Traditional visualization techniques for multidimensional data sets, such as parallel coordinates, glyphs, and scatterplot matrices, do not scale well to high numbers of dimension. A common approach to solving this problem is dimensionality reduction. Existing dimensionality reduction techniques usually generate lower dimensional spaces that have little intuitive meaning to users and allow litt...

This paper addresses the problem of supporting region queries over a dynamically growing set of data in feature spaces with many dimensions. It formulates two principles of indexing data in high-dimensional feature spaces and presents an approach to high-dimensional indexing with these principles in mind. The combined goal of the two principles is to increase the density of index regions, which...

Parallel coordinate plots (PCPs) are among the most useful techniques for the visualization and exploration of high-dimensional data spaces. They are especially useful for the representation of correlations among the dimensions, which identify relationships and interdependencies between variables. However, within these high-dimensional spaces, PCPs face difficulties in displaying the correlatio...

The classification of high dimensional data with kernel methods is considered in this article. Exploiting the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its invers...

Extracting hierarchical structure in graph data is becoming an important problem fields such as natural language processing and developmental biology. Hierarchical structures can be extracted by embedding methods non-Euclidean spaces, Poincaré Lorentz embedding, it now possible to learn efficient taking advantage of the these spaces. In this study, we propose into another type metric space call...