strand-survival-topological-analysis

name	strand-survival-topological-analysis
description	STRAND (Survival Topological Representation ANalysis of Diagrams) treats persistence diagrams as survival data for hypothesis testing, effect sizes, and vectorisation in neuroscience applications.
tags	["neuroscience","topological-data-analysis","persistence-diagrams","survival-analysis","brain-connectivity","fMRI"]
activation_keywords	["STRAND","persistence diagrams","topological data analysis","survival analysis","brain connectivity","fMRI topology"]
version	1.0.0

STRAND: From Persistence to Survival - Topological Features Analysis

Overview

This methodology from arXiv:2606.11911 (June 10, 2026) introduces STRAND (Survival Topological Representation ANalysis of Diagrams), which treats persistence diagrams as survival data, enabling hypothesis testing, interpretable effect sizes, and vectorisation from a single coherent representation.

Authors: Juliette Murris, Bernadette Stolz, Karsten Borgwardt

Core Innovation

Problem Addressed

Persistence diagrams (PDs) are standard in topological data analysis but:

1. Do not naturally live in a vector space
2. Statistical tools for comparing them evolved separately from downstream prediction methods
3. No unified framework linking hypothesis testing and machine learning

Key Breakthrough

STRAND treats (collections of) PDs as survival data:

• Each topological feature with persistence $p = d - b$ is a fully observed time-to-event
• Persistence survival function $S(t) = \mathbb{P}(p > t)$ is central for comparing diagrams

Three Capabilities from One Representation

1. Non-Parametric Two-Sample Test

• Calibrated Type I error
• High power from small number of diagrams
• Applicable to manifold topology comparisons

2. Interpretable Effect Sizes

• Quantifies topological feature differences
• Enables statistical inference beyond p-values

3. 1-Wasserstein-Stable Feature Vector

• Wasserstein-stable vectorisation
• For downstream machine learning tasks
• First unified framework for PD analysis

Methodology

Persistence as Survival Data

# Each feature: time-to-event interpretation
persistence = death_time - birth_time  # time-to-event
survival_function = P(persistence > threshold)

Survival Function Analysis

• Non-parametric estimation from PD collections
• Survival curves capture topological feature persistence
• Enables distribution comparison without parametric assumptions

Vectorisation Strategy

• 1-Wasserstein distance preserved
• Embedding stable to geometric perturbations
• Suitable for ML classifier/regressor inputs

Validation & Performance

Synthetic Validation

• Manifold topology with controlled structure
• Calibration: Type I error matches theoretical
• Power: High detection of topological differences

Benchmark Performance

• 14 graph datasets
• 3D point cloud benchmarks
• Competitive with specialized vectorisation methods

Neuroscience Application

• Functional brain connectivity in fMRI data
• Network topology comparison across conditions
• Detect connectivity pattern differences

Applications

1. Brain Network Analysis

• Compare connectivity topology between groups
• Test cognitive state effects on brain structure
• Detect disease-related topological changes

2. Neuroscience Hypothesis Testing

• Formal statistical tests for topological features
• Effect sizes quantify clinical significance
• Beyond mere classification accuracy

3. Topological ML Pipeline

• Unified framework: test → interpret → predict
• Single representation for all analysis stages
• Reproducible statistical inference

Implementation Guide

Key Concepts

from strand import STRANDAnalyzer

# Initialize with persistence diagrams
analyzer = STRANDAnalyzer(pd_collection)

# Two-sample test
test_result = analyzer.two_sample_test(group1_pds, group2_pds)

# Effect size
effect = analyzer.effect_size(group1_pds, group2_pds)

# Feature vector for ML
features = analyzer.vectorise(pd_collection)

Calibration Guarantee

• Type I error under null hypothesis matches significance level
• No ad-hoc threshold selection
• Proper statistical inference

Technical Details

Survival Function Properties

• Non-parametric Kaplan-Meier style estimation
• Captures persistence distribution structure
• Robust to outlier features

Wasserstein Stability

• 1-Wasserstein metric preserved in embedding
• Geometric perturbations bounded
• Suitable for downstream learning

Statistical Framework

• Hypothesis testing with calibrated p-values
• Effect sizes with confidence intervals
• Vectorisation for prediction tasks

Cross-References

• [[higher-order-brain-networks]] - Higher-order topological analysis
• [[brain-connectivity-analysis]] - Connectivity methods
• [[fmri-foundation-model-batch-effects]] - Batch effects in fMRI
• [[topological-effective-connectivity-hodge]] - Hodge decomposition

Key Insight

STRAND is the first method to provide hypothesis testing, effect sizes, and vectorisation for persistence diagrams from a single coherent and interpretable representation, enabling proper statistical inference in topological neuroscience.

Activation Keywords

Use when working on:

• Persistence diagram analysis
• Topological brain connectivity
• Statistical testing of topological features
• Vectorisation of persistence diagrams
• fMRI network topology comparison