Miks lineaarne mudel ilma tunnuse teisendamiseta ei lahenda ringi sees ja outside punktide eraldamise ülesannet?

The linear model constructs a separating hyperplane that divides the feature space into two parts using a linear equation. In the task of separating points inside and outside a circle, the boundary of separation is a circle, i.e., a non-linear curve. Without feature transformation, a linear model cannot approximate such a non-linear boundary, as it is limited to straight lines (hyperplanes).

To solve this problem, additional features need to be introduced, for example, the squares of coordinates (x², y²), which will allow the linear model to operate in a new feature space where the boundary will be linear. This is called feature transformation or the use of polynomial features.

Example of transformation:

# Original features
X = [[x, y] for x, y in points]

# Adding squares of coordinates
X_transformed = [[x, y, x**2 + y**2] for x, y in points]

# Now the linear model can separate points based on the condition x² + y² < r²