Dimensionality reduction
Dimensionality reduction is a technique used in unsupervised learning to reduce the number of features or variables in a dataset while retaining the most important information. This is done to make the dataset more manageable and easier to analyze, especially when dealing with high-dimensional data.
There are many dimensionality reduction techniques, but two of the most popular ones are principal component analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE).
PCA is a linear dimensionality reduction technique that works by finding the directions of maximum variance in the data and projecting the data onto these directions. The result is a set of new variables, called principal components, that explain most of the variation in the data. PCA is useful for reducing the dimensionality of data while preserving as much information as possible.
t-SNE is a non-linear dimensionality reduction technique that works by modeling the high-dimensional data in a lower-dimensional space. It is particularly good at preserving the local structure of the data, making it useful for visualizing complex datasets with many clusters or subgroups.
Here is an example of how to use PCA and t-SNE for dimensionality reduction and visualization in Python using the scikit-learn library:
import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import load_digits
from sklearn.decomposition import PCA
from sklearn.manifold import TSNE
# Load the digits dataset
digits = load_digits()
# Apply PCA to reduce the dimensionality to 2 components
pca = PCA(n_components=2)
pca_transformed = pca.fit_transform(digits.data)
# Apply t-SNE to reduce the dimensionality to 2 components
tsne = TSNE(n_components=2)
tsne_transformed = tsne.fit_transform(digits.data)
# Plot the results of PCA
plt.scatter(pca_transformed[:, 0], pca_transformed[:, 1], c=digits.target)
plt.title("PCA visualization of digits dataset")
plt.show()
# Plot the results of t-SNE
plt.scatter(tsne_transformed[:, 0], tsne_transformed[:, 1], c=digits.target)
plt.title("t-SNE visualization of digits dataset")
plt.show()
In this example, we load the digits dataset and apply PCA and t-SNE to reduce the dimensionality of the data to 2 components. We then plot the results using a scatter plot, where each point represents a digit and its color represents its label. The resulting plots show how PCA and t-SNE can be used to visualize and understand complex datasets.
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