Suboptimal Comparison of Partitions.

Area of Science:

• Computational statistics
• Machine learning
• Data mining

Background:

• Classification and clustering are distinct data analysis tasks, often differentiated by the availability of prior labels.
• Theoretical analysis reveals that optimal solutions for clustering do not always align with optimal classification, particularly when the data-generating model is known.

Purpose of the Study:

• To explore the divergence between optimal clustering and classification.
• To identify limitations of standard internal and external validation measures in guaranteeing optimal clustering performance.
• To recommend suboptimal evaluation strategies for clustering that offer valuable post hoc interpretation.

Main Methods:

• Theoretical exploration of the relationship between clustering and classification optimality.
• Analysis of standard internal and external validation indices.
• Development and recommendation of alternative evaluation metrics for clustering performance.

Main Results:

• No standard internal or external validation measure can ensure correspondence with optimal clustering.
• Pairwise linkage-based indices offer clear probabilistic interpretations for clustering.
• Triplet-based indices reveal higher-level data structures, and ROC curves from hierarchical clustering dendrograms provide nuanced insights.

Conclusions:

• Standard validation metrics are insufficient for guaranteeing optimal clustering outcomes.
• Suboptimal evaluation methods, including pairwise and triplet indices, are valuable for post hoc cluster interpretation.
• Graphical methods like ROC curves from dendrograms offer richer information than single-number summaries for understanding clustering results.