Centroid-Based Clustering with αβ-Divergences.

Area of Science:

• Machine Learning
• Data Mining
• Statistics

Background:

• Centroid-based clustering, particularly the k-means algorithm, is fundamental in unsupervised learning.
• Algorithm performance is highly dependent on the chosen similarity or divergence measure.
• Existing research often integrates specific divergence measures into traditional hard k-means.

Purpose of the Study:

• To introduce a generalized centroid-based clustering algorithm, alpha beta k-means, utilizing the alpha beta-divergence family.
• To provide a flexible framework for selecting similarity measures in clustering.
• To ensure the algorithm's convergence properties across a range of divergence parameters.

Main Methods:

• Development of a novel iterative algorithm, alpha beta k-means, with closed-form solutions for centroid computation.
• Parameterization of the algorithm using alpha and beta values to encompass various divergences.
• Validation through empirical studies on synthetic and real-world datasets.

Main Results:

• The alpha beta k-means algorithm demonstrates adaptability by incorporating a wide spectrum of commonly used divergences.
• Convergence to local minima is mathematically guaranteed for a broad range of (alpha, beta) parameter pairs.
• Experimental results showcase the algorithm's effectiveness and robustness across diverse data types.

Conclusions:

• The proposed alpha beta k-means algorithm offers a versatile and theoretically sound approach to centroid-based clustering.
• Its fine-tuning capability through (alpha, beta) parameters enhances its applicability in various research and practical domains.
• The study confirms the algorithm's high quality and suitability for diverse clustering tasks.