How to form and minimise custom features for classification in supervised learning I am having an issue in understanding how to form the features based on particular math formula, and how to adjust the weights with.
The aim is to draw ellipses for each unique category of points. Ellipse keeps inside as much of possible selected type of dots, and as little as possible other types (in the picture attached selected yellow ones).
Here is the a formula, with 5 variables, based on which we can draw any ellipse.  https://www.desmos.com/calculator/65hlgysuy7

I can make a model and calculate based on the data set whether the particular point is within the ellipse (score less than 0) or outside, and create accuracy based loss function, or just to use cross entropy for the loss function. Then i could find derivative for cross entropy, but then what's next? How basically i could adjust the weights in such case?

The the big question how i could manipulate those variables (in the link a,b,c,l and h) to form different models, and optimize them with gradient descent (if thats the appropriate technique for such task)?

Can someone please explain me the logic of how custom features in such case can be formed and weights found with gradient descent?
https://en.wikipedia.org/wiki/Support-vector_machine

polynomial kernel of degree 2, with C coefficient >.1 but you would have to figure it out based on your data

I can provide more info on request