Dimensionality Reduction in Machine Learning: PCA and t-SNE.

The provided code snippets demonstrate the use of two popular dimensionality reduction techniques: Principal Component Analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE). Let's break down each part:

1. PCA

Importing Libraries and Data Loading

python
 
1from sklearn.decomposition import PCA
2import numpy as np

• sklearn.decomposition.PCA is used for performing PCA.
• numpy is imported for numerical operations.

Scaling the Data

python
 
1from sklearn.preprocessing import StandardScaler
2
3X_scaled = StandardScaler().fit_transform(X)

• The data X is scaled using StandardScaler, which standardizes features by removing the mean and scaling to unit variance. This step is crucial before applying PCA because PCA is sensitive to the variances of the initial variables.

Running PCA

python
 
1pca = PCA(n_components=2)
2X_pca = pca.fit_transform(X_scaled)
3
4print(pca.explained_variance_ratio_)

• PCA with n_components=2 reduces the dimensionality of the data to 2 principal components.
• The explained variance ratio is printed, which indicates how much information (variance)

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