1. Mathematical Programming in Data Mining Author: O. L. Mangasarian Advisor: Dr. Hsu Graduate: Yan-Cheng Lin

2. Abstract  Describe mathematical programming to feature selection, clustering and robust representation

3. Outline  Motivation  Objective  Problems  Feature Selection  Clustering  Robust Representation  Conclusion

4. Motivation  Mathematical programming has been applied to a great variety of theoretical  Problems can be formulated and effectively solved as mathematical programs

5. Objective  Describe three mathematical- programming-based developments relevant to data mining

6. Problems  Feature Selection  Clustering  Robust Representation

7. Problem - Feature Selection  Discriminating between two finite point sets in n-dimensional feature space and utilizes as few of the feature as possible  Formulated as mathematical program with a parametric objective function and linear constraints

8. Problem - Clustering  Assigning m points in the n- dimensional real space R n to k clusters  Formulated as determining k centers in R n, the sum of distances of each point to the nearest center is minimized

9. Problem - Robust Representation  Modeling a system of relations in a manner that preserves the validity of the representation when the data on which the model is based changes  Use a sufficiently small error זּ is purposely tolerated

10. Feature Selection  Use the simplest model to describe the essence of a phenomenon  Binary classification problem: –discriminating between two given point sets A and B in the n-dimensional real space R n by using as few of the n- dimensions of the space as possible

11. Binary classification W P

12.  the following are some defined:  A  B Feature Selection

13. Successive Linearization Algorithm  w vector is result

14. Experimentation  32-feature Wisconsin Prognostic Breast Cancer(WPBC)  N=32, m = 28, k = 118, r = 0.05, 4 features, increasing tenfold cross-validation correctness by 35.4%

15. Clustering  Determining k cluster centers, the sum of the 1-norm distances of each point in a given database to nearest cluster center is minimized  Minimizing product of two linear functions on a set defined by linear inequalities

16. K-Median Algorithm  Need to solve

17. Experimentation  used as a KDD tool to mine WPBC to discover medical knowledge  key observation is curves are well separated

18. Experimentation

19. Robust Representation  model remains valid under a class of data perturbation  Use זּ -tolerance zone wherein errors are disregarded  Better generalization results than conventional zero-tolerance

20. Robust Representation  A is a m*n matrix, a is a m*1 vector  x is a vector be “ learned ”  find minimize of Ax - a

21. Robust Representation = x Aa זּ זּ -tolerate = x Aa

22. Conclusion  Mathematical programming codes are reliable and robust codes  Problems solved demonstrate mathematical programming as versatile and effective tool for solving important problems in data mining and knowledge discovery in databases

23. Opinion  Mathematical describe can explain about complex problems and convince others, but … you must be understand it first