A Fuzzy Clustering Validity Index Induced by Triple Center Relation

Area of Science:

• Data Science
• Machine Learning
• Pattern Recognition

Background:

• Existing clustering validity indexes (CVIs) struggle with close cluster centers and noisy datasets.
• Current separation mechanisms in CVIs are often simplistic, leading to imperfect results.

Purpose of the Study:

• To introduce a novel clustering validity index (CVI) for fuzzy clustering, named the Triple Center Relation (TCR) index.
• To address the limitations of existing CVIs in determining the correct cluster number, particularly in challenging datasets.

Main Methods:

• Developed a new fuzzy cardinality based on maximum membership degree and a compactness formula.
• Integrated cluster center distances, mean distance, and sample variance to create a 3-D separability expression.
• Combined compactness and separability into the TCR index, analyzing its properties using fuzzy C-means (FCMs).

Main Results:

• The proposed TCR index demonstrated superior performance in identifying the correct cluster number across 36 diverse datasets.
• Experimental results showed the TCR index outperforms 10 other comparative CVIs.
• The index exhibited excellent stability and robustness, even with noisy data.

Conclusions:

• The TCR index offers a significant advancement in fuzzy clustering validity assessment.
• Its novel approach to compactness and separability provides more accurate cluster number determination.
• The TCR index is a reliable and stable tool for various data types, including images and face databases.