I learned that regularized logistic regression helps prevent the model from over-fitting the data. I understand that the function is still technically a high-order polynomial, but the effect is reduced so it looks more like a curve, but here's the part where I may understand incorrectly: The function is regularized by adding a term to the end that penalizes the rest of the parameters.
In a sense, the way I think of this is imagining a sine wave with a very small coefficient, like
0.0001, so the graph of
0.00001 * sin(x) would look much like a straight line compared to the same perspective of
Is this the correct way to look at how regularized logistic regression works, or does the regularization follow some other principle?