Absolute Cluster Validity.

Area of Science:

• Data Science
• Machine Learning
• Computational Statistics

Background:

• Clustering is a fundamental data analysis technique, but its results are subjective and computationally expensive to optimize.
• Existing cluster validation indices are relative, making absolute assessment of clustering quality difficult.
• Applied scenarios often require suboptimal solutions, necessitating robust validation for meaningful interpretation.

Purpose of the Study:

• To propose a novel cluster validation methodology for absolute evaluation of clustering results.
• To develop indices based on geometric measurements, inter/intra-cluster distances, density, and multimodality.
• To enhance the robustness and interpretability of clustering for knowledge discovery.

Main Methods:

• Geometric measurements of the solution space.
• Development of indices assessing inter- and intra-cluster distances.
• Incorporation of density and multimodality measures within clusters.

Main Results:

• The proposed methodology enables absolute evaluations, unlike traditional relative indices.
• Tests demonstrate improved robustness in clustering applications for knowledge discovery.
• The validation index is interpretable, allowing for self-checking capabilities in systems.

Conclusions:

• The new validation methodology offers a significant advancement over existing relative indices.
• It provides a more objective and reliable way to assess clustering quality.
• Enables the development of more transparent and self-aware clustering systems.