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Fuzzy Support Vector Machines

This presentation discusses the integration of fuzzy logic into Support Vector Machines (SVMs), addressing the limitations of traditional SVMs in applications where different data points contribute unequally to the decision surface. By assigning fuzzy memberships to data points, Fuzzy SVMs (FSVMs) improve decision-making accuracy. The paper analyzes the differences between SVMs and FSVMs, presents experiments with various datasets, and identifies the drawbacks of using only toy datasets. This work paves the way for better modeling in diverse applications like credit risk evaluation.

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Fuzzy Support Vector Machines

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  1. Fuzzy Support Vector Machines IEEE Transactions on Neural Networks,2002 Authors: Chun-Fu Lin and Sheng-De Presentation by Zhuang Wang

  2. Outline • Introduction • SVMs vs Fuzzy SVMs • Experiments • My figures • Drawbacks of the paper

  3. Introduction • Motivation: In many applications (eg. evaluation of credit risk), different data points give different contribution to the decision surface. • How? Treat each point differently. (Give each point a weight or fuzzy membership .)

  4. SVMs vs. FSVMs • Traditional SVMs: To solve the optimal hyperplane problem: (treat each point equally)

  5. SVMs vs. FSVMs (cont.) • Fuzzy SVMs: (treat each point differently) Difference: each data point is presented like this: (Xi,Yi,si ), where si is a fuzzy membership between [0, 1], New Problem is:

  6. SVMs vs. FSVMs (cont.) • The optimal problem is different, but the solution is very similar. (only one difference) After reformulation, the problem can be transformed into:

  7. Experiments • Data with time property Assign fuzzy membership according to the time data arrive in the system. • Two class with different weighting Select fuzzy membership as a function of respective class. • Use Class Center to Reduce the Effects of Outliers Assign fuzzy membership according to the distance to class center.

  8. My figures

  9. Figures (cont.)

  10. After decreasing weight 10 times

  11. Drawbacks of the paper • Only toy datasets, no reallife datasets are used in experimental part. • The way to assign fuzzy membership to data points need to be improved.

  12. Thank you! Questions?

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