Some gyrocommutative gyrogroups, also known as Bruck loops or K-loops, admit scalar multiplication, turning themselves into gyrovector spaces. The latter, in turn, form the setting for hyperbolic geometry just as vector spaces form the setting for Euclidean geometry. In classical mechanics the centroid of a triangle in velocity space is the velocity of the center of momentum of three massive ob...

Pseudo-Centroid Clustering replaces the traditional concept of a centroid expressed as a center of gravity with the notion of a pseudo-centroid (or a coordinate free centroid) which has the advantage of applying to clustering problems where points do not have numerical coordinates (or categorical coordinates that are translated into numerical form). Such problems, for which classical centroids ...

This work addresses the problem of detecting local centroid paths, paths within an area of interest on a spatial network that has the highest concentration of activities. The KMR algorithm [1] is used to do clustering on the spatial network, and a new measure of the density of activities on a path, Activity Coverage Rate (ACR), is introduced to locate each such path. We use experiment results t...

In recent years we have seen a tremendous growth in the volume of text documents available on the Internet, digital libraries, news sources, and company-wide intranets. Automatic text categorization, which is the task of assigning text documents to pre-specified classes (topics or themes) of documents, is an important task that can help both in organizing as well as in finding information on th...

The osmotic swelling of intact erythrocytes in hypotonic solutions was measured using microhematocrit tubes, Van Allen tubes, and a calibrated Coulter counter. In agreement with earlier workers the intact cells did not behave as perfect osmometers, the cells swelling less than predicted by the Boyle-van't Hoff law. Erythrocyte ghosts were prepared from fresh intact erythrocytes by one-step hemo...

2 Analysis of a renal cell carcinoma (RCC) cancer dataset 1 2.1 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Resampling to unit resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.3 ...

In this paper, we introduce a family of some modified versions of linear discriminant analysis, called “shrunken centroids regularized discriminant analysis” (SCRDA). These methods generalize the idea of the nearest shrunken centroids of Prediction Analysis of Microarray (PAM) into the classical discriminant analysis. These SCRDA methods are specially designed for classification problems in hig...