Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization.

Area of Science:

• Data Science
• Machine Learning
• Image Analysis

Background:

• Traditional cluster analysis methods often overlook spatial information present in datasets.
• Standard clustering algorithms may not effectively capture spatially coherent classes, particularly in applications like hyperspectral imaging.
• Existing methods struggle with datasets where spatial relationships are crucial for accurate class identification.

Purpose of the Study:

• To develop novel clustering models that incorporate spatial coherence for improved analysis of spatially-aware datasets.
• To introduce Total Variation (TV) regularization within Orthogonal Nonnegative Matrix Factorization (ONMF) for enhanced clustering.
• To address limitations of classical clustering methods in handling datasets with inherent spatial structures.

Main Methods:

• Developed clustering models based on Orthogonal Nonnegative Matrix Factorization (ONMF).
• Integrated Total Variation (TV) regularization into the cluster membership matrix to enforce spatial coherence.
• Explored different optimization techniques, including post-processing and integrated regularization approaches.
• Evaluated 12 TV-regularized ONMF methods on a real-world hyperspectral imaging dataset.

Main Results:

• The proposed TV-regularized ONMF methods significantly improved clustering results compared to classical approaches.
• Spatial coherence enforcement led to more accurate identification of spatially coherent classes.
• The methods demonstrated superior performance on hyperspectral data from matrix-assisted laser desorption/ionization imaging.

Conclusions:

• Orthogonal Nonnegative Matrix Factorization with Total Variation regularization is effective for cluster analysis of spatially structured data.
• The developed methods offer a significant advancement over traditional clustering techniques for hyperspectral imaging and similar applications.
• Incorporating spatial information directly into the clustering process yields more meaningful and accurate results.