In this paper, the discrete method of eigenvectors of covariance matrix has been used to weight minimization of steel frame structures. Eigenvectors of Covariance Matrix (ECM) algorithm is a robust and iterative method for solving optimization problems and is inspired by the CMA-ES method. Both of these methods use covariance matrix in the optimization process, but the covariance matrix calcula...

Stanford University For a random matrix following a Wishart distribution, we derive formulas for the expectation and the covariance matrix of compound matrices. The compound matrix of order m is populated by all m×mminors of the Wishart matrix. Our results yield first and second moments of the minors of the sample covariance matrix for multivariate normal observations. This work is motivated by...

Many multivariate statistical methods rely heavily on the sample covariance matrix. It is well known though that the sample covariance matrix is highly non-robust. One popular alternative approach for “robustifying” the multivariate method is to simply replace the role of the covariance matrix with some robust scatter matrix. The aim of this paper is to point out that in some situations certain...

As high-dimensional data becomes ubiquitous, standard estimators of the population covariance matrix become difficult to use. Specifically, in the case where the number of samples is small (large p small n) the sample covariance matrix is not positive definite. In this paper we explore some recent estimators of sample covariance matrices in the large p, small n setting namely, shrinkage estimat...

The Capon-MVDR (Minimum Variance Distortionless Response) method of frequency-wavenumber spectral estimation requires an invertible spatial covariance estimate. Increasingly, however, one must deal with a singular covariance matrix. The ubiquity of inexpensive sensors implies that the dimension of the covariance matrix is ever-increasing, but coherence times have not changed, so the number of v...

This paper proposes a novel image region descriptor for face recognition, named kernel Gabor-based weighted region covariance matrix (KGWRCM). As different parts are different effectual in characterizing and recognizing faces, we construct a weighting matrix by computing the similarity of each pixel within a face sample to emphasize features. We then incorporate the weighting matrices into a re...

in some statistical process control applications, the quality of the product is characterized by thecombination of both correlated variable and attributes quality characteristics. in this paper, we propose anovel control scheme based on the combination of two multi-layer perceptron neural networks forsimultaneous monitoring of mean vector as well as the covariance matrix in multivariate-attribu...

A new covariance matrix estimator useful for designing classifiers with limited training data is developed. In experiments, this estimator achieved higher classification accuracy than the sample covariance matrix and common covariance matrix estimates. In about half of the experiments, it achieved higher accuracy than regularized discriminant analysis, but required much less computation.