This paper presents a novel method for safe and efficient social navigation, taking into account the growing use of artificial intelligence in robotics and the active development of algorithms for autonomous systems adapting to complex social environments. Existing probabilistic models and safety region generation methods primarily rely on classification approaches and explicit rules, limiting their ability to define safety regions. This study proposes a method for generating explainable safety regions by leveraging topological features through topological data analysis. First, we use a global rule-based classification to distinguish safe from unsafe simulations based on topological characteristics. Next, we define a safety region, $S_\varepsilon$, as a collision-free region in the topological feature space using a tunable SVM classifier and order statistics. This provides a robust and scalable decision boundary that guarantees a minimum classification error $\varepsilon$. By classifying simulations based on the presence or absence of collisions, this study outperforms methods that do not consider topological features. Furthermore, we define a safety region that prevents deadlock and integrate it to define a simulation space that ensures safe and efficient navigation.
