Equations for predicting outputs under SVM regression (RBF or polynomial)

Hello everyone,

I am trying to calculate output (Y) for new input data (X) using a pretrained SVM (trained with kernel function RBF or polynomial).

I know the equations for linear SVM regression:

ex) Y = inputdata * Beta + Bias

However, I am trying to find the equations to calculate the Y response under 'RBF' or 'Polynomial' SVM regression.

Please help

Thank you.

Answer 1

[Angelo Yeo]

Here is one for RBF. This will be good reference for polynomial kernel.

X = readmatrix('inputdata.xlsx', Sheet = "Sheet1");
Y = readmatrix('outputdata.xlsx', Sheet = "Sheet1");
 
Mdl = fitrsvm(X,Y,"Standardize", true, "KernelFunction", "rbf", "KernelScale", "auto");
% pred_val = predict(Mdl, X);
 
 
%% For the new prediction
x_new = [8.9 10.2 42.8 44.8]; % New input variables (4 variables)
 
alpha = Mdl.Alpha;
bias = Mdl.Bias;
kernelScale = Mdl.KernelParameters.Scale;
supportVectors = Mdl.SupportVectors;
 
% standardize input
x_new_norm = (x_new - Mdl.Mu) ./ Mdl.Sigma  ;
 
% scaled Gram matrix
d = (x_new_norm - supportVectors)/kernelScale;
euc_dist_squared = sum(d.^2,2); % Squared Euclidean distance 
G = exp(-euc_dist_squared);
 
% responses
res_direct = sum(alpha .* G) + bias;
res_predict = Mdl.predict(x_new);
 
% Display the result
disp(['Predicted output using direct calculation: ', num2str(res_direct)]);

Predicted output using direct calculation: 0.11385

disp(['Predicted output using predict function: ', num2str(res_predict)]);

Predicted output using predict function: 0.11385

[minhyuk jeung]

Thank you!

[Angelo Yeo]

Happy to help!

Answer 2

[Angelo Yeo]

Here is one for polynomial kernel.

X = readmatrix('inputdata.xlsx', Sheet="Sheet1");
Y = readmatrix('outputdata.xlsx', Sheet="Sheet1");

% Polynomial Kernel's order 
PolynomialOrder = 2;

% Check if polynomial order is positive integer
if PolynomialOrder<=0 || fix(PolynomialOrder)~=PolynomialOrder
    error("PolynomialOrder must be a positive integer");
end

Mdl = fitrsvm(X, Y, "Standardize", true, "KernelFunction", "polynomial", "PolynomialOrder", PolynomialOrder);

% For the new prediction
x_new = [8.9 10.2 42.8 44.8];

alpha = Mdl.Alpha;
bias = Mdl.Bias;
supportVectors = Mdl.SupportVectors;

% Standardize input
x_new_norm = (x_new - Mdl.Mu) ./ Mdl.Sigma;

% Gram matrix
G = (supportVectors * x_new_norm' + 1).^PolynomialOrder;

% responses
res_direct = sum(alpha .* G) + bias;
res_predict = Mdl.predict(x_new);
disp(['Predicted output using direct calculation: ', num2str(res_direct)]);

Predicted output using direct calculation: 0.18437

disp(['Predicted output using predict function: ', num2str(res_predict)]);

Predicted output using predict function: 0.18437