Dimensionality Reduction with Point-distributions Similarity Invariant

A scikit-learn compatible dimensionality reduction technique that preserves point-distribution similarity through multilateration-based embedding.

Overview

This repository implements $\Psi$-DR (or PSIDR): Point-distribution Similarity Invariant Dimensionality Reduction, a novel approach for reducing high-dimensional data while preserving point-distribution similarity structures.

Installation

Requirements

pip install numpy scipy scikit-learn matplotlib torch kbc-clustering 

Quick Start

importnumpyasnpfromPSIDRimportPSIDRfromsklearn.datasetsimportmake_blobsimportmatplotlib.pyplotasplt# Generate sample dataX, y=make_blobs(n_samples=500, n_features=50, centers=5, random_state=42)
# Initialize and fit the reducerpsidr=PSIDR(n_components=2, k=5, random_state=42)
X_embedded=psidr.fit_transform(X)
# Visualize resultsplt.scatter(X_embedded[:, 0], X_embedded[:, 1], c=y, cmap='tab10')
plt.title("PSIDR Embedding")
plt.colorbar(label='Cluster')
plt.show()

Methods

fit(X, y=None)

Fit the model to training data.

• Parameters: X (array-like, shape (n_samples, n_features)), y (ignored)
• Returns: self

transform(X)

Transform new data to the low-dimensional space.

• Parameters: X (array-like, shape (n_samples_new, n_features))
• Returns: X_new (ndarray, shape (n_samples_new, n_components))

fit_transform(X, y=None)

Fit the model and return the transformed training data.

• Returns: X_new (ndarray, shape (n_samples, n_components))

Citation

If you use this method in your research, please cite:

@inproceedings{
PSIDR,
title={Dimensionality Reduction with Point-distributions Similarity Invariant},
author={Zhang, Hang and Ting, Kai Ming},
booktitle={Forty-third International Conference on Machine Learning},
year={2026},
}

License

MIT License - see LICENSE file for details.