where R(*) is a weakly stationary covariance. Thanks to the facts that R(s, s) ^ 0 for every seU1 and R (0) ^ 0 this definition yields R(s) !> 0 for every s e (R__. The definition of local stationarity for random sequences is given in [4]. In this case a covariance function R(-, •), defined on Z x Z (Cartesian product of integers), can be expressed as R(n, m) = R(n + m) R(n m) where R(*) is a s...

Taxonomies have been proposed numerous times in the literature in order to encode semantic relationships between classes. Such taxonomies have been used to improve classification results by increasing the statistical efficiency of learning, as similarities between classes can be used to increase the amount of relevant data during training. In this paper, we show how data-derived taxonomies may ...

Mean square error optimal estimation requires the full correlation structure to be available. Unfortunately, it is not always possible maintain knowledge about correlations. One example decentralized data fusion where cross-correlations between estimates are unknown, partly due information sharing. To avoid underestimating covariance of an estimate in such situations, conservative one option. I...

Complex systems are usually non-stationary and their dynamics is often dominated by collective effects. Collectivity, defined as coherent motion of the whole system or some its parts, manifests itself in time-dependent structures covariance correlation matrices. The largest eigenvalue corresponds to a whole, while other large, isolated, eigenvalues indicate collectivity parts system. In case fi...

Covariances play a fundamental role in the theory of time series and they are critical quantities that are needed in both spectral and time domain analysis. Estimation of covariance matrices is needed in the construction of confidence regions for unknown parameters, hypothesis testing, principal component analysis, prediction, discriminant analysis among others. In this paper we consider both l...

In animal breeding, knowledge of the genetic properties of the traits we are interested in is the first prerequisite in establishing a selection programme. Unless we are concerned with traits controlled by single or few genes, in which case we are generally more interested in gene frequencies, estimation of genetic parameters is synonymous with the estimation of variance components. In this con...

In appearance-based image processing, high-dimensional statistical models are estimated from low numbers of training samples. Sample scatter matrices are unreliable estimators of class covariances, yet many methods rely on them for dimensionality reduction and often for classification too. This paper argues for regularized covariance estimation and introduces a new method suitable for appearanc...