README.md

Custom SVM

A custom implementation of SVM for classification with support for Gaussian RBF kernel, Polynomial kernel and Linear kernel. Uses Fast Gradient Descent algorithm to minimize smoothed hinge loss.

Package includes a wrapper class OneVsOneClassifier for performing multiclass classification on the SVM.

Kernels

Gaussian RBF Kernel

The Gaussian Radial Basis Function is given by

$$k(x,y) = \exp\left(-\frac{1}{2\sigma^2}\|x-y\|^2\right)$$

where $\sigma$ is the parameter called the sigma which needs to be set. Default value of sigma is set to 0.5.

Polynomial Kernel

The Polynomial kernel is given by

$$k(x,y) = (x^{T}y + b)^{p}$$

where $b$ is the parameter bias and $p$ is the parameter power which needs to be set. Default value of bias is set to 1 and default value of power is set to 2.

Linear Kernel

The Linear kernel is given by

$$k(x,y) = (x^{T}y)$$

Demos

For a demo of SVM on a simple simulated dataset (generated using the scikit-learn library):

python demo_simulated.py

For a demo of SVM on a real-world dataset (Digits dataset from the scikit-learn library):

python demo_digits.py

For a demo of the comparison of the custom implementation of SVM vs. the scikit-learn implementation on a real-world dataset (Digits dataset from the scikit-learn library):

python demo_compare_digits.py

For a demo of SVM on a real-world multiclass dataset (Vowel dataset from the book Elements of Statistical Learning) using the one vs. one multiclass classification strategy:

python demo_vowel.py

Usage

from models.svm import CustomSVM
clf = CustomSVM()
clf.fit(X_train, y_train)
predictions = clf.predict(X_test)
accuracy = clf.score(X_test, y_test)

Dependencies

• Python 3
• joblib
• scikit-learn
• numpy
• pandas
• matplotlib
• tqdm
• scipy