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Sparse PCA by Matthias Hein and Thomas Bühler |
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Sparse Principal Component Analysis
Principal Component Analysis (PCA) is a standard technique for dimensionality reduction and data analysis which finds the k-dimensional subspace of maximal variance in the data. However the interpretation of the PCA component is difficult as usually all components are nonzero.
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In sparse PCA one wants to get a small number of features which still capture most of the variance. Thus one needs to enforce sparsity of the PCA component, which yields a trade-off between explained variance and sparsity.
This plays a role for instance in the case of gene expression data where one would like the principal components to consist only of a few significant genes, making it easy to interpret by a human. The right plot shows the variance-cardinality tradeoff curve for three gene expression datasets. As shown in [1], Sparse PCA can be modelled as a nonlinear eigenproblem and efficiently be solved by our nonlinear IPM. An implementation can be downloaded from this website. |
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Download and License
The nonlinear IPM for sparse PCA has been developed by
Matthias Hein
and Thomas Bühler,
Department of Computer Science, Saarland University, Germany.
The code for 1-Spectral Clustering is published as free software under the terms of the
GNU GPL v3.0. Please include a reference to the paper An inverse power method for nonlinear eigenproblems with applications in 1-spectral clustering and sparse PCA and include the original documentation and copyright notice.
Download sparsePCA.rar (Matlab-Code, Version: 1.0)