AI & Data Science

Support Vector Machine (SVM)

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Tutorial lengkap SVM — konsep margin dan hyperplane, berbagai jenis kernel, klasifikasi & regresi, tuning hyperparameter, dan implementasi dengan scikit-learn

📅 3 April 2026 📖 20 menit baca Menengah

🐝

Tim BeebaneLabs Penulis & Kontributor Teknologi

📋 Daftar Isi

Pengenalan SVM
Hyperplane & Margin
Support Vectors & Soft Margin
Kernel Trick & Jenis Kernel
Implementasi Klasifikasi SVM
Klasifikasi Multi-Class dengan SVM
Support Vector Regression (SVR)
Hyperparameter Tuning (C & Gamma)
Kelebihan & Kekurangan
Quiz Pemahaman

1. Pengenalan SVM

Support Vector Machine (SVM) adalah salah satu algoritma Machine Learning paling elegan dan powerful, yang dikembangkan oleh Vladimir Vapnik dan kolega pada tahun 1963-1995. SVM pertama kali dipopulerkan dengan konsep Maximum Margin Classifier dan kemudian diperluas dengan Kernel Trick oleh Boser, Guyon, dan Vapnik pada tahun 1992.

Inti dari SVM sederhana namun powerful: SVM mencari hyperplane terbaik yang memisahkan kelas-kelas data dengan margin terbesar. Margin adalah jarak antara hyperplane dengan data point terdekat dari masing-masing kelas (yang disebut support vectors).

Kapan Menggunakan SVM?

Diagram: Pengaruh Parameter C pada SVM

○ ○ ○ ● ●
C KECIL (misal 0.01): C BESAR (misal 100):
○ ○ ○ ● ●
○ ○ ←margin kecil→ ● ●
○ ○ × × ●
● ● (margin kecil)
● ●
Lebih sedikit
misclassification →
variance tinggi
Overfitting tendency

Python — Perbandingan C pada SVM

import numpy as np
import matplotlib.pyplot as plt
from sklearn.svm import SVC
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split

# Dataset dengan noise (overlapping classes)
X, y = make_classification(
    n_samples=200, n_features=2, n_redundant=0,
    n_informative=2, n_clusters_per_class=1,
    flip_y=0.1, random_state=42  # 10% noise
)

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)

fig, axes = plt.subplots(1, 4, figsize=(20, 5))
C_values = [0.001, 0.01, 1, 100]

for ax, C in zip(axes, C_values):
    svm = SVC(kernel='linear', C=C)
    svm.fit(X_train, y_train)
    
    train_acc = svm.score(X_train, y_train)
    test_acc = svm.score(X_test, y_test)
    n_sv = len(svm.support_)
    
    # Decision boundary
    xx, yy = np.meshgrid(
        np.linspace(X[:, 0].min()-1, X[:, 0].max()+1, 300),
        np.linspace(X[:, 1].min()-1, X[:, 1].max()+1, 300)
    )
    Z = svm.predict(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)
    
    ax.contourf(xx, yy, Z, alpha=0.3, cmap='RdYlBu')
    ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap='RdYlBu', 
               edgecolors='k', s=40)
    
    # Highlight support vectors
    sv = svm.support_vectors_
    ax.scatter(sv[:, 0], sv[:, 1], s=200, facecolors='none', 
               edgecolors='green', linewidths=2)
    
    ax.set_title(f'C = {C}\nTrain: {train_acc:.2f}, Test: {test_acc:.2f}\n'
                 f'SVs: {n_sv}', fontsize=10)
    ax.grid(True, alpha=0.3)

plt.suptitle('Pengaruh Parameter C pada SVM Linear', fontsize=14)
plt.tight_layout()
plt.show()

Jenis-Jenis Kernel

Kernel	Formula	Parameter	Cocok untuk
`linear`	K(x,y) = x·y	—	Data linearly separable, teks (high-dim)
`poly`	K(x,y) = (γx·y + r)^d	degree, gamma, coef0	Polynomial patterns
`rbf (Gaussian)`	K(x,y) = exp(-γ\|\|x-y\|\|²)	gamma	Non-linear data (default, paling umum)
`sigmoid`	K(x,y) = tanh(γx·y + r)	gamma, coef0	Meniru neural network

Python — Support Vector Regression

import numpy as np
import matplotlib.pyplot as plt
from sklearn.svm import SVR
from sklearn.model_selection import train_test_split, cross_val_score
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error

# Generate non-linear data
np.random.seed(42)
X = np.sort(5 * np.random.rand(300, 1), axis=0)
y = np.sin(X).ravel() + 0.2 * np.random.randn(300)

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.3, random_state=42
)

# Scale features
scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

# Bandingkan SVR dengan berbagai kernel
kernels_params = {
    'Linear SVR': {'kernel': 'linear', 'C': 1.0, 'epsilon': 0.1},
    'RBF SVR (C=1)': {'kernel': 'rbf', 'C': 1.0, 'gamma': 'scale', 'epsilon': 0.1},
    'RBF SVR (C=100)': {'kernel': 'rbf', 'C': 100.0, 'gamma': 'scale', 'epsilon': 0.1},
    'Poly SVR (degree=3)': {'kernel': 'poly', 'degree': 3, 'C': 1.0, 'epsilon': 0.1},
}

fig, axes = plt.subplots(2, 2, figsize=(14, 10))
results = {}

for ax, (name, params) in zip(axes.ravel(), kernels_params.items()):
    svr = SVR(**params)
    svr.fit(X_train_scaled, y_train)
    
    y_pred = svr.predict(X_test_scaled)
    r2 = r2_score(y_test, y_pred)
    rmse = np.sqrt(mean_squared_error(y_test, y_pred))
    mae = mean_absolute_error(y_test, y_pred)
    n_sv = len(svr.support_)
    
    results[name] = {'R²': r2, 'RMSE': rmse, 'MAE': mae, 'SVs': n_sv}
    
    # Plot
    X_plot = np.linspace(X_train_scaled.min(), X_train_scaled.max(), 500).reshape(-1, 1)
    y_plot = svr.predict(X_plot)
    
    ax.scatter(X_train_scaled, y_train, c='steelblue', s=15, alpha=0.5, label='Train')
    ax.scatter(X_test_scaled, y_test, c='orange', s=15, alpha=0.5, label='Test')
    ax.plot(X_plot, y_plot, 'r-', linewidth=2, label='Prediksi')
    
    # Epsilon tube
    ax.fill_between(X_plot.ravel(), y_plot - svr.epsilon, y_plot + svr.epsilon,
                     alpha=0.15, color='red', label=f'ε-tube ({svr.epsilon})')
    
    # Support vectors
    ax.scatter(X_train_scaled[svr.support_], y_train[svr.support_], 
               s=100, facecolors='none', edgecolors='green', linewidths=2,
               label=f'SVs ({n_sv})')
    
    ax.set_title(f'{name}\nR²={r2:.3f} | RMSE={rmse:.3f}', fontsize=10)
    ax.legend(fontsize=7)
    ax.grid(True, alpha=0.3)

plt.suptitle('Support Vector Regression — Perbandingan Kernel', fontsize=14)
plt.tight_layout()
plt.show()

# Summary table
print("\n" + "=" * 65)
print("SVR RESULTS SUMMARY")
print("=" * 65)
print(f"{'Model':<25} {'R²':>8} {'RMSE':>8} {'MAE':>8} {'SVs':>6}")
print("-" * 65)
for name, metrics in results.items():
    print(f"{name:<25} {metrics['R²']:>8.4f} {metrics['RMSE']:>8.4f} "
          f"{metrics['MAE']:>8.4f} {metrics['SVs']:>6d}")

8. Hyperparameter Tuning (C & Gamma)

Dua hyperparameter terpenting pada SVM dengan kernel RBF adalah C dan gamma (γ). Memahami interaksi antara keduanya sangat krusial untuk mendapatkan performa terbaik.

C dan Gamma: Interaksi

	Gamma Kecil	Gamma Besar
C Kecil	Bias tinggi, variance rendah → Underfitting	Bias rendah, variance tinggi → Model kompleks
C Besar	Bias sedang, variance sedang → Model moderat	Bias rendah, variance tinggi → Overfitting

Python — Grid Search C & Gamma

import numpy as np
import matplotlib.pyplot as plt
from sklearn.svm import SVC
from sklearn.datasets import load_digits
from sklearn.model_selection import GridSearchCV, StratifiedKFold, train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import Pipeline
import warnings
warnings.filterwarnings('ignore')

# Load digits dataset
X, y = load_digits(return_X_y=True)
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42, stratify=y
)

# Pipeline dengan scaling
pipe = Pipeline([
    ('scaler', StandardScaler()),
    ('svm', SVC(kernel='rbf', random_state=42))
])

# Grid Search: C dan Gamma
param_grid = {
    'svm__C': [0.01, 0.1, 1, 10, 100, 1000],
    'svm__gamma': ['scale', 'auto', 0.001, 0.01, 0.1, 1, 10]
}

cv = StratifiedKFold(n_splits=5, shuffle=True, random_state=42)

grid_search = GridSearchCV(
    pipe, param_grid,
    cv=cv,
    scoring='accuracy',
    n_jobs=-1,
    verbose=1,
    refit=True
)
grid_search.fit(X_train, y_train)

print("=" * 60)
print("GRID SEARCH RESULTS")
print("=" * 60)
print(f"Best Score (CV): {grid_search.best_score_:.4f}")
print(f"Best Parameters: {grid_search.best_params_}")
print(f"Test Score: {grid_search.best_estimator_.score(X_test, y_test):.4f}")

# Visualisasi Heatmap C vs Gamma
import pandas as pd

results = grid_search.cv_results_

# Filter hanya kombinasi numeric gamma
mask_numeric = [isinstance(p, (int, float)) for p in param_grid['svm__gamma'][:len(param_grid['svm__gamma'])]]

C_values = param_grid['svm__C']
gamma_values = ['0.001', '0.01', '0.1', '1', '10']  # numeric only
score_matrix = np.zeros((len(C_values), len(gamma_values)))

for i, c in enumerate(C_values):
    for j, g in enumerate(['0.001', '0.01', '0.1', '1', '10']):
        idx = [k for k, p in enumerate(results['params'])
               if p['svm__C'] == c and str(p['svm__gamma']) == g]
        if idx:
            score_matrix[i, j] = results['mean_test_score'][idx[0]]

plt.figure(figsize=(10, 6))
plt.imshow(score_matrix, cmap='YlOrRd', aspect='auto', interpolation='nearest')
plt.colorbar(label='CV Accuracy')
plt.xticks(range(len(gamma_values)), gamma_values)
plt.yticks(range(len(C_values)), C_values)
plt.xlabel('Gamma')
plt.ylabel('C')
plt.title('Grid Search: Accuracy Heatmap (C vs Gamma)')

# Annotate cells
for i in range(len(C_values)):
    for j in range(len(gamma_values)):
        plt.text(j, i, f'{score_matrix[i, j]:.3f}',
                 ha='center', va='center', fontsize=8,
                 color='white' if score_matrix[i, j] > 0.95 else 'black')

plt.tight_layout()
plt.show()

💡 Tips Tuning SVM

Selalu scaling! SVM sangat sensitif terhadap skala fitur. Gunakan StandardScaler
C: Mulai dari 1.0. Besar = lebih kompleks (overfitting), kecil = lebih sederhana (underfitting)
Gamma: 'scale' (default sklearn) = 1/(n_features * variance(X)). Good starting point
RandomizedSearchCV lebih cepat daripada GridSearchCV untuk eksplorasi awal
SVM training O(n² ~ n³) — untuk dataset > 50k samples, pertimbangkan LinearSVC atau SGDClassifier

9. Kelebihan & Kekurangan

Kelebihan SVM

Kelebihan	Penjelasan
✅ Efektif di high dimension	Performa bagus bahkan jika jumlah fitur > jumlah sampel (e.g., text classification)
✅ Margin maximization	Generalisasi baik karena margin besar → robust terhadap noise
✅ Memory efficient	Hanya menyimpan support vectors (subset data), bukan seluruh dataset
✅ Versatile kernels	Berbagai kernel tersedia untuk berbagai jenis data
✅ Global optimum	Convex optimization → tidak terjebak local minimum (unlike neural network)
✅ Works well with small data	Performa bagus bahkan dengan sedikit data

Kekurangan SVM

Kekurangan	Penjelasan
❌ Scaling sensitif	WAJIB melakukan feature scaling (StandardScaler)
❌ Lambat untuk data besar	Training O(n²~n³) — sangat lambat untuk dataset > 100k samples
❌ Probabilitas tidak langsung	Tidak memberikan probabilitas langsung (butuh probability=True dengan Platt scaling)
❌ Tuning kompleks	C, gamma, kernel type, degree — banyak hyperparameter yang saling berinteraksi
❌ Tidak handle missing values	Perlu imputasi sebelum training
❌ Interpretasi sulit	Model sulit diinterpretasikan (terutama kernel non-linear)

Support Vector Machine (SVM)

1. Pengenalan SVM

Kapan Menggunakan SVM?

4. Kernel Trick & Jenis Kernel

Apa Itu Kernel Trick?

Jenis-Jenis Kernel

8. Hyperparameter Tuning (C & Gamma)

C dan Gamma: Interaksi

9. Kelebihan & Kekurangan

Kelebihan SVM

Kekurangan SVM

10. Quiz: Uji Pemahamanmu!

Pertanyaan 1: Apa yang dimaksud dengan "margin" dalam SVM?

Pertanyaan 2: Mengapa SVM menggunakan "Kernel Trick"?

Pertanyaan 3: Apa efek dari parameter C yang sangat besar pada SVM?

Pertanyaan 4: Mengapa feature scaling sangat penting untuk SVM?

Pertanyaan 5: Kernel mana yang paling umum digunakan untuk data non-linear?

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