# Neural Manifold Isometric Unfolding

Interactive 3D comparison of PCA, Isomap, and t-SNE on high-dimensional neural population activity

> Canonical page: https://elysiatools.com/en/visualizations/neural-manifold-isometric-unfolding

- **Category:** Math

## Overview

Interactive neuroscience visualization of neural manifold geometry. Simulates high-dimensional population activity (10-200 neurons) from three canonical latent scenarios: arm movement direction (circular ring manifold), decision-making (three discrete attractors), and memory replay (re-entrant trajectory). Side-by-side rotatable 3D scatter plots compare PCA, Isomap, and t-SNE dimensionality reduction. Isomap uses k-nearest-neighbor graphs and Floyd-Warshall geodesic distances followed by classical MDS; exact t-SNE uses perplexity-based Gaussian similarities and gradient descent. Metrics panel reports normalized stress (global distance distortion) and local isometry preservation (neighborhood distance-ratio consistency) for each method. Controls include neuron count N, recording duration T, noise level σ, preset scenarios, and regenerate button. Educational content covers neural manifolds (Cunningham & Yu 2014; Stringer et al. 2019), PCA, Isomap (Tenenbaum et al. 2000), t-SNE (van der Maaten & Hinton 2008), and practical interpretation of unfolding quality metrics. Multi-language support (zh, en, es, fr, de, ru, pt).

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