Multi-scale affinities with missing data: Estimation and applications.

Area of Science:

• Machine Learning
• Data Mining
• Computational Statistics

Background:

• Machine learning algorithms rely on data matrix weights for performance.
• Selecting appropriate weights is crucial but often understudied.
• Gaussian kernel affinities work for complete data but fail with missing values.

Purpose of the Study:

• To develop a robust method for computing row and column affinities in data matrices with missing entries.
• To address the challenge of weight selection in incomplete datasets.
• To leverage coupled similarity structures for improved data analysis.

Main Methods:

• A novel co-clustering based technique is proposed.
• The method involves solving optimization problems with multiple cost parameters.
• It iteratively fills missing data with smooth estimates, exploiting row-column coupled similarities.

Main Results:

• The developed method successfully constructs row and column affinities for matrices with missing data.
• These affinities are shown to be effective for various downstream tasks.
• Demonstrated utility in data imputation, clustering, and matrix completion on graphs.

Conclusions:

• The proposed method provides a powerful way to handle missing data in weight computation for machine learning.
• This technique enhances the applicability of similarity-based algorithms to real-world, incomplete datasets.
• The approach offers a unified framework for tasks like imputation and clustering using learned affinities.