Cross-covariance based affinity for graphs.

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Graph-based learning accuracy depends on topological structure and data point affinity, often assuming smooth Riemannian manifolds.
• Euclidean distance-based affinity may inaccurately represent connectivity due to non-linear local structures and neighborhood data distribution.

Purpose of the Study:

• To propose novel techniques, CCGA and CCGA, using cross-covariance based graph affinity (CCGA) for improved data point relationship representation.
• To enhance affinity measures by considering common local neighborhoods and the influence of connected data points' neighborhoods.

Main Methods:

• Developed two techniques: CCGA and CCGA, utilizing cross-covariance based graph affinity (CCGA).
• CCGA incorporates additional connectivity from shared local neighborhoods.
• CCGA further refines affinity by considering the influence of respective neighborhoods of connected data points.

Main Results:

• CCGA accurately represents affinity between data points, leading to superior low-dimensional representations in manifold learning.
• CCGA-based affinity improves classification accuracy in manifold regularization on image datasets.
• The proposed CCGA method significantly outperforms existing state-of-the-art manifold regularization techniques.

Conclusions:

• Cross-covariance based graph affinity (CCGA) offers a more accurate measure of data point relationships.
• The proposed CCGA method enhances manifold learning and regularization, improving classification accuracy.
• CCGA represents a significant advancement over current manifold regularization approaches.