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.
Abstract: Support vector machines (SVMs) are considered to be
the best machine learning algorithms for minimizing the predictive
probability of misclassification. However, their drawback is that for
large data sets the computation of the optimal decision boundary is a
time consuming function of the size of the training set. Hence several
methods have been proposed to speed up the SVM algorithm. Here
three methods used to speed up the computation of the SVM
classifiers are compared experimentally using a musical genre
classification problem. The simplest method pre-selects a random
sample of the data before the application of the SVM algorithm. Two
additional methods use proximity graphs to pre-select data that are
near the decision boundary. One uses k-Nearest Neighbor graphs and
the other Relative Neighborhood Graphs to accomplish the task.