Transform¶
Principal Components Analysis (PCA)¶
Principal Component Analysis (PCA) is important because it simplifies complex datasets by reducing their dimensionality while preserving most of the essential information. By transforming correlated variables into a smaller set of uncorrelated components, PCA helps reveal hidden patterns, improves data visualization, and reduces noise. This makes it especially valuable for speeding up machine learning algorithms, preventing overfitting, and handling high-dimensional data more efficiently. Overall, PCA enhances both the interpretability and performance of data analysis processes.
In [2]:
import numpy as np
import matplotlib.pyplot as plt
import sklearn
import pandas as pd
data = pd.read_csv("~/work/kelzang-wangdi/datasets/StudentsPerformance.csv")
print("Columns available in your dataset:\n", data.columns)
# Choose FEATURES and LABEL correctly
# Example: label = gender, features = math score, reading score, writing score
y = data["parental level of education"].astype('category').cat.codes # convert text → numbers
X = data[["math score", "reading score", "writing score"]].values
print(f"Your data shape (records, features): {X.shape}")
# Scatter plot: use first two features
plt.scatter(X[:,0], X[:,1], c=y)
plt.xlabel("math score")
plt.ylabel("reading score")
plt.title("Students Performance: Two Features")
plt.colorbar(label="parental level of education")
plt.show()
# Standardize
X = X - np.mean(X, axis=0)
std = np.std(X, axis=0)
Xscale = X / np.where(std > 0, std, 1)
# PCA 3 components (only 3 features exist)
pca = sklearn.decomposition.PCA(n_components=3)
Xpca = pca.fit_transform(Xscale)
plt.plot(pca.explained_variance_, 'o')
plt.xlabel("component")
plt.ylabel("explained variance")
plt.show()
# PCA scatter
plt.scatter(Xpca[:,0], Xpca[:,1], c=y)
plt.xlabel("PC1")
plt.ylabel("PC2")
plt.title("PCA of Student Performance")
plt.colorbar(label="parental level of education")
plt.show()
Columns available in your dataset:
Index(['gender', 'race/ethnicity', 'parental level of education', 'lunch',
'test preparation course', 'math score', 'reading score',
'writing score'],
dtype='object')
Your data shape (records, features): (1000, 3)
