Discretization of parametrizable signal manifolds.

Area of Science:

• Signal Processing
• Machine Learning
• Computer Vision

Background:

• Transformation-invariant analysis is crucial for signal classification.
• Estimating distances to transformation manifolds is computationally expensive.
• Approximating manifold distances using grids is a practical solution.

Purpose of the Study:

• Develop an efficient algorithm for selecting samples from transformation manifolds.
• Propose a method for joint discretization of multiple manifolds for improved classification.
• Optimize transformation-invariant classification accuracy.

Main Methods:

• Algorithm for selecting manifold samples to minimize distance estimation error.
• Joint optimization of multiple manifold discretizations.
• Asymmetric distribution of samples based on geometric structures.

Main Results:

• Individual manifold sampling minimizes distance estimation error, outperforming baselines in registration and classification.
• Joint optimization of samples further enhances classification performance.
• Asymmetric sample distribution can increase classification accuracy compared to equal distribution.

Conclusions:

• Optimized manifold sampling strategies significantly improve transformation-invariant signal classification.
• Joint optimization and asymmetric sample distribution are effective techniques for enhancing classification accuracy.
• The proposed methods offer a practical and efficient approach to manifold distance approximation for classification tasks.