K-means clustering: a half-century synthesis

Area of Science:

• Data Science
• Machine Learning
• Statistical Analysis

Background:

• The K-means clustering algorithm is a fundamental technique in unsupervised machine learning.
• Its widespread application necessitates a comprehensive understanding of its theoretical basis and practical considerations.

Purpose of the Study:

• To synthesize fifty years of research on the K-means clustering method.
• To provide a unifying treatment of K-means and its various extensions.
• To identify future research directions for enhancing K-means performance.

Main Methods:

• Review and synthesis of existing literature on K-means clustering.
• Discussion of theoretical statistical results related to the algorithm.
• Exploration of different formulations, initialization techniques, and preprocessing schemes.

Main Results:

• A comprehensive overview of K-means clustering, including its core principles and loss function formulations.
• Detailed discussion of methods for selecting the number of clusters, initialization, variable preprocessing, and data reduction.
• Presentation of theoretical statistical results and extensions of the K-means algorithm using different metrics and modifications.

Conclusions:

• The paper offers a unifying perspective on K-means clustering and its related methods.
• Identifies key areas for future research to address performance subtleties.
• Emphasizes the enduring relevance and adaptability of K-means in data analysis.