2nd/10_Wiki/Topics/AI_and_ML/Kernel-Methods-and-SVMs.md

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

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

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)

from sklearn.svm import LinearSVC
clf = LinearSVC(C=1.0).fit(X, y)  # 매 fast for large N

CV-tune C and gamma

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)

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

One-class SVM (anomaly)

from sklearn.svm import OneClassSVM
clf = OneClassSVM(gamma='auto').fit(X_normal)
anomalies = clf.predict(X_test) == -1

Custom kernel

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)

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)

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)

from sklearn.multiclass import OneVsRestClassifier
clf = OneVsRestClassifier(SVC()).fit(X, y)

Calibrated probabilities

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)

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)

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)

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)

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
• 변형: SVM
• 응용: Anomaly-Detection
• Adjacent: Gaussian-Processes

🤖 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