The study of rare events in molecular and atomic systems such as conformal changes cluster rearrangements has been one the most important research themes chemical physics. Key challenges are associated with long waiting times rendering simulations inefficient, high dimensionality impeding use PDE-based approaches, complexity or breadth transition processes limiting predictive power asymptotic m...

One of the basic problems in data analysis lies in choosing the optimal rescaling (change of coordinate system) to study properties of a given data-set Y . The classical Mahalanobis approach has its basis in the classical normalization/rescaling formula Y 3 y → Σ Y · (y − mY ), where mY denotes the mean of Y and ΣY the covariance matrix . Based on the cross-entropy we generalize this approach a...

This paper focuses on the problem of kernelizing an existing supervised Mahalanobis distance learner. The following features are included in the paper. Firstly, three popular learners, namely, “neighborhood component analysis”, “large margin nearest neighbors” and “discriminant neighborhood embedding”, which do not have kernel versions are kernelized in order to improve their classification per...

In molecular biology, the issue of quantifying the similarity between two biological sequences is very important. Past research has shown that word-based search tools are computationally efficient and can find some new functional similarities or dissimilarities invisible to other algorithms like FASTA. Recently, under the independent model of base composition, Wu, Burke, and Davison (1997, Biom...

In this paper, we investigate the asymptotic distributions of two types Mahalanobis distance (MD): leave-one-out MD and classical with both Gaussian- non-Gaussian-distributed complex random vectors, when sample size n dimension variables p increase under a fixed ratio c=p/n→∞. We distributional properties samples are independent, but not necessarily identically distributed. Some results regardi...