---
id: wiki-2026-0508-kernel-methods-and-svms
title: Kernel Methods and SVMs
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [SVM, kernel methods, RBF kernel, kernel trick, support vector machine]
duplicate_of: none
source_trust_level: A
confidence_score: 0.95
verification_status: applied
tags: [machine-learning, svm, kernel, classical-ml, scikit-learn]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: scikit-learn / libsvm
---

# Kernel Methods and SVMs

## 매 한 줄
> **"매 implicit feature space 의 의 의 의 inner product"**. 매 kernel trick — 매 high-dim transform 의 explicit X. 매 SVM (Vapnik) 의 의 의 dominant pre-DL. 매 modern: 매 small data 의 still 매 strong baseline. 매 GP 의 covariance 도 kernel.

## 매 핵심

### 매 SVM
- **Hard-margin**: 매 separable.
- **Soft-margin** (slack): 매 misclassify allow.
- **Dual form**: 매 의 의 의 의 kernel trick.

### 매 kernel
- **Linear**: K(x, y) = x·y.
- **Polynomial**: (γ x·y + r)^d.
- **RBF / Gaussian**: exp(-γ ||x-y||²).
- **Sigmoid**: tanh(γ x·y + r).
- **String, Graph kernels** (specialized).

### 매 응용
1. **Small-data classification**.
2. **Text classification** (TF-IDF + linear SVM 의 historically strong).
3. **Anomaly** (1-class SVM).
4. **Regression** (SVR).
5. **Bioinformatics**.

## 💻 패턴

### Basic SVM (sklearn)
```python
from sklearn.svm import SVC
clf = SVC(kernel='rbf', C=1.0, gamma='scale').fit(X_train, y_train)
preds = clf.predict(X_test)
```

### Linear SVM (large-scale)
```python
from sklearn.svm import LinearSVC
clf = LinearSVC(C=1.0).fit(X, y)  # 매 fast for large N
```

### CV-tune C and gamma
```python
from sklearn.model_selection import GridSearchCV
params = {'C': [0.1, 1, 10, 100], 'gamma': [0.001, 0.01, 0.1, 1]}
grid = GridSearchCV(SVC(kernel='rbf'), params, cv=5)
grid.fit(X, y)
```

### SVR (regression)
```python
from sklearn.svm import SVR
model = SVR(kernel='rbf', C=1.0, epsilon=0.1).fit(X, y)
```

### One-class SVM (anomaly)
```python
from sklearn.svm import OneClassSVM
clf = OneClassSVM(gamma='auto').fit(X_normal)
anomalies = clf.predict(X_test) == -1
```

### Custom kernel
```python
def my_kernel(X, Y):
    return X @ Y.T + 1  # 매 example

clf = SVC(kernel=my_kernel).fit(X, y)
```

### Kernel trick (manual feature mapping vs)
```python
import numpy as np
def rbf_kernel(x, y, gamma=1.0):
    return np.exp(-gamma * np.linalg.norm(x - y) ** 2)

def poly_kernel(x, y, d=2, gamma=1.0, r=0):
    return (gamma * x @ y + r) ** d
```

### TF-IDF + linear SVM (text classic)
```python
from sklearn.feature_extraction.text import TfidfVectorizer
from sklearn.pipeline import Pipeline

pipe = Pipeline([('tfidf', TfidfVectorizer(max_features=20000)), ('svm', LinearSVC(C=1.0))])
pipe.fit(train_texts, train_labels)
```

### Multi-class (one-vs-rest)
```python
from sklearn.multiclass import OneVsRestClassifier
clf = OneVsRestClassifier(SVC()).fit(X, y)
```

### Calibrated probabilities
```python
from sklearn.calibration import CalibratedClassifierCV
clf = CalibratedClassifierCV(SVC(kernel='rbf'), cv=5).fit(X, y)
probs = clf.predict_proba(X_test)
```

### Kernel approximation (large data)
```python
from sklearn.kernel_approximation import RBFSampler
rbf_feature = RBFSampler(gamma=1, n_components=100, random_state=0)
X_features = rbf_feature.fit_transform(X)
# 매 매 linear SVM 의 의 OK
clf = LinearSVC().fit(X_features, y)
```

### String kernel (text)
```python
from sklearn.feature_extraction.text import CountVectorizer
def n_gram_kernel(X, Y, n=3):
    vec = CountVectorizer(analyzer='char', ngram_range=(n, n))
    Xv = vec.fit_transform(X).toarray()
    Yv = vec.transform(Y).toarray()
    return Xv @ Yv.T
```

### Graph kernel (Weisfeiler-Lehman)
```python
from grakel.kernels import WeisfeilerLehman
from grakel import GraphKernel
gk = GraphKernel(kernel='weisfeiler_lehman', n_iter=5)
K_train = gk.fit_transform(graphs_train)
K_test = gk.transform(graphs_test)
clf = SVC(kernel='precomputed').fit(K_train, y_train)
```

### Plot decision boundary (2D)
```python
import matplotlib.pyplot as plt
def plot_boundary(clf, X, y):
    h = 0.02
    x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
    y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)
    plt.contourf(xx, yy, Z, alpha=0.3)
    plt.scatter(X[:, 0], X[:, 1], c=y)
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Small data | RBF SVM |
| High-dim text | Linear SVM (TF-IDF) |
| Anomaly | One-class SVM |
| Graph data | WL graph kernel |
| Large-scale | Linear SVM or kernel approx |
| Modern DL data | Use DL instead |

**기본값**: 매 small N + tabular = RBF SVM. 매 text = Linear + TF-IDF. 매 large = kernel approximation. 매 modern era — DL win on most.

## 🔗 Graph
- 부모: [[Machine-Learning]] · [[Classical-ML]]
- 변형: [[SVM]] · [[SVR]] · [[One-Class-SVM]]
- 응용: [[Text-Classification]] · [[Anomaly-Detection]]
- Adjacent: [[Gaussian-Processes]] · [[Neural-Tangent-Kernel]]

## 🤖 LLM 활용
**언제**: 매 small data. 매 baseline. 매 anomaly.
**언제 X**: 매 large data (DL win).

## ❌ 안티패턴
- **No scaling**: 매 RBF 의 의 의 critical.
- **RBF on huge N**: 매 O(N²) 의 fail.
- **Default C / gamma**: 매 always tune.
- **No probability calibration**: 매 SVM 의 raw decision 의 not probability.

## 🧪 검증 / 중복
- Verified (Vapnik 1995, Schölkopf, scikit-learn docs).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — kernels + 매 SVM / SVR / OCSVM / approx / graph code |
