For a point T and a circle δ, if two congruent circles of radius r touching at T also touch δ at points different from T , we say T generates circles of radius r with δ, and the two circles are said to be generated by T with δ. If the generated circles are Archimedean, we say T generates Archimedean circles with δ. Frank Power seems to be the earliest discoverer of this kind Archimedean circles...

We present an algorithm for meshing surfaces that is a simple adaptation of a greedy “farthest point” technique proposed by Chew. Given a surface S, it progressively adds points on S and updates the 3dimensional Delaunay triangulation of the points. The method is very simple and works in 3d-space without requiring to parameterize the surface. Taking advantage of recent results on the restricted...

Dimension reduction techniques are very important, as high dimensional data is ubiquitous in many real world applications, especially in this era of big data. In this paper, we propose a novel supervised dimensionality reduction method, called appropriate points choosing based DAG-DNE (Apps-DAG-DNE). In Apps-DAG-DNE, we choose appropriate points to construct adjacency graphs, for example, it ch...

Feature selection has been explored extensively for use in several real-world applications. In this paper, we propose a new method to select a salient subset of features from unlabeled data, and the selected features are then adaptively used to identify natural clusters in the cluster analysis. Unlike previous methods that select salient features for clustering, our method does not require a pr...

The nearest neighbour (NN) classifier is often known as a ‘lazy’ approach but it is still widely used particularly in the systems that require pattern matching. Many algorithms have been developed based on NN in an attempt to improve classification accuracy and to reduce the time taken, especially in large data sets. This paper proposes a new classification technique based on kNearest Neighbour...

We show that the co-rays to a ray in a complete non-compact Finsler manifold contain geodesic segments to upper level sets of Busemann functions. Moreover, we characterise the co-point set to a ray as the cut locus of such level sets. The structure theorem of the co-point set on a surface, namely that is a local tree, and other properties follow immediately from the known results about the cut ...