Support Vector Regression (SVR)

Support Vector Regression (SVR)

Support Vector Regression (SVR)

Support Vector Regression (SVR) is a type of regression analysis that uses Support Vector Machines (SVMs) to perform linear or nonlinear regression. Similar to SVMs for classification, SVR identifies a hyperplane that best fits the training data while maximizing the margin between the hyperplane and the data points. However, instead of finding a hyperplane that separates the data into classes, SVR finds a hyperplane that predicts the continuous output variable (i.e., the target variable) given the input variables.

In SVR, the goal is to minimize the error between the predicted values and the actual values while satisfying a certain margin of error (epsilon). The margin of error allows some data points to be within a certain distance from the predicted values, which can be useful for dealing with noisy data or outliers. The parameter C controls the trade-off between maximizing the margin and minimizing the error.

To solve the optimization problem in SVR, quadratic programming is often used. The optimization problem involves finding the values of alpha, which are Lagrange multipliers that determine the support vectors (i.e., the data points that lie on or within the margin). Once alpha is obtained, the weights and bias terms can be calculated to predict new output values for unseen input values.

Overall, SVR is a powerful technique for regression analysis that can handle linear and nonlinear relationships between variables and can incorporate different types of kernels to capture complex patterns in the data.

Note:

The "SVR1.m" file is a MATLAB code that utilizes built-in library functions to implement Support Vector Regression (SVR). However, "SVR2.m & SVR3.m " are standalone codes that are written independently, without relying on any pre-existing MATLAB library functions.