Self-weighted low-rank representation for multivariate compositional data

Area of Science:

• Data Science
• Machine Learning
• Statistical Analysis

Background:

• Compositional data analysis is crucial for understanding relative proportions within a whole.
• Clustering multivariate compositional data presents challenges due to complex structures and uninformative variables.
• Existing methods often struggle to handle these specific challenges effectively.

Purpose of the Study:

• To propose a novel self-weighted low-rank representation (SWLRR) method for clustering multivariate compositional data.
• To address the limitations of existing methods in handling uninformative variables and complex data structures.
• To enhance the accuracy and robustness of clustering for compositional datasets.

Main Methods:

• Developed a variable weighting strategy to identify and prioritize informative variables.
• Integrated global and local structure learning using generalized self-expressive properties and graph constraints.
• Employed a low-rank constraint for enhanced representation robustness.
• Utilized the alternating direction method of multipliers (ADMM) for optimization.

Main Results:

• The proposed SWLRR method demonstrated superior performance on synthetic and practical datasets compared to existing clustering techniques.
• The variable weighting strategy effectively highlighted informative variables, improving clustering outcomes.
• The method successfully captured both global and local data structures within the weighted space.

Conclusions:

• The SWLRR method offers an effective solution for clustering multivariate compositional data.
• The approach successfully addresses challenges posed by uninformative variables and complex data structures.
• The method provides insights into the contribution of individual variables to the clustering process.