produces the data matrix of size 𝑁 × (𝑀 + 1) using the feature mapping in matlab

To produce a data matrix of size 𝑁 × (𝑀 + 1) using the feature mapping in Matlab, you can follow the steps below:

1. Define your feature mapping function. This function should take in an input vector of size 𝑀 and return a feature vector of size 𝐾.

main.m
function feature_vector = feature_mapping(input_vector)
    % Define your feature mapping here
    feature_vector = ... 
end
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2. Create your data matrix. Initialize a matrix of size 𝑁 × (𝑀 + 1) with zeros.

main.m
data_matrix = zeros(N, M+1);
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3. Loop through each data point and compute its corresponding feature vector. Store the feature vector in the data matrix along with a bias term of 1.

main.m
for i = 1:N
    % Get the input vector for this data point
    input_vector = ... 
    
    % Compute the feature vector including the bias term
    feature_vector = [feature_mapping(input_vector); 1];
    
    % Store the feature vector in the data matrix
    data_matrix(i,:) = feature_vector';
end
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At the end of this process, the variable data_matrix will contain the 𝑁 × (𝑀 + 1) data matrix where each row corresponds to a data point and each column corresponds to a feature including the bias term of 1.