
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part I
Controlled complete ARMA independent process analysis
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Accurate estimation of ICA weight matrix by implicit constraint imposition using lie group
IEEE Transactions on Neural Networks
Using state space differential geometry for nonlinear blind source separation
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Performing nonlinear blind source separation with signal invariants
IEEE Transactions on Signal Processing
Separation theorem for independent subspace analysis and its consequences
Pattern Recognition
Uniqueness of linear factorizations into independent subspaces
Journal of Multivariate Analysis
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Recent authors have investigated the use of manifolds and Lie group methods for independent component analysis (ICA), including the Stiefel and the Grassmann manifolds and the orthogonal group O(n). In this paper we introduce a new class of manifold, the generalized flag manifold, which is suitable for independent subspace analysis. The generalized flag manifold is a set of subspaces which are orthogonal to each other, and includes the Stiefel and the Grassmann manifolds as special cases. We describe how the independent subspace analysis problem can be tackled as an optimization on the generalized flag manifold. We propose a Riemannian optimization method on the generalized flag manifold by adapting an existing geodesic formula for the Stiefel manifold, and present a new learning algorithm for independent subspace analysis based on this approach. Experiments confirm the effectiveness of our method.