grease-embeddings 0.1.0

Generalizable and Efficient Approximate Spectral Embeddings

GrEASE

This is the official PyTorch implementation of GrEASE from the paper "Generalizable Spectral Embedding with Applications to UMAP.
One of many applications of ScaSE is UMAP initialization, as shown in the following figure:

Initializing UMAP with ScaSE results in a similar embedding to the one obtained by UMAP itself (initialized with Spectral Embedding), but with a much faster runtime for a large number of samples.

Installation

To install the package, simply use the following command:

pip install grease

Usage

The basic functionality is quite intuitive and easy to use, e.g.,

from grease import GrEASE

grease = GrEASE(n_components=10)  # n_components is the number of dimensions in the low-dimensional representation
grease.fit(X)  # X is the dataset and it should be a torch.Tensor
X_reduced = grease.transfrom(X)  # Get the low-dimensional representation of the dataset
Y_reduced = grease.transform(Y)  # Get the low-dimensional representation of a test dataset

You can read the code docs for more information and functionalities.

Out of many applications, ScaSE can be used for UMAP initialization, Fiedler vector and value approximation, and Diffusion Maps approximation. The following is examples of how to use ScaSE for each of these applications:

UMAP initialization

from scase import ScaSE
from umap import UMAP

scase = ScaSE(n_components=2)
se = scase.fit_transform(X)
umap = UMAP(n_components=2, init=se)
X_reduced = umap.fit_transform(X)

Fiedler vector and value approximation

from scase import ScaSE

scase = ScaSE(n_components=1)
fiedlerVector = scase.fit_transform(X)
fiedlerValue = scase..get_eigenvalues()

Diffusion Maps approximation

from scase import ScaSE

scase = ScaSE(n_components=10)
diffusionMaps = scase.fit_transform(X, t=5)  # t is the diffusion time

Running examples

In order to run the model on the moon dataset, you can either run the file, or using the command-line command:
python -m examples.reduce_moon
This will run the model on the moon dataset and plot the results.

The same can be done for the circles dataset:
python -m examples.reduce_circles