Transforming Complex Problems Into K-Means Solutions.

Area of Science:

• Computer Science
• Data Science
• Machine Learning

Background:

• K-means is a foundational clustering algorithm known for its simplicity and efficiency.
• Existing research highlights K-means equivalence to PCA, NMF, and spectral clustering under specific conditions (squared Euclidean distance).
• Challenges arise when applying standard K-means to complex, real-world problems requiring algorithm generalization.

Purpose of the Study:

• To provide a unified perspective on generalized K-means algorithms.
• To explore various approaches for extending K-means to address complex clustering tasks.
• To review diverse applications transformed via modified K-means formulations.

Main Methods:

• The review categorizes K-means generalizations into four key aspects: data representation, distance measure, label assignment, and centroid updating.
• It analyzes how modifications in these aspects enable K-means to tackle advanced problems.
• The paper surveys existing literature on generalized K-means and its applications.

Main Results:

• Generalizations of K-means can be systematically understood through the four identified aspects.
• Modified K-means formulations are effective for a range of complex applications.
• The review demonstrates the versatility and adaptability of the K-means framework.

Conclusions:

• Generalized K-means offers a powerful and flexible framework for diverse data analysis challenges.
• Understanding the four aspects of generalization provides a roadmap for adapting K-means to new problems.
• The reviewed applications showcase the broad utility of extended K-means algorithms in data science and machine learning.