# Linear Discriminant Analysis for newbie (What is the meaning of dataset is linear separable?)

What is the meaning of "LDA dataset is linear separable"?

"the classes are non-linearly separated"

"the features have nonlinear relationships"

As I know in maths for linear equation and non-linear equation.

If the classes are linearly separable, there exists a hyperplane (on the same feature space) to separate them. When there is not, the classes are either non-separable or separated by other types of hyper-surfaces, e.g. if instead of a line, a parabola in 2D feature space can separate the classes, it's said non-linearly separable. Features having non-linear relationships is like having features $$x,y$$ where $$y=x^2$$. When you add new features using the old ones, to be able to separate your samples in a higher dimensional space linearly (so non-linearly in the original feature space), you add new features that are nonlinearly related to the original ones.
• LDA is not handling features, it handles the classes. Features can surely have nonlinear relationships. For example, we can add a new feature $x^2$ that makes the classes more separable, which means LDA will do a good job. – gunes May 26 at 16:47