1. Linear can be divided into
For a data set:
If there is a hyper-planar x that can precisely divide the positive and negative samples in D into the sides of S, the hyper-plane is as follows:
Then the data set D is linearly divided, otherwise, it is not possible to be divided.
W is called the normal vector, which determines the direction of the super plane, and B is the displacement amount, which determines the distance between the super plane and the origin point.
The distance from any point in the sample space X to the super-plane X (the content of the chapter that can be used to review the space geometry in higher numbers) can be written as:
The following two-form training samples are called support vectors:
The sum of two heterogeneous support vectors (one equals +1, one equals 1) to the hyper-plane distance:
It's called "interval."
To find the maximum interval dividing the hyper plane, is to make the maximum:
Equivalent to:
This is the basic model of support vector machines.
Dual problem:
The Lagrangian function of the upper type can be written as:
which
The derivation of the parameters W and B can be:
The upper is brought into the Lagrangian function, and the W and B are eliminated to obtain the dual expression:
The solution of duality problem is accomplished by SMO algorithm:
Original paper Address: Http://www-ai.cs.uni-dortmund.de/LEHRE/SEMINARE/SS09/AKTARBEITENDESDM/FOLIEN/Joerg_Nitschke_Sequential_ Minimal_optimization.pdf
Support Vector Machine (SVM) algorithm analysis--Zhou Zhihua's Watermelon book Study