Abstract: In the proposed method for Web page-ranking, a
novel theoretic model is introduced and tested by examples of order
relationships among IP addresses. Ranking is induced using a
convexity feature, which is learned according to these examples
using a self-organizing procedure. We consider the problem of selforganizing
learning from IP data to be represented by a semi-random
convex polygon procedure, in which the vertices correspond to IP
addresses. Based on recent developments in our regularization
theory for convex polygons and corresponding Euclidean distance
based methods for classification, we develop an algorithmic
framework for learning ranking functions based on a Computational
Geometric Theory. We show that our algorithm is generic, and
present experimental results explaining the potential of our approach.
In addition, we explain the generality of our approach by showing its
possible use as a visualization tool for data obtained from diverse
domains, such as Public Administration and Education.
Abstract: A chord of a simple polygon P is a line segment [xy]
that intersects the boundary of P only at both endpoints x and y. A
chord of P is called an interior chord provided the interior of [xy] lies
in the interior of P. P is weakly visible from [xy] if for every point v
in P there exists a point w in [xy] such that [vw] lies in P. In this
paper star-shaped, L-convex, and convex polygons are characterized
in terms of weak visibility properties from internal chords and starshaped
subsets of P. A new Krasnoselskii-type characterization of
isothetic star-shaped polygons is also presented.