A Persistent Homology Pipeline for the Analysis of Neural Spike Train Data

2025-12-09

AI Summary

Conventional neural decoding fails when individual neurons exhibit weak stimulus selectivity. Method: This paper proposes a topological data analysis (TDA)-based framework for population-level neural activity decoding—first applying persistent homology to point process ensembles and integrating it with the Victor–Purpura distance to construct stable, multi-scale topological features; theoretical guarantees of feature robustness are provided via stability theorems and probabilistic stability analysis. Contribution/Results: Applied to murine insular cortex recordings during oral thermal stimulation, the method uncovers network-level cooperative structures undetectable via single-unit analysis, enabling significant discrimination among non-noxious thermal stimuli—even when no individual neuron shows statistically significant selectivity. This work establishes an interpretable, geometrically robust paradigm for decoding information from low-selectivity neural populations.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Learning with Manifolds
• Humans and AI: Brain-Sensing and Analysis

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

In this article, we introduce a Topological Data Analysis (TDA) pipeline for neural spike train data. Understanding how the brain transforms sensory information into perception and behavior requires analyzing coordinated neural population activity. Modern electrophysiology enables simultaneous recording of spike train ensembles, but extracting meaningful information from these datasets remains a central challenge in neuroscience. A fundamental question is how ensembles of neurons discriminate between different stimuli or behavioral states, particularly when individual neurons exhibit weak or no stimulus selectivity, yet their coordinated activity may still contribute to network-level encoding. We describe a TDA framework that identifies stimulus-discriminative structure in spike train ensembles recorded from the mouse insular cortex during presentation of deionized water stimuli at distinct non-nociceptive temperatures. We show that population-level topological signatures effectively differentiate oral thermal stimuli even when individual neurons provide little or no discrimination. These findings demonstrate that ensemble organization can carry perceptually relevant information that standard single-unit analysis may miss. The framework builds on a mathematical representation of spike train ensembles that enables persistent homology to be applied to collections of point processes. At its core is the widely-used Victor-Purpura (VP) distance. Using this metric, we construct persistence-based descriptors that capture multiscale topological features of ensemble geometry. Two key theoretical results support the method: a stability theorem establishing robustness of persistent homology to perturbations in the VP metric parameter, and a probabilistic stability theorem ensuring robustness of topological signatures.

Problem

• Analyzes neural spike train ensembles to understand stimulus discrimination.
• Uses topological data analysis to detect population-level encoding patterns.
• Addresses challenges in extracting meaningful information from coordinated neural activity.

Innovation

• Topological Data Analysis pipeline for neural spike trains
• Persistent homology applied to point process collections
• Victor-Purpura distance enables multiscale topological feature extraction