Linear separable, linear model

Linearly separable and linearly inseparable

Linear separability means that a linear function can be used to separate two types of samples (note that this is a linear function), such as a straight line in two-dimensional space, a plane in three-dimensional space, and a hyperplane in high-dimensional space . The term separable here refers to the separation without a trace of error, and the linear inseparability refers to the phenomenon that some samples will be classified incorrectly when divided by the linear classification surface.

Linear model

The coefficient w before the independent variable x in the multiplication formula. If a w affects only one x, then the model is a linear model, such as $and=w_0+w_1\ast x$
when you need to fit$and=w_0+w_1\ast x+w_2\ast x^2$ , you can change$x^2$ Replace with$z$ , that is, using ascending dimension to transform a polynomial regression model into a linear regression model.

Determine whether the data is linearly separable

The convex hull is a convex closed curve (surface) that just encloses all the data.

Check whether the convex hull (convex hull) intersects, which can be used as a basis for judging whether the data is linearly separable.

1. Use quickhull algorithm to find the convex hull of the data

2. The sweepline algorithm determines whether the edges of the convex hull intersect

    两个步骤的复杂度都是O(nlogn)
   

Among them, quickhull has been implemented in the software package qhull (http://www.qhull.org/).

To be continued. . .