  K-Means clustering still plays an important role in many computer vision
problems. While the conventional Lloyd method, which alternates between
centroid update and cluster assignment, is primarily used in practice, it may
converge to a solution with empty clusters. Furthermore, some applications may
require the clusters to satisfy a specific set of constraints, e.g., cluster
sizes, must-link/cannot-link. Several methods have been introduced to solve
constrained K-Means clustering. Due to the non-convex nature of K-Means,
however, existing approaches may result in sub-optimal solutions that poorly
approximate the true clusters. In this work, we provide a new perspective to
tackle this problem. Particularly, we reconsider constrained K-Means as a
Binary Optimization Problem and propose a novel optimization scheme to search
for feasible solutions in the binary domain. This approach allows us to solve
constrained K-Means where multiple types of constraints can be simultaneously
enforced. Experimental results on synthetic and real datasets show that our
method provides better clustering accuracy with faster runtime compared to
several commonly used techniques.
