Elucidating the solution structure of the K-means cost function using energy landscape theory

Area of Science:

• Computational statistics
• Data mining
• Machine learning

Background:

• K-means clustering is widely used but sensitive to initial conditions.
• Understanding the cost function landscape is key to improving K-means performance.
• Locating the global minimum can be challenging due to multiple solutions.

Purpose of the Study:

• To analyze the K-means cost function topography using an energy landscape approach.
• To investigate the influence of initial cluster coordinates on K-means solutions.
• To elucidate the structure of the K-means solution landscape for Fisher's Iris dataset.

Main Methods:

• Employed the energy landscape approach.
• Analyzed the cost function surface topography for K-means.
• Utilized Fisher's Iris dataset for empirical analysis.
• Quantified inter-solution barriers and analyzed kinetic analogs.

Main Results:

• K-means solution landscapes exhibit a funneled structure for all cluster numbers.
• Funneled structures arise from small barriers between most clustering solutions.
• The funneled structure degrades as the number of clusters increases, complicating global minimum identification.

Conclusions:

• The energy landscape approach reveals a funneled topography in K-means solutions, suggesting efficient optimization.
• Small inter-solution barriers contribute to the funneled structure.
• Increasing cluster numbers reduces landscape definition, posing challenges for finding the global optimum.