My view of SVM (I.)

Recently, we have learned about the principles of SVM (support vector machines) for vector machine. Sort out what you understand by the way.

Do not talk about the background, directly cut into the subject.

First, what is support vector machine

As you can say, we now have a lot of circles and forks on a plane, as shown in 1.1.

Figure 1.1

Now it takes a straight line to separate the circle from the fork, and you can imagine that there will be a lot of possible lines, but there will be an optimal dividing line l,1.2 as shown.

Figure 1.2

The shortest distance from the Green fork to L is D1, the shortest distance from red circle to L is D2, the D1=D2 is guaranteed, and the value of D1+D2 is the largest, then this line is the best dividing line. The specific representation is shown in 1.3

Figure 1.3

In Figure 1.3, the blue dashed lines are H1 and H2, each circle and fork can be seen as a vector, and the forks and circles falling on the edge are called "support vectors", so no vectors on the edge are "non-supported vectors".

In addition, in SVM, we often hear the concept of "super plane". What is a hyper-plane? When the circle and fork in the graph are two-dimensional, then L is a straight line; when the circle and fork in the graph are three-dimensional, l is a plane; when the circle and fork are three-dimensional, then L is a super-plane.

Each circle and fork in the graph is a sample, and the dimensions of the circle and fork represent the number of characteristics of the sample.

Second, How to use math to describe a super plane

2.1, the normal vector of the Super plane L is set , and a sample vector is \[\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{u}\] , the projection on is on .

For all the circle samples (positive sample), there are:

, which is a positive sample vector

For all fork samples (negative samples), there are:

, where a negative sample vector

Figure 2.1

Order, you can get:

①

Because and both are unknown quantities, while scaling and having no effect on the results, it is advisable to:

Ii

The result of the classification of the sample I.

For negative samples, so that for positive samples, the combination of inequalities in ②, you can get:

Well, now that we've pushed to so many formulas, let's sum up, 2.2 shows,

The point x on the plane L satisfies:

The point x on the planar H1 satisfies:

The point x on the planar H2 satisfies:

Figure 2.2

At this point, we understand what is support vector machine, and complete the mathematical description of the hyper-plane, here is how to find such a super-plane problem, please see the next blog post.

My view of SVM (I.)