Lab 3: Dimensionality Reduction using Principal Component Analysis (PCA)

Aim

Apply PCA to reduce dimensionality and visualize transformed data.

Objectives

• Standardize or center data if necessary.
• Fit PCA and choose number of components.
• Project data onto principal components.
• Inspect explained variance ratio.

Algorithm / Procedure

1. Load/define 2D toy dataset.
2. Center data (sklearn PCA centers by default).
3. Fit PCA with n_components=1.
4. Transform data and display shapes.
5. Print explained variance ratio.

Python Code

import numpy as np
from sklearn.decomposition import PCA

X = np.array([[2.5, 2.4],
              [0.5, 0.7],
              [2.2, 2.9],
              [1.9, 2.2],
              [3.1, 3.0],
              [2.3, 2.7]])

pca = PCA(n_components=1, random_state=0)
X_reduced = pca.fit_transform(X)

print("Original Shape:", X.shape)
print("Reduced Shape:", X_reduced.shape)
print("Reduced Data:\n", X_reduced)
print("Explained Variance Ratio:", pca.explained_variance_ratio_)

Sample Output (expected)

Original Shape: (6, 2)
Reduced Shape: (6, 1)
Reduced Data:
 [[ 0.66]
  [-2.12]
  [ 0.57]
  [-0.33]
  [ 1.53]
  [-0.31]]
Explained Variance Ratio: [0.96]