W Code - Pattern-Based DSA Learning Platform

Bhanu Bisht

Support Vector Machines

Maximum Margin Classifiers with the Kernel Trick

Topics

sklearn

Implementation

🇮🇳

Indian Context

Mango Classification, Handwritten Devanagari Recognition, Vehicle Number Plate OCR

What is SVM?

Concept Level: Beginner

Python Implementation

# UNDERSTANDING SVM BASICS

import numpy as np
import matplotlib.pyplot as plt
from sklearn.svm import SVC
from sklearn.datasets import make_blobs

# Create a simple 2D classification dataset
# Like sorting Alphonso vs Badami mangoes by size and sweetness
np.random.seed(42)
X, y = make_blobs(n_samples=100, centers=2, cluster_std=1.2, random_state=42)

# Train SVM with linear kernel
svm_model = SVC(kernel='linear', C=1.0)
svm_model.fit(X, y)

# Get the support vectors
support_vectors = svm_model.support_vectors_
print(f"Number of Support Vectors: {len(support_vectors)}")
print(f"Support Vectors per class: {svm_model.n_support_}")

# Plot the data and decision boundary
plt.figure(figsize=(10, 8))
plt.scatter(X[:, 0], X[:, 1], c=y, cmap='RdYlBu', edgecolor='black', s=50)

# Highlight support vectors
plt.scatter(support_vectors[:, 0], support_vectors[:, 1], 
            s=200, facecolors='none', edgecolors='green', linewidth=2,
            label='Support Vectors')

# Plot decision boundary and margins
ax = plt.gca()
xlim = ax.get_xlim()
ylim = ax.get_ylim()

# Create grid for decision boundary
xx, yy = np.meshgrid(np.linspace(xlim[0], xlim[1], 50),
                     np.linspace(ylim[0], ylim[1], 50))
Z = svm_model.decision_function(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)

# Plot decision boundary and margins
plt.contour(xx, yy, Z, colors='k', levels=[-1, 0, 1], 
            linestyles=['--', '-', '--'], linewidths=[1, 2, 1])

plt.xlabel('Feature 1 (Size)')
plt.ylabel('Feature 2 (Sweetness)')
plt.title('SVM: Maximum Margin Classifier')
plt.legend()
plt.grid(True, alpha=0.3)
plt.show()

Key Takeaways

SVM finds the hyperplane with maximum margin between classes

Support Vectors are the critical points defining the margin

Larger margin leads to better generalization

Only support vectors matter - other points can be removed

# UNDERSTANDING SVM BASICS import numpy as np import matplotlib.pyplot as plt from sklearn.svm import SVC from sklearn.datasets import make_blobs # Create a simple 2D classification dataset # Like sorting Alphonso vs Badami mangoes by size and sweetness np.random.seed(42) X, y = make_blobs(n_samples=100, centers=2, cluster_std=1.2, random_state=42) # Train SVM with linear kernel svm_model = SVC(kernel='linear', C=1.0) svm_model.fit(X, y) # Get the support vectors support_vectors = svm_model.support_vectors_ print(f"Number of Support Vectors: {len(support_vectors)}") print(f"Support Vectors per class: {svm_model.n_support_}") # Plot the data and decision boundary plt.figure(figsize=(10, 8)) plt.scatter(X[:, 0], X[:, 1], c=y, cmap='RdYlBu', edgecolor='black', s=50) # Highlight support vectors plt.scatter(support_vectors[:, 0], support_vectors[:, 1], s=200, facecolors='none', edgecolors='green', linewidth=2, label='Support Vectors') # Plot decision boundary and margins ax = plt.gca() xlim = ax.get_xlim() ylim = ax.get_ylim() # Create grid for decision boundary xx, yy = np.meshgrid(np.linspace(xlim[0], xlim[1], 50), np.linspace(ylim[0], ylim[1], 50)) Z = svm_model.decision_function(np.c_[xx.ravel(), yy.ravel()]) Z = Z.reshape(xx.shape) # Plot decision boundary and margins plt.contour(xx, yy, Z, colors='k', levels=[-1, 0, 1], linestyles=['--', '-', '--'], linewidths=[1, 2, 1]) plt.xlabel('Feature 1 (Size)') plt.ylabel('Feature 2 (Sweetness)') plt.title('SVM: Maximum Margin Classifier') plt.legend() plt.grid(True, alpha=0.3) plt.show()