Clustering methods: To optimize or to not optimize?

Area of Science:

• Data Science
• Psychological Statistics
• Machine Learning

Background:

• Clustering problems often involve optimizing an objective criterion.
• Globally optimal solutions may not always be the most interpretable or aligned with true structures.
• Suboptimal solutions have sometimes been observed to align better with known cluster structures in simulations.

Purpose of the Study:

• To investigate the relationship between global optimality in clustering and the recovery of known cluster structures.
• To examine K-median clustering performance when deviations from global optimality are controlled.
• To evaluate the practical implications of accepting suboptimal solutions in clustering.

Main Methods:

• Conducted simulation studies using K-median clustering.
• Carefully controlled deviations from global optimality in clustering solutions.
• Analyzed the correspondence between optimized clustering criteria and the recovery of underlying cluster structures.

Main Results:

• Suboptimal K-median clustering solutions occasionally yielded marginally better recovery for experimental data with less defined structures.
• A perfect correspondence between the optimized clustering criterion and the recovery of known cluster structure was not consistently observed.
• The study controlled for departures from global optimality to assess its impact.

Conclusions:

• While suboptimal solutions may offer slight advantages in specific, poorly defined scenarios, accepting them generally is an unwise practice.
• Sacrificing some degree of optimization is principled when it meets desirable constraints or improves other relevant criteria.
• The findings caution against the misconception that suboptimal clustering methods are consistently preferable to superior ones.