TESSERA

Topological Entity Similarity Structure for Emergent Response Analysis

A domain-general framework for detecting and exploiting geometric structure in multi-dimensional feature spaces for predictive classification.

Targeting: Nature Computational Science

Core Hypothesis

When entities are characterized by multi-dimensional features and outcomes depend on relational position in feature space, similarity network topology carries predictive information that direct feature-based classifiers miss.

Three Failure Geometries

TESSERA detects geometrically distinct response regions in entity similarity space:

1. Ecotone — responses cluster at boundaries between stable operational domains (analogous to ecological transition zones)
2. Isolated cluster — responses occupy a distinct region, separate from main domains
3. Diffuse — responses scattered within domains, driven by individual feature thresholds

Three Demonstration Domains

Validation Protocol

1. Phase 1 — Ablation: GNN vs. MLP, RF, XGBoost, LogReg (justify network)
2. Phase 2 — Similarity: 7 measures compared (Simpson, Cosine, Bray-Curtis, Jaccard, Pearson, Euclidean, Mahalanobis)
3. Phase 3 — Bin sensitivity: n_bins = 2, 3, 4, 5 (Simpson only)
4. Phase 4 — Temporal: 5-fold temporal cross-validation

Project Structure

tessera/
├── __init__.py                    # Package init (v0.1.0)
├── core/
│   ├── __init__.py
│   ├── similarity.py              # 7 similarity measures
│   └── network.py                 # Graph construction (threshold, kNN, weighted)
├── synthetic/
│   ├── __init__.py
│   ├── landscape.py               # Feature space topology builder
│   ├── outcomes.py                # Failure pattern assignment (3 types + mixed)
│   └── visualize.py               # Diagnostic plots
├── data_acquisition.py            # Real dataset download & preprocessing
├── test_generator.py              # Synthetic data validation
└── test_pipeline.py               # End-to-end pipeline test

Current Status

• Synthetic data generator (3 patterns + mixed, with entity injection)
• Similarity engine (7 measures, vectorized)
• Network construction (threshold, kNN, weighted)
• Pipeline validation (data → similarity → graph)
• GNN model
• Real dataset acquisition (coral bleaching, SECOM)
• Validation pipeline (4 phases)
• Methods section
• Results
• Introduction, Discussion, Conclusions

Paper Writing Order

1. Methods
2. Results
3. Introduction
4. Discussion
5. Conclusions
6. Abstract (last)

References

• van Woesik, R. & Kratochwill, C. (2022). A global coral-bleaching database, 1980–2020. Scientific Data, 9(20).
• McCann, M. & Johnston, A. (2008). SECOM Dataset. UCI ML Repository.
• Tonini, J. (2025). NØMAD-HPC. Journal of Open Research Software.