Smooth eigenvalue correction

Smooth eigenvalue correction

Second-order statistics play an important role in data modeling. Nowadays, there is a tendency toward measuring more signals with higher resolution (e.g., high-resolution video), causing a rapid increase of dimensionality of the measured samples, while the number of samples remains more or less the same. As a result the eigenvalue estimates are significantly biased as described by the Marčenko ...

Eigenvalue correction results in face recognition

Eigenvalues of sample covariance matrices are often used in biometrics. It has been known for several decades that even though the sample covariance matrix is an unbiased estimate of the real covariance matrix [3], the eigenvalues of the sample covariance matrix are biased estimates of the real eigenvalues [6]. This bias is particularly dominant when the number of samples used for estimation is...

Subspace Correction Methods for Eigenvalue Problems 313

Smooth Convex Approximation to the Maximum Eigenvalue Function

In this paper, we consider smooth convex approximations to the maximum eigenvalue function. To make it applicable to a wide class of applications, the study is conducted on the composite function of the maximum eigenvalue function and a linear operator mapping m to n, the space of n-by-n symmetric matrices. The composite function in turn is the natural objective function of minimizing the maxim...

A multi-level correction scheme for eigenvalue problems

In this paper, a type of multi-level correction scheme is proposed to solve eigenvalue problems by the finite element method. This type of multilevel correction method includes multi correction steps in a sequence of finite element spaces. In each correction step, we only need to solve a source problem on a finer finite element space and an eigenvalue problem on the coarsest finite element spac...