Extracting preference relations from data: Clustering with transitive centroids.

Area of Science:

• Data Science
• Machine Learning
• Computational Statistics

Background:

• Clustering algorithms are essential for data analysis.
• Existing methods like k-modes may not capture complex relational structures.
• Preference data often exhibits transitivity despite individual heterogeneity.

Purpose of the Study:

• To introduce a novel clustering algorithm, k-orders, designed for extracting transitive relations.
• To propose and evaluate two adjustment procedures: transitive centroid adjustment (TCA) and greedy TCA.
• To demonstrate the algorithm's utility in analyzing heterogeneous, transitive individual preferences.

Main Methods:

• The k-orders algorithm modifies k-modes by incorporating transitive centroid adjustment.
• Two adjustment procedures, TCA and greedy TCA, were developed.
• Performance was evaluated through simulation studies comparing k-orders (TCA and greedy TCA) against k-modes.
• Latent class models were used for empirical testing of extracted centroids.

Main Results:

• Both k-orders versions significantly outperformed k-modes when dealing with transitive relation centroids.
• The TCA algorithm demonstrated superior performance over greedy TCA in two-component option scenarios.
• An empirical application successfully illustrated the practical use of k-orders for preference analysis.

Conclusions:

• The k-orders algorithm is a valuable tool for extracting transitive relations from data.
• TCA and greedy TCA offer improved clustering for data with inherent transitive structures.
• K-orders provides a robust method for analyzing complex individual preferences.