[Analysis of AI Principles] — Principle of Support Vector Machine
2024-07-08
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Table of contents
1. Overview of Support Vector Machine (SVM)
2. Hyperplane and support vector
3. Maximize intervals
4. Optimization Problem
5. Kernel Function
6. Conclusion
1. Overview of Support Vector Machine (SVM)
- definition：Support vector machine is a supervised learning model, mainly used for data classification problems. Its basic idea is to split data points through a hyperplane so that data points of different categories are located on both sides of the hyperplane.
- Classification: Support vector machines are mainly divided into three categories: linearly separable support vector machines, linear support vector machines and nonlinear support vector machines.
2. Hyperplane and support vector
- Hyperplane: In n-dimensional space, a hyperplane is an n-1-dimensional subspace. In two-dimensional space, it is a straight line; in three-dimensional space, it is a plane. The hyperplane can be expressed as w^T * xb = 0, where w is the normal vector, b is the intercept, and x is the sample point.
- Support Vectors: The sample points closest to the hyperplane are called support vectors. These points play a decisive role in determining the position of the hyperplane.
3. Maximize intervals
- Function interval：For a given training set and hyperplane, the function interval from the sample point (x_i, y_i) to the hyperplane is r_i
