A minor subspace algorithm based on neural Stiefel dynamics

Area of Science:

• Numerical Analysis
• Machine Learning
• Computational Mathematics

Background:

• Iterative minor subspace analysis is crucial for various data analysis tasks.
• Existing algebraic methods can be computationally intensive.
• Neural network approaches offer potential for improved efficiency.

Purpose of the Study:

• To introduce a novel neural approach for iterative minor subspace analysis.
• To investigate the effectiveness and efficiency of this neural method.
• To compare the proposed approach with existing algebraic algorithms.

Main Methods:

• A neural approach based on weight flow on the Stiefel manifold was developed.
• Four novel neural algorithms were designed and discussed.
• A purely algebraic algorithm from the literature was included for comparison.

Main Results:

• Numerical experiments demonstrated the effectiveness of the proposed neural approach.
• Computational complexity estimates confirmed the efficiency of the neural algorithms.
• The neural approach showed comparable or superior performance to the algebraic method.

Conclusions:

• The proposed neural approach provides an effective and efficient method for iterative minor subspace analysis.
• This work contributes a new perspective using neural networks on the Stiefel manifold.
• The findings support the practical applicability of neural algorithms in subspace analysis.