An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
ICA using spacings estimates of entropy
The Journal of Machine Learning Research
Beyond independent components: trees and clusters
The Journal of Machine Learning Research
Undercomplete Blind Subspace Deconvolution
The Journal of Machine Learning Research
On variants of the Johnson–Lindenstrauss lemma
Random Structures & Algorithms
Independent process analysis without a priori dimensional information
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Independent subspace analysis using k-nearest neighborhood distances
ICANN'05 Proceedings of the 15th international conference on Artificial neural networks: formal models and their applications - Volume Part II
Cross-Entropy optimization for independent process analysis
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Distributed high dimensional information theoretical image registration via random projections
Digital Signal Processing
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The estimation of relevant information theoretical quantities, such as entropy, mutual information, and various divergences is computationally expensive in high dimensions. However, for this task, one may apply pairwise Euclidean distances of sample points, which suits random projection (RP) based low dimensional embeddings. The Johnson-Lindenstrauss (JL) lemma gives theoretical bound on the dimension of the low dimensional embedding. We adapt the RP technique for the estimation of information theoretical quantities. Intriguingly, we find that embeddings into extremely small dimensions, far below the bounds of the JL lemma, provide satisfactory estimates for the original task. We illustrate this in the Independent Subspace Analysis (ISA) task; we combine RP dimension reduction with a simple ensemble method. We gain considerable speed-up with the potential of real-time parallel estimation of high dimensional information theoretical quantities.