SVM (Support Vector Machine)
SVM is a kind of supervised learning by the way the data is binary classification of generalized linear classifiers, decision boundary is learning samples solving the maximum margin hyperplane. Just need to know, SVM is a supervised classifier can be.
Start from the first introduced Introduction SVM kernel function, SVM is a linear classifier linearly separable processing data. For data on the right below, SVM can not be a very good response.
Case 1: When to linearly inseparable data, how to deal with? Converting the high-dimensional data into low-dimensional data may be linearly inseparable data into linearly separable data. As shown below:
Case 2: When the non-linear data sharing:
The original linear equation as: F (x) = wx + b, when faced with the above, the process can not be effectively classified. We can use a quadratic function, make that distinction.
Among them, we will be the original one-dimensional three-dimensional map:
We turn first to the dual problem, the original SVM objective function is transformed into the following form:
In this case, x should be replaced by H (x):
So, what is the kernel? In the calculation, x1 and x2 can not map to plot the high-dimensional space is calculated by the H (*), but in the low-dimensional space is calculated directly. We use the K (*) to represent the kernel, kernel function role is to:
Avoid low-dimensional mapping from a high-dimensional process.
for example:
In the present embodiment, the low-dimensional kernel function calculation results completely equivalent to the original problem, therefore, we avoid the direct calculation in the high-dimensional space. So the question is, kernel function is fixed it? Obviously not, there are many kernel function, select the appropriate kernel function based on the difference between the issue and the data. This paper lists common kernel functions as follows:
to sum up:
SVM is a second-class classification model, the basic model is defined as the maximum interval linear classifier in the feature space, which is to support learning strategy is to maximize the distance vector machine, eventually transformed into solving a convex quadratic programming problems . Or simply as will be appreciated it is to find a reasonable hyperplane in multidimensional spaces separated by the data points, which relates to the non-linear data mapping of high-dimensional data for the purpose of linearly separable.