A Generalized Divergence Measure for Nonnegative Matrix Factorization
@article{Kompass2007AGD, title={A Generalized Divergence Measure for Nonnegative Matrix Factorization}, author={Raul Kompass}, journal={Neural Computation}, year={2007}, volume={19}, pages={780-791} }
This letter presents a general parametric divergence measure. The metric includes as special cases quadratic error and Kullback-Leibler divergence. A parametric generalization of the two different multiplicative update rules for nonnegative matrix factorization by Lee and Seung (2001) is shown to lead to locally optimal solutions of the nonnegative matrix factorization problem with this new cost function. Numeric simulations demonstrate that the new update rule may improve the quadratic…
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References
SHOWING 1-9 OF 9 REFERENCES
Algorithms for Non-negative Matrix Factorization
- Computer ScienceNIPS
- 2000
Two different multiplicative algorithms for non-negative matrix factorization are analyzed and one algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence.
Non-negative matrix factorization with alpha-divergence
- Computer SciencePattern Recognit. Lett.
- 2008
On alpha-divergence based nonnegative matrix factorization for clustering cancer gene expression data
- Computer ScienceArtif. Intell. Medicine
- 2008
Learning the parts of objects by non-negative matrix factorization
- Computer ScienceNature
- 1999
An algorithm for non-negative matrix factorization is demonstrated that is able to learn parts of faces and semantic features of text and is in contrast to other methods that learn holistic, not parts-based, representations.
Neural Networks, Principal Components, and Subspaces
- Computer ScienceInt. J. Neural Syst.
- 1989
A single neuron with Hebbian-type learning for the connection weights, and with nonlinear internal feedback, has been shown to extract the statistical principal components of its stationary input pattern sequence, which yields a multi-dimensional, principal component subspace.
Backpropagation Applied to Handwritten Zip Code Recognition
- Computer ScienceNeural Computation
- 1989
This paper demonstrates how constraints from the task domain can be integrated into a backpropagation network through the architecture of the network, successfully applied to the recognition of handwritten zip code digits provided by the U.S. Postal Service.
Preintegration Lateral Inhibition Enhances Unsupervised Learning
- Computer Science, BiologyNeural Computation
- 2002
It is argued that preintegration lateral inhibition has computational advantages over conventional neural network architectures while remaining equally biologically plausible.
Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper
- Engineering
- 1977
Vibratory power unit for vibrating conveyers and screens comprising an asynchronous polyphase motor, at least one pair of associated unbalanced masses disposed on the shaft of said motor, with the…
CBCL face database #1
- Available online at http://cbcl.mit.edu/cbcl/software-datasets/facedata2.html.
- 2000