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- 1. A.RahimK.Mohammadi<br />Spring 2011<br />Support Vector Machine for ECG Beat Classification<br />
- 2. Maximum Margin<br />Support Vector Machine (SVM)<br />Multi-class SVM<br />Result and Discussion<br />Outline <br />
- 3. Maximum Margin<br /> denotes +1<br /> denotes -1<br />Any of these would be fine..<br />..but which is best?<br />
- 4. Linear Classifiers<br /> denotes +1<br /> denotes -1<br />How would you classify this data?<br />Misclassified<br /> to +1 class<br />
- 5. Maximum Margin<br />SVM is a binary classification which separates classes in feature space<br />The maximum margin linear classifier is the linear classifier with the maximum margin.<br />This is the simplest kind of SVM (Called an LSVM)<br />Support Vectors are those datapoints that the margin pushes up against<br />Linear SVM<br />
- 6. SVM<br />
- 7. SVM<br /> Given the training sample<br /> and kernel function K <br />SVM will find a coefficient ai for each xi through an quadratic maximization programming<br />π=1πππβΒ 12π,π=1ππππππ¦ππ¦ππΎππ,πππ π’πππππ‘Β π‘πΒ 0β€ππβ€πΆ,Β Β π=1,2,β¦,πΒ πππΒ π=1ππππ¦π=0<br />Wher C is TheΒ cost parameterΒ <br />Every new pattern x is classified to either one of the two categories <br />Β <br />ππ₯=π ππππ=1ππ¦ππππΎπ,ππ+π<br />Β <br />
- 8. Non-linear SVMs: Feature spaces<br /><ul><li>General idea: the original input space can always be mapped to some higher-dimensional feature space where the training set is separable:</li></ul>Ξ¦: x->Ο(x)<br />
- 9. One-against-all (OAA) SVMs<br />Multi-class SVM<br />
- 10. One-Against-One (OAO) SVMs<br />Multi-class SVM<br />
- 11. ECG beat Classification System<br />
- 12. Results<br />
- 13. Some Issues<br />Choice of kernel<br /> - Gaussian or polynomial kernel is default<br /> - if ineffective, more elaborate kernels are needed<br /> - domain experts can give assistance in formulating appropriate similarity measures<br />Choice of kernel parameters<br /> - e.g. Ο in Gaussian kernel<br /> - Ο is the distance between closest points with different classifications <br /> - In the absence of reliable criteria, applications rely on the use of a validation set or cross-validation to set such parameters. <br />Optimization criterion β Hard margin v.s. Soft margin<br /> - a lengthy series of experiments in which various parameters are tested <br />
- 14. SVMs are currently among the best performers for a number of classification tasks<br />SVMs can be applied to complex data types beyond feature vectors (e.g. graphs, sequences, relational data) by designing kernel functions for such data.<br />SVM successfully applied for multi-class classification<br />The result shows the high performance of SVM in ECG beat classification<br />SVM is good when we have high dimension feature space and lots of train patterns<br />Conclusion<br />
- 15. An excellent tutorial on VC-dimension and Support Vector Machines:<br />C.J.C. Burges. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2(2):955-974, 1998. <br />The VC/SRM/SVM Bible:<br />Statistical Learning Theory by Vladimir Vapnik, Wiley-Interscience; 1998<br />Some Resources<br />http://www.kernel-machines.org/<br />
- 16. Chih-Wei Hsu and Chih-Jen Lin (2002). "A Comparison of Methods for Multiclass Support Vector Machines".Β IEEE Transactions on Neural Networks<br />http://www.iro.umontreal.ca/~pift6080/H09/documents/papers/svm_tutorial.ppt<br />Chih-Chung Chang and Chih-Jen Lin, LIBSVM: a library for support vector machines, 2001<br />Reference<br />
- 17. Thank YouWelcome your comments and questions<br />

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