Name
Title | ||
|---|---|---|
Covariance Matrix Estimation with Multi-Regularization Parameters based on MDL Principle |
Abstract | ||
|---|---|---|
Regularization is a solution for the problem of unstable estimation of covariance matrix with a small sample set in Gaussian classifier. In many applications such as image restoration, sparse representation, we have to deal with multi-regularization parameters problem. In this paper, the case of covariance matrix estimation with multi-regularization parameters is investigated, and an estimate method called as KLIM_L is derived theoretically based on Minimum Description Length (MDL) principle for the small sample size problem with high dimension setting. KLIM_L estimator can be regarded as a generalization of KLIM estimator in which local difference in each dimension is considered. Under the framework of MDL principle, a selection method of multi-regularization parameters is also developed based on the minimization of the Kullback-Leibler information measure, which is simply and directly estimated by point estimation under the approximation of two-order Taylor expansion. The computational cost to estimate multi-regularization parameters with KLIM_L method is less than those with RDA (Regularized Discriminant Analysis) and LOOC (leave-one-out covariance matrix estimate) in which cross validation technique is adopted. Experiments show that higher classification accuracy can be achieved by using the proposed KLIM_L estimator. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s11063-012-9272-7 | Neural Processing Letters |
Keywords | Field | DocType |
Gaussian classifier,Covariance matrix estimation,Multi-regularization parameters selection,Minimum description length Principle | Applied mathematics,Regularization (mathematics),Gaussian process,L-estimator,Artificial intelligence,Estimation of covariance matrices,Pattern recognition,Sparse approximation,Minimum description length,Covariance matrix,Statistics,Mathematics,Estimator | Journal |
Volume | Issue | ISSN |
38 | 2 | 1370-4621 |
Citations | PageRank | References |
2 | 0.37 | 9 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| XiuLing Zhou | 1 | 9 | 3.02 |
| Ping Guo | 2 | 601 | 85.05 |
| C. L. Chen | 3 | 2 | 0.37 |