"Cs229-lecture7" Support vector machine (SVM)

SVM Good learning materials:

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Blog:http://www.blogjava.net/zhenandaci/category/31868.html

The above information, the SVM interpretation (including the various concepts) is more detailed. Therefore, it is not to record each of the points of knowledge, and more is to clarify the idea of the algorithm.

For the classification of data, we first divided it into linear and linear can not be divided into two categories. As shown in the following:

General idea:

Linear can be divided

take two dimensions as an example:

Low dimensional linear non-fractal

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mapping to high-dimensional, using kernel function avoidance to calculate directly in high-dimensional space

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High dimensional linearity can be divided into

Intuitive understanding of kernel functions: The function of calculating the inner product of two vectors in the space after implicit mapping is called the kernel function (Kernel functions).

One-dimensional linear non-divided:

Mapping into two-dimensional linear can be divided into:

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Kernel function Objective: to project the data in the original coordinate system into another space with kernel, so as to make the data linearly divided in the new space.

features of the kernel function:

1) The introduction of kernel functions avoids the "dimension catastrophe" and greatly reduces the computational amount. The dimension n of the input space has no effect on the kernel function matrix, so the kernel function method can effectively handle the high-dimensional input.

2) No need to know the form and parameters of the nonlinear transformation function φ.

3) The change of the form and parameters of the kernel function implicitly changes the mapping from the input space to the feature space, and then influences the properties of the feature space, and finally changes the performance of various kernel function methods.

4) The kernel function method can be combined with different algorithms to form many different methods based on kernel function technology, and the design of these two parts can be carried out separately, and can choose different kernel functions and algorithms for different applications.

Concept: Relaxation variables --for handling outliers

loss Function --the extent to which errors are predicted

"Cs229-lecture7" Support vector machine (SVM)