The minimum sum-of-squares clustering problem (MSSC) consists of partitioning n
observations into k clusters in order to minimize the sum of squared distances from the …

We introduce the ratio-cut polytope defined as the convex hull of ratio-cut vectors
corresponding to all partitions of n points in R^m into at most K clusters. This polytope is …

We present a unified geometrical analysis on the completely positive programming (CPP)
reformulations of quadratic optimization problems (QOPs) and their extension to polynomial …

In [SIAM J. Optim., 2022], the authors introduced a new linear programming (LP) relaxation
for K-means clustering. In this paper, we further investigate both theoretical and …

We study the problem of finding the Löwner–John ellipsoid (ie, an ellipsoid with minimum
volume that contains a given convex set). We reformulate the problem as a generalized …

We study a sketch-and-solve approach to speed up the Peng–Wei semidefinite relaxation of-
means clustering. When the data are appropriately separated we identify the-means optimal …

Many clustering problems are combinatorial optimization problems, which are hard to solve
directly. In this dissertation, we consider relaxing these clustering problems to convex …

The minimum sum-of-squares clustering problem is a very important problem in data mining
and machine learning with very many applications in, eg, medicine or social sciences …

In this study, we examine the various extensions of the doubly nonnegative (DNN) cone,
frequently used in completely positive programming (CPP) to achieve a tighter relaxation …