Manifold Learning with Scikit-Learn

Introduction

In this lab, we will explore manifold learning, which is an approach to non-linear dimensionality reduction. Dimensionality reduction is often used to visualize high-dimensional datasets, as it can be difficult to interpret data in more than three dimensions. Manifold learning algorithms aim to find a lower-dimensional representation of the data that preserves the underlying structure.

In this lab, we will use the scikit-learn library to perform manifold learning on various datasets. We will explore different algorithms and compare their performance and outputs.

VM Tips

After the VM startup is done, click the top left corner to switch to the Notebook tab to access Jupyter Notebook for practice.

Sometimes, you may need to wait a few seconds for Jupyter Notebook to finish loading. The validation of operations cannot be automated because of limitations in Jupyter Notebook.

If you face issues during learning, feel free to ask Labby. Provide feedback after the session, and we will promptly resolve the problem for you.

Skills Graph

Isomap

The Isomap algorithm is one of the earliest approaches to manifold learning. It seeks a lower-dimensional embedding that maintains geodesic distances between all points.

from sklearn.manifold import Isomap

## Create an instance of the Isomap algorithm
isomap = Isomap(n_components=2)

## Fit the algorithm to the data and transform the data to the lower-dimensional space
X_transformed = isomap.fit_transform(X)

Locally Linear Embedding (LLE)

Locally Linear Embedding (LLE) is another manifold learning algorithm. It seeks a lower-dimensional projection of the data that preserves distances within local neighborhoods.

from sklearn.manifold import LocallyLinearEmbedding

## Create an instance of the LLE algorithm
lle = LocallyLinearEmbedding(n_components=2)

## Fit the algorithm to the data and transform the data to the lower-dimensional space
X_transformed = lle.fit_transform(X)

t-distributed Stochastic Neighbor Embedding (t-SNE)

t-SNE is a popular manifold learning method that converts affinities of data points to probabilities. It is particularly effective at visualizing high-dimensional data.

from sklearn.manifold import TSNE

## Create an instance of the t-SNE algorithm
tsne = TSNE(n_components=2)

## Fit the algorithm to the data and transform the data to the lower-dimensional space
X_transformed = tsne.fit_transform(X)

Compare Results

Compare the results of the different manifold learning algorithms. Visualize the transformed data to see how the algorithms have preserved the underlying structure of the data.

import matplotlib.pyplot as plt

## Create a scatter plot of the transformed data
plt.scatter(X_transformed[:, 0], X_transformed[:, 1], c=y)
plt.title('Manifold Learning')
plt.xlabel('Component 1')
plt.ylabel('Component 2')
plt.show()

Summary

Manifold learning is a powerful tool for visualizing high-dimensional datasets. It allows us to reduce the dimensionality of the data while preserving the underlying structure. In this lab, we explored three different manifold learning algorithms: Isomap, Locally Linear Embedding (LLE), and t-SNE. We applied these algorithms to various datasets and compared their results. By using manifold learning, we can gain insights into the structure of complex datasets and more effectively analyze and visualize high-dimensional data.