3 research outputs found
Correlation Clustering with Low-Rank Matrices
Correlation clustering is a technique for aggregating data based on
qualitative information about which pairs of objects are labeled 'similar' or
'dissimilar.' Because the optimization problem is NP-hard, much of the previous
literature focuses on finding approximation algorithms. In this paper we
explore how to solve the correlation clustering objective exactly when the data
to be clustered can be represented by a low-rank matrix. We prove in particular
that correlation clustering can be solved in polynomial time when the
underlying matrix is positive semidefinite with small constant rank, but that
the task remains NP-hard in the presence of even one negative eigenvalue. Based
on our theoretical results, we develop an algorithm for efficiently "solving"
low-rank positive semidefinite correlation clustering by employing a procedure
for zonotope vertex enumeration. We demonstrate the effectiveness and speed of
our algorithm by using it to solve several clustering problems on both
synthetic and real-world data