Matrix Completion Discriminant Analysis.

Area of Science:

• Machine Learning
• Statistical Analysis
• Data Science

Background:

• Semi-supervised learning challenges arise with high missingness and numerous predictors.
• Existing methods may struggle with large datasets and incomplete information.

Purpose of the Study:

• Introduce Matrix Completion Discriminant Analysis (MCDA) for high-missingness semi-supervised learning.
• Develop a method that handles situations where predictors far exceed cases.

Main Methods:

• MCDA maps class labels to simplex vertices in Euclidean space.
• Data matrices are augmented with vertex coordinates and completed using matrix completion (minimizing sum of squares + nuclear norm penalty).
• MM algorithm and singular value decomposition are employed for matrix completion, with tuning constants selected via cross-validation.

Main Results:

• Unlabeled cases are assigned to the class vertex closest to their completed data point.
• MCDA demonstrates competitiveness on traditional problems.
• MCDA significantly outperforms alternative methods on large-scale problems with high missingness.

Conclusions:

• MCDA provides an effective solution for semi-supervised learning with substantial missing data.
• The method is robust and scalable, offering advantages for complex datasets.