Hyperplane of support vector machine for machine learning


Support vector machine

Given training sample set D = {(x_1, y_1), (x_2, y_2),…, (x_m, y_m)}, y_ I \ in {- 1, + 1}, the basic idea of classification learning is to find a partition hyperplane in the sample space based on training set D to separate samples of different categories, but there may be many partition hyperplanes that can separate training samples, as shown in Figure 6.1. Which one should we find?

We should define a performance indicator, and then calculate the value of the performance indicator on each line. The line with the largest value is the most suitable.

Hyperplane of support vector machine for machine learning

Intuitively, we should find the partition hyperplane located in the “middle” of the two training samples, because the partition hyperplane has the best “tolerance” to the local disturbance of the training samples, that is, it has the strongest partition ability to the unseen examples.

In the sample space, the partition hyperplane can be described by the following linear equation:

\mathbf{w}^T\mathbf{x}+ b = 0

amongw=(w_1; w_2;…; w_d) is the normal vector, which determines the direction of the hyperplane; B is the displacement term, which determines the distance between the hyperplane and the origin. Obviously, the partition hyperplane can be divided into normal vectorswAnd displacement B determination

be careful:xVector andwSame vector dimension

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