In optimization or machine learning problems we are given a set of items, usually points in
some metric space, and the goal is to minimize or maximize an objective function over some …

The monograph Data Clustering: Theory, Algorithms, and Applications was published in
2007. Starting with the common ground and knowledge for data clustering, the monograph …

In this paper, we show the existence of small coresets for the problems of computing k-
median and k-means clustering for points in low dimension. In other words, we show that …

The paradigm of coresets has recently emerged as a powerful tool for efficiently
approximating various extent measures of a point set P. Using this paradigm, one quickly …

Frieze, Kannan, and Vempala (JACM 2004) proved that a small sample of rows of a given
matrix A spans the rows of a low-rank approximation D that minimizes A− Df within a small …

We present an algorithm for approximating the Laplace-Beltrami operator from an arbitrary
point cloud obtained from ak-dimensional manifold embedded in the d-dimensional space …

Given a set of points P⊂ Rd and value ε> 0, an ε-core-setS⊂ P has the property that the
smallest ball containing S has radius within 1+ ε of the radius of the smallest ball containing …

We prove the existence of small core-sets for solving approximate k-center clustering and
related problems. The size of these core-sets is considerably smaller than the previously …

A coreset of a point set P is a small weighted set of points that captures some geometric
properties of P. Coresets have found use in a vast host of geometric settings. We forge a link …

Spectral methods refer to the use of eigenvalues, eigenvectors, singular values, and
singular vectors. They are widely used in Engineering, Applied Mathematics, and Statistics …