Latent Space Visualization Lab

A friendly guide for understanding PCA, SNE, t-SNE, UMAP, and modern latent-space visualization.

This repo focuses on:

• interactive animations, including 2D and 3D views;
• reproducible PCA/t-SNE/UMAP experiments;
• generated visualizations and GIFs;
• hyperparameter sensitivity on handwritten digits;
• examples from toy geometry, nonlinear dynamics, and handwritten-digit embeddings.

Visual Highlights

The repo opens with the artifacts, because the fastest way to understand these methods is to see what changes.

3D Manifold And Projection Animations

Swiss Roll: 3D Geometry	Swiss Roll: Collapse To 2D

Lorenz Attractor: Dynamical-System Geometry	4D Hypercube Shadow: Higher-Dimensional Projection

Hyperparameter Sensitivity On Handwritten Digits

t-SNE Perplexity Sweep	UMAP n_neighbors Sweep

Static Comparison Figures

UMAP Graph Construction	Digits t-SNE Grid

PnP/RED Reconstruction Trajectory Gallery

The gallery below shows representative reconstruction dynamics across forward models, algorithm families, and denoiser profiles. These images are lightweight reproducible demonstrators; the pretrained denoiser runner loads DRUNet, DnCNN, or DiffUNet-style models from DeepInverse at runtime and does not store weights in the repo.

Cross-Case Reconstruction Overview	Gaussian Deblur Residual Trajectories

Gaussian Deblur Trajectory Embedding	Super-Resolution Trajectory Embedding

For the full interactive experience, run a local server and open:

• index.html for algorithm animations;
• visual3d.html for 3D and higher-dimensional projection geometry;
• dashboard.html for side-by-side method comparison.

Quick Start

Open the interactive animation lab:

index.html

For the comparison dashboard, start a local server:

python -m http.server 8000

Then visit:

http://localhost:8000/dashboard.html

Open the 3D/higher-dimensional visual lab:

http://localhost:8000/visual3d.html

What Is Included

Interactive Tools

• index.html: animated PCA, SNE, t-SNE, and UMAP intuition lab.
• dashboard.html: side-by-side comparison dashboard for generated handwritten-digit embeddings.
• visual3d.html: orbitable 3D and higher-dimensional projection lab.

Guides

• docs/theory_guide.md: PCA, SNE, t-SNE, UMAP, TriMap, and PaCMAP theory.
• docs/comparison_guide.md: hyperparameter sensitivity, timing, metrics, and UMAP graph intuition.
• docs/pnp_red_trajectory_guide.md: optional PnP/RED trajectory visualization with DeepInverse denoisers.
• latent_space_visualization_tutorial.md: beginner-friendly tutorial.

Generated Results

• results_canonical/: rings and Lorenz attractor PCA/t-SNE/UMAP results.
• results_digits/: handwritten-digits sweeps, GIFs, metrics, and browser-loadable embeddings.
• results_3d/: exported 3D rotations, projection comparisons, and 3D-to-2D collapse GIFs.
• results_pnp_red_gallery/: PnP/RED reconstruction snapshots, residual trajectories, and trajectory embeddings.

Reproducible Scripts

• scripts/generate_canonical_results.py
• scripts/generate_digits_sensitivity.py
• scripts/generate_3d_artifacts.py
• scripts/generate_pnp_red_gallery.py
• scripts/generate_results.js
• scripts/run_pnp_red_trajectory.py

Install dependencies:

pip install -r requirements.txt

Regenerate canonical results:

python scripts/generate_canonical_results.py

Regenerate handwritten-digits sweeps:

python scripts/generate_digits_sensitivity.py

On Windows, if UMAP/Numba needs a local cache:

$env:NUMBA_CACHE_DIR="$PWD\.numba_cache"
python scripts\generate_digits_sensitivity.py

Regenerate 3D exports:

python scripts/generate_3d_artifacts.py

Regenerate the public PnP/RED visual gallery:

python scripts/generate_pnp_red_gallery.py

Optional PnP/RED reconstruction trajectory demo:

pip install -r requirements-inverse.txt
python scripts/run_pnp_red_trajectory.py --task gaussian_deblur --denoiser drunet --iters 2000

Denoiser weights are loaded at runtime through DeepInverse and are not stored in this repository.

Learning Path

1. Open index.html.
2. Try PCA on Swiss roll.
3. Switch to SNE and t-SNE to see local neighborhoods form.
4. Switch to UMAP and inspect graph links.
5. Open visual3d.html and animate 3D-to-2D projection collapse.
6. Open dashboard.html and compare PCA, t-SNE, and UMAP side by side.
7. Read docs/comparison_guide.md.
8. Read docs/theory_guide.md.
9. Inspect results_digits/summary.md and results_digits/metrics.csv.

3D and Higher-Dimensional Visual Lab

The 3D lab adds:

• orbit and zoom controls;
• Swiss roll, Lorenz attractor, helix, nested rings, and 4D hypercube shadow;
• PCA, random, and radial 2D projection targets;
• k-nearest-neighbor graph edges;
• projection trails;
• animated collapse from original geometry to a 2D projection.

This is the best page for understanding the geometric difference between:

the object itself
the shadow we see
the projection method we choose

Exported 3D artifacts:

• results_3d/swiss_3d_rotation.gif
• results_3d/swiss_collapse_to_2d.gif
• results_3d/lorenz_3d_rotation.gif
• results_3d/lorenz_collapse_to_2d.gif
• results_3d/hypercube4d_3d_rotation.gif
• results_3d/hypercube4d_collapse_to_2d.gif
• results_3d/summary.md

Current Handwritten-Digits Results

Method	Hyperparameter	Value	kNN overlap	Trustworthiness
PCA	n_components	2	0.137	0.817
t-SNE	perplexity	5	0.468	0.974
t-SNE	perplexity	15	0.508	0.980
t-SNE	perplexity	30	0.517	0.982
t-SNE	perplexity	50	0.513	0.982
UMAP	n_neighbors	5	0.433	0.968
UMAP	n_neighbors	15	0.448	0.974
UMAP	n_neighbors	50	0.425	0.970
UMAP	n_neighbors	100	0.418	0.965
UMAP	min_dist	0.0	0.435	0.974
UMAP	min_dist	0.1	0.433	0.971
UMAP	min_dist	0.35	0.431	0.969
UMAP	min_dist	0.7	0.404	0.962

Interpretation Rules

• Always ask what the method preserves.
• Always compare against PCA.
• Always sweep important hyperparameters.
• Treat t-SNE/UMAP axes as arbitrary.
• Treat beautiful maps as hypothesis generators, not proof.

References

• Pearson, K. "On Lines and Planes of Closest Fit to Systems of Points in Space." 1901.
• Hotelling, H. "Analysis of a Complex of Statistical Variables into Principal Components." 1933.
• Hinton, G. E. and Roweis, S. T. "Stochastic Neighbor Embedding." 2002.
• van der Maaten, L. and Hinton, G. "Visualizing Data using t-SNE." JMLR, 2008.
• McInnes, L., Healy, J., and Melville, J. "UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction." 2018.
• Amid, E. and Warmuth, M. K. "TriMap: Large-scale Dimensionality Reduction Using Triplets." 2019.
• Wang, Y., Huang, H., Rudin, C., and Shaposhnik, Y. "Understanding How Dimension Reduction Tools Work..." 2021.