this presentation gives an introduction to SVM and its idea. At the end an show the result of the SVM in ECG beat classification and comparison with Neural Networks

1. A.RahimK.Mohammadi Spring 2011 Support Vector Machine for ECG Beat Classification

2. Maximum Margin Support Vector Machine (SVM) Multi-class SVM Result and Discussion Outline

3. Maximum Margin denotes +1 denotes -1 Any of these would be fine.. ..but which is best?

4. Linear Classifiers denotes +1 denotes -1 How would you classify this data? Misclassified to +1 class

5. Maximum Margin SVM is a binary classification which separates classes in feature space The maximum margin linear classifier is the linear classifier with the maximum margin. This is the simplest kind of SVM (Called an LSVM) Support Vectors are those datapoints that the margin pushes up against Linear SVM

6. SVM

7. SVM Given the training sample and kernel function K SVM will find a coefficient ai for each xi through an quadratic maximization programming 𝑖=1𝑛𝑎𝑖− 12𝑖,𝑗=1𝑛𝑎𝑖𝑎𝑗𝑦𝑖𝑦𝑗𝐾𝒙𝑖,𝒙𝑗𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 0≤𝑎𝑖≤𝐶, 𝑖=1,2,…,𝑛 𝑎𝑛𝑑 𝑖=1𝑛𝑎𝑖𝑦𝑖=0 Wher C is The cost parameter Every new pattern x is classified to either one of the two categories 𝑓𝑥=𝑠𝑖𝑔𝑛𝑖=1𝑛𝑦𝑖𝑎𝑖𝐾𝒙,𝒙𝒊+𝑏

9. One-against-all (OAA) SVMs Multi-class SVM

10. One-Against-One (OAO) SVMs Multi-class SVM

11. ECG beat Classification System

12. Results

13. Some Issues Choice of kernel - Gaussian or polynomial kernel is default - if ineffective, more elaborate kernels are needed - domain experts can give assistance in formulating appropriate similarity measures Choice of kernel parameters - e.g. σ in Gaussian kernel - σ is the distance between closest points with different classifications - In the absence of reliable criteria, applications rely on the use of a validation set or cross-validation to set such parameters. Optimization criterion – Hard margin v.s. Soft margin - a lengthy series of experiments in which various parameters are tested

14. SVMs are currently among the best performers for a number of classification tasks SVMs can be applied to complex data types beyond feature vectors (e.g. graphs, sequences, relational data) by designing kernel functions for such data. SVM successfully applied for multi-class classification The result shows the high performance of SVM in ECG beat classification SVM is good when we have high dimension feature space and lots of train patterns Conclusion

15. An excellent tutorial on VC-dimension and Support Vector Machines: C.J.C. Burges. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2(2):955-974, 1998. The VC/SRM/SVM Bible: Statistical Learning Theory by Vladimir Vapnik, Wiley-Interscience; 1998 Some Resources http://www.kernel-machines.org/

16. Chih-Wei Hsu and Chih-Jen Lin (2002). "A Comparison of Methods for Multiclass Support Vector Machines". IEEE Transactions on Neural Networks http://www.iro.umontreal.ca/~pift6080/H09/documents/papers/svm_tutorial.ppt Chih-Chung Chang and Chih-Jen Lin, LIBSVM: a library for support vector machines, 2001 Reference

17. Thank YouWelcome your comments and questions