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?
β β β β β
C KECIL (misal 0.01): C BESAR (misal 100):
β β β β β
β β βmargin kecilβ β β
β β Γ Γ β
β β (margin kecil)
β β
Lebih sedikit
misclassification β
variance tinggi
Overfitting tendency
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()
4. Kernel Trick & Jenis Kernel
Salah satu keunggulan terbesar SVM adalah Kernel Trick β kemampuan untuk menangani data yang tidak bisa dipisahkan secara linear dengan memproyeksikannya ke dimensi yang lebih tinggi tanpa secara eksplisit menghitung koordinat di dimensi tersebut.
Apa Itu Kernel Trick?
Jenis-Jenis Kernel
| Kernel | Formula | Parameter | Cocok untuk |
|---|---|---|---|
linear | K(x,y) = xΒ·y | β | Data linearly separable, teks (high-dim) |
poly | K(x,y) = (Ξ³xΒ·y + r)^d | degree, gamma, coef0 | Polynomial patterns |
rbf (Gaussian) | K(x,y) = exp(-Ξ³||x-y||Β²) | gamma | Non-linear data (default, paling umum) |
sigmoid | K(x,y) = tanh(Ξ³xΒ·y + r) | gamma, coef0 | Meniru neural network |
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] = {'RΒ²': 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'Ξ΅-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}\nRΒ²={r2:.3f} | RMSE={rmse:.3f}', fontsize=10)
ax.legend(fontsize=7)
ax.grid(True, alpha=0.3)
plt.suptitle('Support Vector Regression β Perbandingan Kernel', fontsize=14)
plt.tight_layout()
plt.show()
# Summary table
print("\n" + "=" * 65)
print("SVR RESULTS SUMMARY")
print("=" * 65)
print(f"{'Model':<25} {'RΒ²':>8} {'RMSE':>8} {'MAE':>8} {'SVs':>6}")
print("-" * 65)
for name, metrics in results.items():
print(f"{name:<25} {metrics['RΒ²']:>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 (Ξ³). Memahami interaksi antara keduanya sangat krusial untuk mendapatkan performa terbaik.
C dan Gamma: Interaksi
| Gamma Kecil | Gamma Besar | |
|---|---|---|
| C Kecil | Bias tinggi, variance rendah β Underfitting | Bias rendah, variance tinggi β Model kompleks |
| C Besar | Bias sedang, variance sedang β Model moderat | Bias rendah, variance tinggi β Overfitting |
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()
- 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(nΒ² ~ nΒ³) β untuk dataset > 50k samples, pertimbangkan LinearSVC atau SGDClassifier
9. Kelebihan & Kekurangan
Kelebihan SVM
| Kelebihan | Penjelasan |
|---|---|
| β Efektif di high dimension | Performa bagus bahkan jika jumlah fitur > jumlah sampel (e.g., text classification) |
| β Margin maximization | Generalisasi baik karena margin besar β robust terhadap noise |
| β Memory efficient | Hanya menyimpan support vectors (subset data), bukan seluruh dataset |
| β Versatile kernels | Berbagai kernel tersedia untuk berbagai jenis data |
| β Global optimum | Convex optimization β tidak terjebak local minimum (unlike neural network) |
| β Works well with small data | Performa bagus bahkan dengan sedikit data |
Kekurangan SVM
| Kekurangan | Penjelasan |
|---|---|
| β Scaling sensitif | WAJIB melakukan feature scaling (StandardScaler) |
| β Lambat untuk data besar | Training O(nΒ²~nΒ³) β sangat lambat untuk dataset > 100k samples |
| β Probabilitas tidak langsung | Tidak memberikan probabilitas langsung (butuh probability=True dengan Platt scaling) |
| β Tuning kompleks | C, gamma, kernel type, degree β banyak hyperparameter yang saling berinteraksi |
| β Tidak handle missing values | Perlu imputasi sebelum training |
| β Interpretasi sulit | Model sulit diinterpretasikan (terutama kernel non-linear) |
10. Quiz: Uji Pemahamanmu!
Setelah membaca tutorial di atas, jawablah 5 pertanyaan berikut untuk menguji pemahamanmu tentang SVM: