approx-umap 0.1.2

Modification of the UMAP algorithm to allow for fast approximate projections of new data points.

Approximate UMAP

Modification of the UMAP algorithm to allow for fast approximate projections of new data points.

Description

This package provides a class ApproxUMAP that allows for fast approximate projections of new data points in the target space.

The fit and fit_transform methods of ApproxUMAP are nearly identical to those of umap.UMAP; they simply fit an additional sklearn.neighbors.NearestNeighbors estimator.

Only the transform method significantly differs; it approximates the projection of new data points in the embedding space to improve the projection speed. The projections are approximated by finding the nearest neighbors in the source space and computing their weighted average in the embedding space. The weights are the inverse of the distances in the source space.

Formally, the projection of a new point $x$ is approximated as follows: $$u=\sum_i^k\frac{\frac{1}{d_i}}{\sum_j^k\frac{1}{d_j}}u_i$$ with $x_1\dots x_k$ the $k$ nearest neighbours of $x$ in the source space among the points used for training (i.e., passed to fit or fit_transform), $d_i=distance(x, x_i)$, and $u_1\dots u_i$ the exact UMAP projections of $x_1\dots x_k$.

Installation

The package can be installed via pip:

pip install approx-umap

Usage

The usage of ApproxUMAP is similar to that of any scikit-learn transformer:

import numpy as np
from approx_umap import ApproxUMAP

X = np.random.rand(100, 10)
emb_exact = ApproxUMAP().fit_transform(X)  # exact UMAP projections
emb_approx = ApproxUMAP().fit(X).transform(X)  # approximate UMAP projection

Citation

Please, cite this work as:

@inproceedings{approx-umap2024,
    title = {Approximate UMAP allows for high-rate online visualization of high-dimensional data streams},
    author = {Peter Wassenaar and Pierre Guetschel and Michael Tangermann},
    year = {2024},
    month = {September},
    booktitle = {9th Graz Brain-Computer Interface Conference},
    address = {Graz, Austria},
    url = {https://arxiv.org/abs/2404.04001},
}