Support Vector Regression (SVR) and Custom Kernel Methods

Version: 1.0
Release Date: June 2024

Overview

This repository provides implementations of Support Vector Regression (SVR) with:

• Huber Loss for robust regression.
• Custom Kernel Functions for advanced flexibility.
• Error Metrics for model evaluation.

It includes examples for training SVR models, computing results, and customizing kernel methods for specific regression tasks.

Features

• SVR Training: Train SVR models using Huber loss and regularization.
• Custom Kernels: Define your own kernel functions for improved performance.
• Performance Evaluation: Compute accuracy metrics like MSE, RMSE, and residual errors.
• Precompiled Solvers: Use optimized .dll files for faster execution.

Installation

Clone the repository:

git clone https://github.com/IPL-UV/svr_e_huber.git
cd svr_e_huber

Add paths to MATLAB:

addpath(pwd);

Verify your MATLAB environment and ensure .dll files match your operating system.

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Usage

Example 1: SVR with Huber Loss

Run DemoEHuberSVR.m to train an SVR model using Huber loss and Gaussian kernels.

% Demo: SVR with Huber Loss
clear; clc; close all;

% Load data
load meris_data.mat;
X = meris_data(:, 1);  % Input features
Y = meris_data(:, 2);  % Output targets

% SVR training parameters
C = 10;        % Regularization parameter
epsilon = 0.1; % Epsilon-tube
sigma = 2;     % Gaussian kernel width

% Train SVR model
model = mysvr(X, Y, C, epsilon, sigma);

% Predict outputs
Y_pred = svroutput(X, model);

% Compute results
results = ComputeResults(Y, Y_pred);
disp('SVR Results:');
disp(results);

% Plot predictions
figure;
plot(Y, 'b'); hold on;
plot(Y_pred, 'r--');
legend('True', 'Predicted');
title('SVR Predictions with Huber Loss');

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Example 2: Using Custom Kernels

You can implement your own kernel function using mysvkernel2.m. For example:

% Custom Gaussian kernel implementation
function K = mysvkernel2(X1, X2, sigma)
    D = pdist2(X1, X2, 'euclidean');
    K = exp(-(D.^2) / (2 * sigma^2));
end

To use this kernel in SVR:

% Compute custom kernel
K = mysvkernel2(X, X, sigma);

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Example 3: Free Parameter SVR

Use svrFreeParam.m for flexible SVR training with optimized parameters:

% Free Parameter SVR Example
C = 1; epsilon = 0.01; sigma = 1;

% Train model with free parameters
model = svrFreeParam(X, Y, C, epsilon, sigma);

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Results and Visualization

Accuracy Metrics:

• Mean Squared Error (MSE)
• Root Mean Squared Error (RMSE)
• R-Squared (R²)

Visualizations

• Prediction vs Ground Truth plots
• Residual Analysis for error distribution

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Dependencies

• MATLAB R2021b or later.
• Root Mean Squared Error (RMSE)
• R-Squared (R²)

Visualizations

• Prediction vs Ground Truth plots
• Precompiled SVR solvers (mysvr.dll, svrFreeParam.dll).

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Authors

• Gustavo Camps-Valls
• Jordi Muñoz-Marí

Copyright © 2006

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License

This project is distributed under the MIT License.

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