Master of Science / Department of Statistics / Kun Chen / The singular value decomposition (SVD) is a commonly used matrix factorization technique
in statistics, and it is very e ective in revealing many low-dimensional structures in
a noisy data matrix or a coe cient matrix of a statistical model. In particular, it is often
desirable to obtain a sparse SVD, i.e., only a few singular values are nonzero and their
corresponding left and right singular vectors are also sparse. However, in several existing
methods for sparse SVD estimation, the exact orthogonality among the singular vectors are
often sacri ced due to the di culty in incorporating the non-convex orthogonality constraint
in sparse estimation. Imposing orthogonality in addition to sparsity, albeit di cult, can be
critical in restricting and guiding the search of the sparsity pattern and facilitating model
interpretation. Combining the ideas of penalized regression and Bregman iterative methods,
we propose two methods that strive to achieve the dual goal of sparse and orthogonal SVD
estimation, in the general framework of high dimensional multivariate regression. We set
up simulation studies to demonstrate the e cacy of the proposed methods.
| Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/15992 |
| Date | January 1900 |
| Creators | Khatavkar, Rohan |
| Publisher | Kansas State University |
| Source Sets | K-State Research Exchange |
| Language | English |
| Detected Language | English |
| Type | Report |
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