For generating polynomial features up to the 3rd degree (or any specified degree) in MATLAB, especially when x2fx does not directly support higher degrees beyond quadratic terms, you can create a custom function to automate this process. While MATLAB does not have an out-of-the-box function equivalent to PolynomialFeatures from scikit-learn, the process can be implemented manually with a bit of coding.
Given your requirements and the complexity involved in manually specifying interactions for a 4-variable matrix to the 3rd degree, a more generalized approach would be beneficial. Here's a way to generate polynomial features up to the 3rd degree, including interaction terms, for any given matrix:
Step 1: Define the Function
You can define a function that takes in your original matrix and the degree of polynomial features you want to generate. This function will iterate through each combination of features up to the specified degree, including the interaction terms.
function polyFeatures = generatePolyFeatures(X, degree)
% X is the input matrix of size m x n
% degree is the polynomial degree to generate features for
% Initialize polyFeatures with the bias term
polyFeatures = ones(size(X,1), 1);
% Iterate through degrees
for d = 1:degree
% Generate all combinations for the current degree
combos = nchoosek(1:size(X,2), d);
for i = 1:size(combos, 1)
% For each combination, calculate the product (for interaction terms)
comboFeatures = X(:, combos(i, 1));
for j = 2:size(combos, 2)
comboFeatures = comboFeatures .* X(:, combos(i, j));
end
% For each combination, also generate individual powers
for k = 1:d
polyFeatures = [polyFeatures, comboFeatures.^k];
end
end
end
end
Step 2: Use the Function
You can then use this function to generate polynomial features for your matrix up to the 3rd degree:
matrix = magic(4);
polyFeatures = generatePolyFeatures(matrix, 3);
