Sharp-SSL: Selective High-Dimensional Axis-Aligned Random Projections for Semi-Supervised Learning.

Area of Science:

• Machine Learning
• Statistical Learning Theory

Background:

• High-dimensional data presents challenges for traditional semi-supervised learning.
• Identifying relevant variables is crucial for accurate class assignment in complex datasets.

Purpose of the Study:

• To develop a novel algorithm, Sharp-SSL, for high-dimensional semi-supervised learning.
• To enhance variable selection for improved class distinction in projected data.
• To provide theoretical guarantees for the algorithm's performance.

Main Methods:

• Proposing Sharp-SSL, which aggregates results from a low-dimensional procedure on random data projections.
• Scoring projections based on class-distinguishing ability using generalized Rayleigh quotient.
• Assigning variable importance weights by aggregating over high-scoring projections.

Main Results:

• Sharp-SSL recovers signal coordinates with high probability under theoretical conditions.
• New analysis of Gaussian EM base procedure performance in semi-supervised settings.
• Empirical validation on simulated and real colon tumor data demonstrates excellent performance.

Conclusions:

• Sharp-SSL offers an effective approach for variable selection in high-dimensional semi-supervised learning.
• The method demonstrates robust performance across diverse datasets.
• Theoretical analysis supports the algorithm's ability to identify important variables.