Research Paper Analysis
Enhancing the interpretability of the mapper algorithm
Authors: Padraig Fitzpatrick¹ · Anna Jurek-Loughrey¹ · Paweł Dłotko²
Publication: Data Mining and Knowledge Discovery (2026) 40:23
Keywords: XAI · TDA · Mapper · Topology · Explainability
Abstract: The Mapper Algorithm is a powerful tool for representing the topology of a dataset's structure as a similarity graph for the purposes of exploratory analysis. Despite Mapper's ability to simplify complex high-dimensional data representations, interpreting the structure of the output graph remains a challenge. The conventional method of interpreting the Mapper graph by coloring nodes by features values is infeasible for high-dimensional data due to time limitations and the potential for subjectivity-related oversights. We present a novel method to enhance the interpretability of the Mapper algorithm. Specifically, we propose adapting eXplainable Artificial Intelligence techniques to determine feature importance, offering both local and global interpretations. Our approach can be used to assist domain experts in understanding functional differences across Mapper graphs, enabling them to draw meaningful conclusions from the graph's structure. To validate our approach, we conducted experiments on five real-world medical datasets and the MNIST handwritten digit dataset. Our evaluation methods consist of a combination of visualization, classification tasks, and alignment of interpretations to existing literature. The results demonstrate our method's effectiveness in providing a means to interpret Mapper graphs by highlighting the roles of specific features in the graph—such as pixel regions in MNIST and genes in TCGA datasets.
Executive Impact & Key Findings
This research addresses a critical limitation in Topological Data Analysis (TDA)—the interpretability of the Mapper algorithm's output. By integrating eXplainable AI (XAI) techniques, we unlock deeper insights into complex datasets, offering clear, data-driven explanations that reduce subjectivity and enhance decision-making.
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Enhanced Local Interpretation (MNIST F1 Score)
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Improvement in Local Fidelity (MNIST)
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Improved Global Graph Fidelity (MNIST F1 Score)
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Improvement in Global Fidelity (MNIST)
Deep Analysis & Enterprise Applications
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The Challenge of Mapper Interpretability
The Mapper Algorithm excels at visualizing high-dimensional data topology, revealing underlying structures as similarity graphs. However, interpreting these complex graphs, especially in high-dimensional contexts, presents significant challenges. Traditional node-coloring methods are often time-consuming, subjective, and prone to overlooking critical relationships, leading to a 'black-box' problem similar to advanced AI models.
This research highlights the need for a more robust, objective approach to understand Mapper graphs. The inherent instability of Mapper to input data perturbations also complicates the direct application of many existing XAI techniques, requiring a tailored solution.
Integrating XAI for Enhanced Mapper Interpretation
Our proposed method adapts eXplainable Artificial Intelligence (XAI) techniques to provide both local and global interpretations of Mapper graphs. This allows domain experts to uncover functional differences and draw meaningful conclusions about graph structures.
Mapper Algorithm Pipeline
Data Filtration
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Covering over Filtration
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Clustering
→
Graph Construction
Local Feature Importance
To provide local interpretations, we first apply community detection (using InfoMap) to partition the Mapper graph into distinct regions. For each community, we create a region-specific dataset and train a local surrogate model (Random Forest). We then extract feature importances (Gini importance, with a noisy feature baseline) to identify features that differentiate a community from its neighbors. This approach reveals key attributes responsible for specific local structures, such as pixel regions in images or gene expressions in medical data.
Global Feature Importance
For global interpretations, we aggregate local importance scores across all communities. This process identifies features that consistently influence the overall topological representation and relationships within the entire Mapper graph. It provides a broader understanding of how features universally shape the data structure, complementing the granular insights from local analysis.
MNIST Digit Recognition: Pixel Importance Revealed
Our method effectively highlights specific pixel regions crucial for distinguishing handwritten digits within the Mapper graph communities. This visual corroboration aligns perfectly with human intuition about how digits are recognized.
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Local F1 Score (Macro) on MNIST with Selected Features (vs 0.903 for All Features)
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Global F1 Score (Macro) on MNIST with Selected Features (vs 0.867 for All Features)
Structural Similarity of Mapper Graphs (MNIST)
When reconstructing the Mapper graph using only the most important features identified by our method, we observe high structural similarity to the original graph. This demonstrates that our selected features indeed capture the core topological information.
| Measure | Most Important (x=295) | Least Important (x=295) | Random (x=295) |
|---|---|---|---|
| Jaccardian Distance | 0.685 | 0.988 | 0.743 ± 0.014 |
| Laplacian Spectral Distance | 384.952 | 6757.565 | 500.186 ± 88.638 |
| Normalized Mutual Information (NMI) | 0.908 | 0.129 | 0.847 ± 0.022 |
Insight: Lower Jaccardian and Laplacian distances, along with higher NMI, indicate greater similarity to the original graph. Our "Most Important" features consistently outperform "Least Important" and "Random" selections, validating their relevance.
TCGA-BRCA: Uncovering Prognostic Gene Markers
In the TCGA-BRCA dataset, our method identified key genes associated with breast cancer subtypes and prognosis. For Luminal A subtype samples, the BCL2 gene was found to be the most explanatory feature in distinguishing neighboring communities, consistent with literature on its prognostic role for 5-year relapse-free survival.
For HER2+ subtype samples, the GRB7 gene was highlighted as most explanatory, known to be coamplified with aggressive phenotypes. FGFR4 also showed high importance, potentially indicating subtype switching in metastatic tumors, offering valuable insights for personalized treatment strategies.
Reaven-Miller Diabetes: Prioritizing Disease Indicators
For the Reaven-Miller diabetes dataset, our analysis ranked features by their local and global importance, aligning with established medical understanding:
| Community Type | 1st Most Important | 2nd Most Important | 3rd Most Important |
|---|---|---|---|
| Normal Samples (Community 0) | Glucose | Relative Weight (rw) | Steady State Plasma Glucose (sspg) |
| Overt Diabetes (Community 1) | Steady State Plasma Glucose (sspg) | Fasting Plasma Glucose (fpg) | Glucose |
| Chemical & Normal (Community 2) | Insulin | Relative Weight (rw) | Fasting Plasma Glucose (fpg) |
| Global Ranking | Glucose | Relative Weight (rw) | Insulin |
Insight: Glucose consistently ranks as globally most important, reflecting its central role in diabetes. Locally, features like insulin and steady-state plasma glucose become more prominent in specific communities, indicating nuanced mechanisms of disease progression.
Conclusion & Future Outlook
This paper successfully integrates the Mapper Algorithm with community detection and XAI techniques to provide a robust framework for interpreting complex data representations. Our experiments on MNIST, TCGA, and Reaven-Miller datasets demonstrate that the proposed method effectively identifies explanatory features at both local and global scales, with results consistent with existing literature.
The ability to pinpoint crucial features, whether pixel regions in images or specific genes in medical data, significantly enhances the usability and transparency of Mapper graphs. This approach holds immense practical implications for developing more accurate machine learning models, improving disease diagnosis and prognosis, and designing targeted treatment strategies.
Future work will focus on fine-tuning classification models and exploring diverse parameter settings to further optimize the performance and interpretability of the framework.
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Your AI Interpretability Roadmap
A structured approach to integrating advanced XAI techniques for better data understanding.
Phase 1: Discovery & Assessment
Conduct a comprehensive review of existing data analysis pipelines and identify key areas where Mapper interpretability can deliver the highest impact. Define success metrics and prioritize datasets for initial implementation.
Phase 2: XAI Integration & Model Development
Implement the proposed XAI framework, configuring community detection, local surrogate models, and feature importance extraction. Develop custom visualizations for domain experts to interact with the enhanced Mapper graphs.
Phase 3: Validation & Iteration
Validate the interpretability and fidelity of the new framework using classification tasks and expert corroboration. Gather feedback from domain experts to refine models, improve feature selection, and optimize visualization tools.
Phase 4: Scalable Deployment & Training
Deploy the validated XAI-enhanced Mapper system into production environments. Provide extensive training for data scientists and domain experts, empowering them to leverage the new insights for informed decision-making and strategic planning.
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