GhostUMAP2

Measuring and Analyzing (r,d)-Stability of UMAP

Installation

GhostUMAP2 can be installed in two ways:

1. Installation from Git (development version):

git clone https://github.com/jjmmwon/ghostumap2.git
cd ghostumap2
hatch shell

2. Installation via pip (PyPI release version):

pip install ghostumap

How to use GhostUMAP

from ghostumap import GhostUMAP2
from sklearn.datasets import fetch_openml

mnist = fetch_openml("mnist_784")
X, y = mnist["data"], mnist["target"]

mapper = GhostUMAP2()
O, G, active_ghosts = mapper.fit_transform(X, n_ghosts=16) 

mapper.visualize(label=y, legend=[str(i) for i in range(10)])

API

Function 'fit_transform'

def fit_transform(X, n_ghosts, r, ghost_gen, dropping, init_dropping):

Fit X into an embedded space with ghosts and return the transformed outputs.

Parameters

• X: array, shape (n_samples, n_features) or (n_samples, n_samples). If the metric is 'precomputed' X must be a square distance matrix. Otherwise, it contains a sample per row.

Ghost Configuration

• n_ghosts: The number of ghost points to embed in the embedding space. Default is 16.
• r: Radius for ghost generation. Default is 0.1.
• ghost_gen: Ghost generation parameter. Default is 0.2.

Dropping Scheme

• dropping: Whether to drop ghosts during optimization. Default is True.
• init_dropping: Initial dropping parameter. Default is 0.4.

Returns

• O: array, shape (n_samples, n_components) Embedding of the original data points, identical to the output of UMAP. It represents the transformed coordinates in the low-dimensional space.
• G: array, shape (n_samples, n_ghosts, n_components) Embedding of ghost points which are clones of the original points. These ghost points are used to evaluate the instability of each data instance.
• active_ghosts: array, shape (n_samples,) Boolean array indicating the presence of active ghost points for each data instance.

Function 'visualize'

def visualize(title=None, label=None, legend=None):

Returns an interactive visualization widget.

Parameters

• title: Title of the visualization.
• label: Labels for the data points.
• legend: Legend for the visualization.

Returns

• widget: An interactive visualization widget.

Function 'get_distances'

Get the distances between the original and ghost projections.

def get_distances(sensitivity=1):

Parameters

sensitivity: Sensitivity for distance calculation. Default is 1.

Returns

distances: array, shape (n_samples,). The distances between original and ghost embeddings.

Function 'get_unstable_ghosts'

Get the boolean array indicating unstable ghost points.

def get_unstable_ghosts(distance=0.1, sensitivity=1):

Parameters

distance: Distance threshold for determining instability. Default is 0.1. sensitivity: Sensitivity for instability calculation. Default is 1.

Returns

unstable_ghosts`: array, shape (n_samples,).