Singular-Value-Decomposition-Based Matrix Surgery.

Area of Science:

• Artificial Intelligence
• Medical Image Analysis
• Linear Algebra

Background:

• Deep learning (DL) training for medical imaging faces challenges with model overfitting and robustness.
• The conditioning of convolution filters significantly impacts DL model performance and stability.
• Existing methods may require additional parameters or complex adjustments.

Purpose of the Study:

• To introduce a simple strategy, SVD surgery, to stabilize DL training.
• To reduce the condition numbers of convolution filters.
• To investigate the impact of this strategy on model overfitting and robustness in medical image analysis.

Main Methods:

• The proposed SVD surgery involves Singular Value Decomposition (SVD) of a matrix.
• It modifies smaller singular values relative to the largest one.
• The matrix is then reconstructed via reverse SVD, applied during DL model training.

Main Results:

• SVD surgery acts as spectral regularization for DL models without extra parameters.
• The strategy effectively reduces square matrix condition numbers.
• Empirical analysis shows SVD surgery brings persistent diagrams (PDs) of matrices closer to those of their inverses.

Conclusions:

• SVD surgery offers a straightforward yet effective method for enhancing DL model stability in medical imaging.
• This technique improves robustness and mitigates overfitting by controlling filter conditioning.
• The findings suggest a correlation between matrix condition numbers and the spatial distributions of point clouds and their inverses.