1 / 21

Fundamentals of Non-Linear Support Vector Machines: A Comprehensive Guide

Discover the basics of Non-Linear Support Vector Machines (SVM) in this comprehensive guide by Jean-Philippe Vert from Kyoto University, Japan. Learn about linear and non-linear SVM, training in the feature space, kernel functions, popular selections, and the approach for Non-linear SVM. Understand classification with polynomial and Gaussian kernels and the importance of Non-linear SVM in binary classification. Explore the challenging task of selecting the right kernel and parameters, highlighting the need for experimentation and fine-tuning in machine learning development.

jenniehowell
Download Presentation

Fundamentals of Non-Linear Support Vector Machines: A Comprehensive Guide

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to Non-linear Support Vector Machine (SVM) Author:Jean-Philippe Vert Bioinformatics Center, Kyoto University, Japan Advisor: Dr.Hsu Graduate: Ching-Wen Hong

  2. Outline • 1.Linear SVM • 2.Non-linear SVM • 3.Training a SVM in the feature space • 4.Kernal • 5.Popular kernals • 6.The approach for Non-linear SVM • 7. Classification with a Polynomial kernel • 8. Classification with a Gaussian kernel • 9.Conclusion

  3. Linear SVM

  4. Linear SVM

  5. Linear SVM

  6. Linear SVM

  7. Linear SVM

  8. Linear SVM

  9. Linear SVM

  10. Linear SVM

  11. Non-linear SVM

  12. Non-linear SVM

  13. Non-linear SVM

  14. Training a SVM in the feature space • (1)Input:a training set S={(x1,y1),…,(XN,YN)} is not linearly separable. • (2)A mapping Φ(xi)=( Φ1(xi) , … , ΦM(Xi) ) , i=1,…,N • (3)The training set Φ(S)={ (Φ(x1),y1),…,(Φ(xN), yN) } can be linearly separable in the feature space. • (4)The dual problem is to maximize • Max LD=∑αi-1/2∑αiαjyiyjΦ(xi)․Φ(xj) • S.t. 0 ≤ αi ≤ C , i=1,…,N ,and ∑ αiyi = 0 • (5)We can find the decision function • f(x)=w․Φ(x)+b = ∑αiyiΦ(xi)․Φ(x) + b • K(x,x‘) =Φ(x)․Φ(x') is a Kernel function

  15. Kernel • (1).Kernel K(x,x‘)=Φ(x)․Φ(x‘) • (x,x‘) is any two points in the input space • Φ(x) is a mapping to a feature space

  16. Popular Kernels

  17. Popular Kernels

  18. The approach for Non-linear SVM • The following steps: • (1).Input a training set S={(x1,y1),…,(xN,yN)} • (2).Choose a Kernel K(․,․) • (3).Training a SVM in the feature space • i.e.To find the decision function f(x)=∑αiyiK(xi,x) • (4).Classify any new object and to test efficiency on the research of data. • There is usually no automatic way to choose a Kernel and to adjust the corresponding parameters,Therefore we usually has to try different Kernels and paramters.

  19. Classification with a Polynomial kernel

  20. Classification with a Gaussian kernel

  21. Conclusion • Non-linear SVM is a extremely powerful learning algorithm for binary classification. • It is important to find Kernel but it is difficult. • If we can find a way to Kernel,That is a nice thing to develop in the machine learning.

More Related