Similarity-Based Kernel Optimization

This repository contains an implementation of the paper Learning Kernel Parameters for Support Vector Classification Using Similarity Embeddings, presented in ESANN 24. It consists of a similarity-based approach for optimizing the width parameter (sigma) in radial basis function (RBF) kernels.

Supported kernel types are:

• Gaussian kernel: $K(x_i, x_j) = \exp\left(-\frac{1}{2}\frac{||x_i - x_j||2}{\sigma2}\right)$.
• Laplacian kernel: $K(x_i, x_j) = \exp\left(-\frac{1}{2}\frac{||x_i - x_j||}{\sigma}\right)$.

Files

• similarity_optimization.py: Contains the core functions for generating similarity spaces, computing RBF loss, and optimizing the kernel width.

Functions

generate_similarity_space(X, y, sigma, kernel="gaussian")

Generates a similarity space using a specified kernel function (Gaussian or Laplacian).

rbf_loss(X, y, sigma, kernel="gaussian")

Computes the RBF loss based on class mean similarities.

optimize_width(X, y)

Finds the optimal sigma value to minimize the RBF loss using numerical optimization.

Usage

This module can be used for tuning kernel parameters in machine learning tasks where similarity-based representations are important. Import the functions and apply them to your dataset to determine the best kernel width for classification tasks.

Dependencies

• numpy
• scipy

License

This project is open-source and available under the Apache 2.0 License.