PyGlimmerMDS 1.0.0

Python Implementation of the Glimmer algorithm for multidimensional scaling

PyGlimmerMDS

Multidimensional scaling (MDS) for large data sets - a python implementation of the Glimmer algorithm.
[Glimmer: Multilevel MDS on the GPU - 2009 - IEEE TVCG - Ingram, Munzner, Olano]

Glimmer performs dimensionality reduction on high-dimensional data sets of many instances, avoiding the quadratic runtime behavior of naive MDS implementations by employing a multilevel (coarse to fine) approach. This implementation does not utilize the GPU, but gives considerable speedup nonetheless and makes MDS on large data sets feasible.

Glimmer is a metric MDS and uses Euclidean distance in the high-dimensional space as the dissimilarity measure. This is not the classical MDS that has a linear projection solution. Instead it solves the following optimization problem:

$$\underset{y_1,..,y_n}{\mathrm{argmin}} ~ \sum_{i=1}^n \sum_{j=i+1}^n \Big(\lVert x_i-x_j \rVert - \lVert y_i-y_j \rVert\Big) ^2 \quad \mathrm{where} x_i \in \mathbb{R}^D \mathrm{and} y_i \in \mathbb{R}^{d \ll D}$$

Installation

PyGlimmerMDS is available on PyPi and can be installed through pip.

pip install PyGlimmerMDS

or if you want to install a specific commit use

pip install git+https://github.com/hageldave/PyGlimmerMDS@<commit_hash>

How to use

Very briefly

Performing Glimmer on a data set works like this:

mds = Glimmer(decimation_factor=2, stress_ratio_tol=1-1e-5, rng=rng)
projection = mds.fit_transform(data) # alternative: projection, stress = execute_glimmer(data)
print(f"final stress={mds.stress}")

Complete example

Jittering the Iris data set to produce a data set of 38,400 points. Performing Glimmer on this data set.

from pyglimmermds import Glimmer, execute_glimmer
from sklearn import preprocessing as prep
from sklearn import datasets
import numpy as np
import matplotlib.pyplot as plt

rng = np.random.default_rng(seed=0xBA0BAB)

# get iris data
dataset = datasets.load_iris()
data = dataset.data
labels = dataset.target
# duplicate data with added noise
for _ in range(8):
  data = np.vstack((data,data+(rng.random((data.shape[0], data.shape[1]))*0.2-.1)))
  labels = np.append(labels,labels)
print(data.shape)
print(labels.shape)

# perform MDS
data = prep.StandardScaler().fit_transform(data)
mds = Glimmer(decimation_factor=2, stress_ratio_tol=1-1e-5, rng=rng)
projection = mds.fit_transform(data) # alternative: projection, stress = execute_glimmer(data)
print(f"final stress={mds.stress}")

# show scatter plot
fig, ax = plt.subplots()
scatter = ax.scatter(projection[:, 0], projection[:, 1], c=labels, s=0.02)
ax.axis('equal')
plt.show(fig)

This video shows the layouting happening per level and iteration

https://github.com/user-attachments/assets/aa9f7a8c-1c03-46a3-8ee1-19b3d2d4033e