We study the problem of efficiently clustering protein sequences in a limited information setting. We assume that we do not know the distances between the sequences in advance, and must query them during the execution of the algorithm. Our goal is to find an accurate clustering using few queries. We model the problem as a point set S with an unknown metric d on S, and assume that we have access...

Clustering is a data mining technique used to make groups of objects that are somehow similar in characteristics. The criterion for checking the similarity is implementation dependent. Clustering analyzes data objects without consulting a known class label or category i. e. it is an unsupervised data mining technique. K-means is a widely used clustering algorithm that chooses random cluster cen...

Maximizing the separating margin is crucial for the good generalization performance of Support Vector Machines (SVMs). Analogous to the definition of separation distance or separating margin in SVMs, we propose a definition on separation distance in clustering tasks when a hyperplane is used to separate clusters. For given training data and a given metric distance, by maximizing the proposed se...

In this paper, we mainly consider the problem of spherical distribution of 5 points, that is, how toconfigure 5 points on a sphere such that the mutual distance sum attains the maximum. It is conjecturedthat the sum of distances is maximal if 5 points form a bipyramid configuration in which case two pointsare positioned at two poles of the sphere and the other three are position...

The eccentricity of a vertex $v$ is the maximum distance between $v$ and anyother vertex. A vertex with maximum eccentricity is called a peripheral vertex.The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum ofthe distances between all pairs of peripheral vertices of $G.$ In this paper, weinitiate the study of the peripheral Wiener index and we investigate its basicproperti...

The Wiener index W(G) of a connected graph G is defined as the sum of the distances between all unordered pairs of vertices of G. The eccentricity of a vertex v in G is the distance to a vertex farthest from v. In this paper we obtain the Wiener index of a graph in terms of eccentricities. Further we extend these results to the self-centered graphs.

Based on recent findings of a formation mechanism of substructure in tidal tails by Küpper, Macleod & Heggie (2008) we investigate a more comprehensive set of N -body models of star clusters on orbits about a Milky-Way-like potential. We find that the predicted epicyclic overdensities arise in any tidal tail no matter which orbit the cluster follows as long as the cluster lives long enough for ...

The reverse degree distance of a connected graph $G$ is defined in discrete mathematical chemistry as [ r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u), ] where $n$, $m$ and $d$ are the number of vertices, the number of edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$, $D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the...