# Mathematics Colloquium

#### K-means clustering with optimization

**Speaker:**
Soledad Villar, NYU

**Location:**
Warren Weaver Hall 1302

**Date:**
Monday, March 5, 2018, 3:45 p.m.

**Synopsis:**

K-means clustering aims to partition a set of n points into k clusters in such a way that each observation belongs to the cluster with the nearest mean, and such that the sum of squared distances from each point to its nearest mean is minimal. In the worst case, this is a hard optimization problem, requiring an exhaustive search over all possible partitions of the data into k clusters in order to find the optimal clustering. At the same time, fast heuristic algorithms for k-means are widely used for data science applications, despite only being guaranteed to converge to local minimizers of the k-means objective.