Motivated by recent developments in numerical Lie group integrators, we introduce a family of local coordinates on Lie groups denoted generalized polar coordinates. Fast algorithms are derived for the computation of the coordinate maps, their tangent maps and the inverse tangent maps. In particular we discuss algorithms for all the classical matrix Lie groups and optimal complexity integrators ...

Parallel coordinates is a well-known technique used for visualization of multivariate data. When the size of the data sets increases the parallel coordinates display results in an image far too cluttered to perceive any structure. We tackle this problem by constructing high-precision textures to represent the data. By using transfer functions that operate on the high-precision textures, it is p...

The order and arrangement of dimensions (variates) is crucial for the effectiveness of a large number of visualization techniques such as parallel coordinates, scatterplots, recursive pattern, and many others. In this paper, we describe a systematic approach to arrange the dimensions according to their similarity. The basic idea is to rearrange the data dimensions such that dimensions showing a...

Often multidimensional data are visualized by splitting n-D data to a set of low dimensional data. While it is useful it destroys integrity of n-D data, and leads to a shallow understanding complex n-D data. To mitigate this challenge a difficult perceptual task of assembling low-dimensional visualized pieces to the whole n-D vectors must be solved. Another way is a lossy dimension reduction by...

In this paper, a face recognition system for personal identification and verification using Principal Component Analysis (PCA) with Modified Back Propagation Neural Networks (MBPNN) is proposed. The dimensionality of face image is reduced by the PCA and the recognition is done by the MBPNN. The system consists of a database of a set of facial patterns for each individual. The characteristic fea...

It has recently been suggested by Mu et al. [Proteins 58, 45 (2005)] to use backbone dihedral angles instead of Cartesian coordinates in a principal component analysis of molecular dynamics simulations. Dihedral angles may be advantageous because internal coordinates naturally provide a correct separation of internal and overall motion, which was found to be essential for the construction and i...

background: cutaneous leishmaniasis is one of the most important parasitic diseases in humans. in this disease, one of the responsible organisms is leishmania major, which is transmitted by sandfly vector. there are specific differences in biochemical profiles and metabolite pathways in logarithmic and stationary phases of leishmania parasites. in the present study, 1h nmr spectroscopy was used...

Traditional visualization techniques for multidimensional data sets, such as parallel coordinates, star glyphs, and scatterplot matrices, do not scale well to high dimensional data sets. A common approach to solve this problem is dimensionality reduction. Existing dimensionality reduction techniques, such as Principal Component Analysis, Multidimensional Scaling, and Self Organizing Maps, have ...

Abstract High‐dimensional compositional data are commonplace in the modern omics sciences, among others. Analysis of requires proper choice a log‐ratio coordinate representation, since their relative nature is not compatible with direct use standard statistical methods. Principal balances, particular class orthonormal coordinates, well suited to this context as they constructed so that first fe...