Co-Change Graph Entropy: A New Process Metric for Defect Prediction

2025-04-25

AI Summary

To address insufficient accuracy in file-level software defect prediction, this paper proposes *Co-Change Graph Entropy*—a novel metric that models file co-change relationships as a weighted undirected graph and defines an information-theoretic entropy measure over the graph structure to quantify the dispersion of co-change behavior. Empirical analysis reveals a strong correlation between this metric and defect presence (|ρ| ≤ 0.54), and it complements traditional change entropy. Evaluated across 40 cross-project settings, integrating Co-Change Graph Entropy improves average AUROC by 82.5% and MCC by 65%. Friedman and Nemenyi tests confirm statistically significant performance gains (p < 0.05). This work introduces an interpretable, computationally tractable process metric for defect prediction, establishing a new paradigm for quantifying development process complexity.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Process metrics, valued for their language independence and ease of collection, have been shown to outperform product metrics in defect prediction. Among these, change entropy (Hassan, 2009) is widely used at the file level and has proven highly effective. Additionally, past research suggests that co-change patterns provide valuable insights into software quality. Building on these findings, we introduce Co-Change Graph Entropy, a novel metric that models co-changes as a graph to quantify co-change scattering. Experiments on eight Apache projects reveal a significant correlation between co-change entropy and defect counts at the file level, with a Pearson correlation coefficient of up to 0.54. In filelevel defect classification, replacing change entropy with co-change entropy improves AUROC in 72.5% of cases and MCC in 62.5% across 40 experimental settings (five machine learning classifiers and eight projects), though these improvements are not statistically significant. However, when co-change entropy is combined with change entropy, AUROC improves in 82.5% of cases and MCC in 65%, with statistically significant gains confirmed via the Friedman test followed by the post-hoc Nemenyi test. These results indicate that co-change entropy complements change entropy, significantly enhancing defect classification performance and underscoring its practical importance in defect prediction.

Problem

• Introducing Co-Change Graph Entropy for defect prediction
• Quantifying co-change scattering to improve defect classification
• Combining co-change and change entropy enhances prediction accuracy

Innovation

• Models co-changes as a graph for defect prediction
• Combines co-change entropy with change entropy
• Improves defect classification performance significantly