Kernel k-means clustering can correctly identify and extract a far more varied collection of cluster structures than the linear k-means clustering algorithm. However, kernel kmeans clustering is computationally expensive when the non-linear feature map is highdimensional and there are many input points. Kernel approximation, e.g., the Nyström method, has been applied in previous works to approx...

these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...

We study geometric versions of the min-size k-clustering problem, a clustering problem which generalizes clustering to minimize the sum of cluster radii and has important applications. We prove that the problem can be solved in polynomial time when the points to be clustered are located on a line. For Euclidean spaces of higher dimensions, we show that the problem is NP-hard and present polynom...

The problem of constrained k-center clustering has attracted significant attention in the past decades. In this paper, we study balanced k-center cluster where the size of each cluster is constrained by the given lower and upper bounds. The problem is motivated by the applications in processing and analyzing large-scale data in high dimension. We provide a simple nearly linear time 4-approximat...

The superconducting instabilities of the doped repulsive 2D Hubbard model are studied in the intermediate to strong coupling regime with the help of the dynamical cluster approximation. To solve the effective cluster problem we employ an extended noncrossing approximation, which allows for a transition to the broken symmetry state. At sufficiently low temperatures we find stable d-wave solution...

We consider the clustering with diversity problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least ` points, all of which have distinct colors. We give a 2-approximation to this problem for any ` when the objective is to minimize the maximum radius of any cluster. We show that the approximation ratio is optimal unless P = NP, by ...