A penalized matrix decomposition, and its applications
Abstract/Contents
- Abstract
- We present a penalized matrix decomposition, a new framework for computing a low-rank approximation for a matrix. This low-rank approximation is a generalization of the singular value decomposition. While the singular value decomposition usually yields singular vectors that have no elements that are exactly equal to zero, our new decomposition results in sparse singular vectors. This decomposition has a number of applications. When it is applied to a data matrix, it can yield interpretable results. One can apply it to a covariance matrix in order to obtain a new method for sparse principal components, and one can apply it to a crossproducts matrix in order to obtain a new method for sparse canonical correlation analysis. Moreover, when applied to a dissimilarity matrix, this leads to a method for sparse hierarchical clustering, which allows for the clustering of a set of observations using an adaptively chosen subset of the features. Finally, if this decomposition is applied to a between-class covariance matrix then it yields penalized linear discriminant analysis, an extension of Fisher's linear discriminant analysis to the high-dimensional setting.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2010 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Witten, Daniela Mottel |
|---|---|
| Associated with | Stanford University, Department of Statistics |
| Primary advisor | Tibshirani, Robert |
| Thesis advisor | Tibshirani, Robert |
| Thesis advisor | Rajaratnam, Balakanapathy |
| Thesis advisor | Taylor, Jonathan E |
| Advisor | Rajaratnam, Balakanapathy |
| Advisor | Taylor, Jonathan E |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Daniela M. Witten. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2010. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2010 by Daniela Mottel Witten
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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