Reciprocal Isomap

Reciprocal Isomap is a reciprocal variant of Isomap for robust non-linear dimensionality reduction in Python.

The ReciprocalIsomap transformer was inspired by scikit-learn’s implementation of Isomap, but the reciprocal variant enforces shared connectivity in the underlying k-nearest neighbors graph (i.e., two points are only considered neighbors if each is a neighbor of the other).

Related Projects

• NeuMapper is a scalable Mapper algorithm for neuroimaging data analysis. The Matlab implementation was designed specifically for working with complex, high-dimensional neuroimaging data and produces a shape graph representation that can be annotated with meta-information and further examined using network science tools.

Setup

Dependencies

Python 3.6+

Required Python Packages

• numpy
• scipy
• scikit-learn
• networkx

Install using pip

Assuming you have the required dependencies, you should be able to install using pip.

pip install git+https://github.com/calebgeniesse/reciprocal_isomap.git

Alternatively, you can also clone the repository and build from source.

git clone git@github.com:calebgeniesse/reciprocal_isomap.git
cd reciprocal_isomap

pip install -r requirements.txt
pip install -e .

Usage

The ReciprocalIsomap object

Here, we will walk through a simple example using ReciprocalIsomap.

import numpy as np 
from reciprocal_isomap import ReciprocalIsomap

# generate some random data points.
X = np.random.random((100, 10))

# configure the ReciprocalIsomap object
r_isomap = ReciprocalIsomap(n_neighbors=8)

# fit and transform the data in a single step
embedding = r_isomap.fit_transform(X)

We can also fit the data, and then project points into the embedding.

# fit the data and then transform a subset of the data
embedding = r_isomap.fit(X).transform(X[1::2])

Similarly, we can project new unseen data points into the embedding.

# fit a subset of the data and then transform the other half of the data 
embedding = r_isomap.fit(X[0::2]).transform(X[1::2])

Comparison with Isomap

Here, we compare embeddings created using Isomap and ReciprocalIsomap across several values of the n_neighbors parameter.

First, let’s plot the embeddings from Isomap.

from sklearn.manifold import Isomap
import matplotlib.pyplot as plt

try_n_neighbors = [3, 4, 5, 6]

fig, axes = plt.subplots(1, 4, figsize=(24, 5))
for i,n_neighbors in enumerate(try_n_neighbors):
    isomap = Isomap(n_neighbors=n_neighbors)
    embedding = isomap.fit_transform(X)
    axes[i].scatter(embedding[:,0], embedding[:,1], c=y, cmap='Spectral_r')
    axes[i].set_title(f"Isomap(n_neighbors={n_neighbors})", fontweight='bold') 

Now, let’s plot the embeddings from ReciprocalIsomap.

from reciprocal_isomap import ReciprocalIsomap
import matplotlib.pyplot as plt

try_n_neighbors = [3, 4, 5, 6]

fig, axes = plt.subplots(1, 4, figsize=(24, 5))
for i,n_neighbors in enumerate(try_n_neighbors):
    r_isomap = ReciprocalIsomap(n_neighbors=n_neighbors)
    embedding = r_isomap.fit_transform(X)
    axes[i].scatter(embedding[:,0], embedding[:,1], c=y, cmap='Spectral_r')
    axes[i].set_title(f"ReciprocalIsomap(n_neighbors={n_neighbors})", fontweight='bold')

Citation

If you find Reciprocal Isomap useful, please consider citing:

Geniesse, C., Chowdhury, S., & Saggar, M. (2022). NeuMapper: A Scalable Computational Framework for Multiscale Exploration of the Brain’s Dynamical Organization. Network Neuroscience, Advance publication. doi:10.1162/netn_a_00229