Inverse Projections

A Python package implementing inverse projection techniques for dimensionality reduction. It maps points from low-dimensional visualizations back to high-dimensional space, using a scikit-learn-style API for research prototypes, visual analytics workflows, and reproducible method comparisons.

Research Software Signals

• Packaged Python implementation published as inverse-projections.
• Reusable estimators with fit(), transform(), and inverse_transform() methods.
• Multiple inverse projection baselines in one API: NNinv, iLAMP, RBF inverse mapping, and multilateration.
• Example notebooks for method comparison and gradient-map quality assessment.
• MIT licensed for reuse in research and teaching projects.

Features

• Neural Network Inverse (NNinv): Deep learning approach using PyTorch
• Inverse LAMP (ILAMP): Local Affine Multidimensional Projection inverse mapping
• RBF Inverse: Radial Basis Function interpolation
• Multilateration: Geometric triangulation-based approach
• Gradient Maps: Quality assessment for inverse projections

Installation

pip install inverse-projections

For local development from a checkout:

uv sync

Quick Start

from inverse_projections import NNinv, ILAMP, RBFinv
import numpy as np
from sklearn.manifold import TSNE

# Your high-dimensional data
X = np.random.rand(1000, 50)

# Create 2D projection
X2d = TSNE().fit_transform(X)

# Train inverse projection
nninv = NNinv()
nninv.fit(X2d, X)

# Map new 2D points back to high-dimensional space
new_2d_points = np.random.rand(10, 2)
reconstructed = nninv.transform(new_2d_points)

Examples

See the examples/ directory for detailed demonstrations:

• demo.ipynb: MNIST dataset comparison
• demo_gradient_map.ipynb: Quality assessment with gradient maps

Methods

All methods follow sklearn-compatible API with fit(), transform(), and inverse_transform() methods.

Repository Structure

• src/inverse_projections/: package source code.
• examples/: demonstration notebooks.
• pyproject.toml: package metadata and dependencies.
• uv.lock: locked development environment.

Reference

Based on the following research papers:

• iLAMP: dos Santos Amorim, E. P., Brazil, E. V., Daniels, J., Joia, P., Nonato, L. G., & Sousa, M. C. (2012). iLAMP: Exploring high-dimensional spacing through backward multidimensional projection. Proc. IEEE VAST. https://doi.org/10.1109/VAST.2012.6400489

• RBFinv: Amorim, E., Vital Brazil, E., Mena-Chalco, J., Velho, L., Nonato, L. G., Samavati, F., & Costa Sousa, M. (2015). Facing the high-dimensions: Inverse projection with radial basis functions. Computers & Graphics. https://doi.org/10.1016/j.cag.2015.02.009

• NNinv: Espadoto, M., Rodrigues, F. C. M., Hirata, N. S. T., & Hirata Jr, R. (2019). Deep Learning Inverse Multidimensional Projections. Proc. EuroVA. https://doi.org/10.2312/eurova.20191118

• NNinv: Espadoto, M., Appleby, G., Suh, A., Cashman, D., Li, M., Scheidegger, C. E., Anderson, E. W., Chang, R., & Telea, A. C. (2021). UnProjection: Leveraging Inverse-Projections for Visual Analytics of High-Dimensional Data. IEEE TVCG. https://doi.org/10.1109/TVCG.2021.3125576

• MDSinv: Blumberg, D., Wang, Y., Telea, A., Keim, D. A., & Dennig, F. L. (2024). Inverting Multidimensional Scaling Projections Using Data Point Multilateration. Proceed EuroVA

License

This repository is released under the MIT License. See LICENSE for details.