Data Intelligence, Business Analytics
The strategy is very easy to describe:
1. Divide the domain of your function in k sub intervals.
2. Initialize k monomials;
3. Consider the monomials as centroids of your clustering algorithm.
4. Assign the points of the function to each monomial in compliance to the cluster algo.
5. Use the gradient descent to adjust the parameters of each monomial.
6. Go to 4. until the accuracy is good enough.
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On the left side the original function,
on the right side the hyperplanes (monomials) found by gradient descent cluster based.
The below graph shows the plane described by the original function.
In blue the points belonging to the original function.
In orange the fitting obtained using the clustering based procedure