Graph Quality Matters on Revealing the Semantics Behind the Data in Physical World

Area of Science:

• Graph theory applications in data science and life sciences.
• Network analysis and representation learning.

Background:

• Graphs are fundamental to representing complex systems in various domains.
• Understanding how graph structure influences semantic representation for machine learning tasks remains a challenge.

Purpose of the Study:

• To introduce novel metrics for evaluating graph quality: structural complexity and homophily.
• To mathematically establish the relationship between graph quality metrics and task performance.
• To develop a graph augmentation tool (Graph+) to enhance graph structures and improve general task performance.

Main Methods:

• Defined structural complexity as a measure of graph symmetry and homophily as a measure of intra-class edge consistency.
• Developed mathematical proofs for the correlation between these metrics and task performance.
• Designed and implemented the Graph+ tool for graph augmentation.
• Empirically validated Graph+ on Alzheimer's diagnosis and breast cancer subtype identification tasks.

Main Results:

• Structural complexity positively correlates with general task performance.
• Homophily exhibits a "J"-shaped correlation with general task performance.
• Graph+ effectively enhances graph structures and improves performance in medical diagnosis and subtype identification tasks.
• The study reveals underlying data semantics through improved graph representations.

Conclusions:

• Graph quality metrics, structural complexity and homophily, are crucial for understanding and improving graph-based machine learning.
• The Graph+ tool offers a practical method for enhancing graph structures, leading to better performance in real-world applications.
• This work bridges the gap between graph structure analysis and semantic representation for enhanced data understanding.