Support Vector Machines Cheat Sheet

A cheat sheet for Support Vector Machines covering kernels, margin maximization, the C and gamma hyperparameters, and scikit-learn usage.

2 PagesIntermediateFeb 25, 2026

Classifier with scikit-learn

Fit a scaled RBF-kernel SVM.

python

from sklearn.svm import SVCfrom sklearn.preprocessing import StandardScalerfrom sklearn.pipeline import make_pipelineclf = make_pipeline(    StandardScaler(),    SVC(kernel='rbf', C=1.0, gamma='scale', probability=True))clf.fit(X_train, y_train)print('Accuracy:', clf.score(X_test, y_test))

Kernel Comparison

Common kernel choices for SVC.

python

from sklearn.svm import SVClinear_svm = SVC(kernel='linear', C=1.0)poly_svm = SVC(kernel='poly', degree=3, C=1.0)rbf_svm = SVC(kernel='rbf', gamma=0.1, C=1.0)      # default kernelsigmoid_svm = SVC(kernel='sigmoid', C=1.0)

Hyperparameter Grid Search

Tune C and gamma with cross-validation.

python

from sklearn.model_selection import GridSearchCVparam_grid = {'C': [0.1, 1, 10, 100], 'gamma': [1, 0.1, 0.01, 0.001]}grid = GridSearchCV(SVC(kernel='rbf'), param_grid, cv=5, scoring='f1')grid.fit(X_train, y_train)print(grid.best_params_)

Key Concepts

Core theory behind SVMs.

Support vectors- Training points closest to the decision boundary; they alone define the margin
Margin- Distance between the decision boundary and the nearest points; SVM maximizes this distance
Kernel trick- Implicitly maps data into a higher-dimensional space to find a linear separator, without computing the mapping explicitly
C (regularization)- Trades off margin width against classification error; a large C allows less margin violation
gamma (RBF kernel)- Controls the influence radius of a single training point; high gamma risks overfitting
Feature scaling- SVMs rely on distances, so features should always be standardized before fitting

Pro Tip

Always scale features before training an SVM — because the algorithm depends on distances and dot products, an unscaled feature with a large numeric range will dominate the margin calculation and quietly degrade model performance.

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