Name
Title | ||
|---|---|---|
Covariance Estimation for High Dimensional Data Vectors Using the Sparse Matrix Transform |
Abstract | ||
|---|---|---|
Covariance estimation for high dimensional vectors is a classically difcult prob- lem in statistical analysis and machine learning. In this paper, we propose a maximum likelihood (ML) approach to covariance estimation, which employs a novel sparsity constraint. More specically , the covariance is constrained to have an eigen decomposition which can be represented as a sparse matrix transform (SMT). The SMT is formed by a product of pairwise coordinate rotations known as Givens rotations. Using this framework, the covariance can be efciently esti- mated using greedy minimization of the log likelihood function, and the number of Givens rotations can be efciently computed using a cross-validation proce- dure. The resulting estimator is positive denite and well-conditioned even when the sample size is limited. Experiments on standard hyperspectral data sets show that the SMT covariance estimate is consistently more accurate than both tradi- tional shrinkage estimates and recently proposed graphical lasso estimates for a variety of different classes and sample sizes. |
Year | Venue | Keywords |
|---|---|---|
2008 | NIPS | covariance estimation,statistical analysis,maximum likelihood,sparse matrix,machine learning,cross validation,high dimensional data,likelihood function,sample size |
Field | DocType | Citations |
Covariance function,Estimation of covariance matrices,Pattern recognition,Rational quadratic covariance function,Covariance intersection,Artificial intelligence,Matérn covariance function,Mathematics,Covariance mapping,Sparse matrix,Covariance | Conference | 23 |
PageRank | References | Authors |
2.40 | 6 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Guangzhi Cao | 1 | 90 | 8.94 |
| Charles A. Bouman | 2 | 2740 | 473.62 |