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CS558 Project

CS558 Project. Local SVM Classification based on triangulation (on the plane) Glenn Fung. Outline of Talk. Classification problem on the plane All of the recommended stages were applied: Sampling Ordering: Clustering Triangulation Interpolation (Classification)

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CS558 Project

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  1. CS558 Project Local SVM Classification based on triangulation (on the plane) Glenn Fung

  2. Outline of Talk • Classification problem on the plane • All of the recommended stages were applied: • Sampling • Ordering: • Clustering • Triangulation • Interpolation (Classification) • SVM: Support vector Machines • Optimization: Number of training points increased • Evaluation: • Checkerboard dataset • Spiral dataset

  3. Given m points in 2 dimensional space • Represented by an m-by-2 matrix A • Membership of each in class +1 or –1 Classification Problem in

  4. SAMPLING: 1000 randomly sampled points

  5. ORDERING: Clustering • A Fuzzy-logic based clustering algorithm was used. • 32 cluster centers were obtained

  6. ORDERING: Delaunay Triangulation • Algorithms to triangulate and to get the Delaunay triangulation from HWKs 3 and 4 were used. • Given a point,the random point approach is used to localize the triangle that contains it.

  7. Interpolation: SVM • SVM : Support Vector Machine Classifiers • A different nonlinear Classifier is used for each triangle • The triangle structure is efficiently used for both training and testing phases and for defining a “simple” and fast nonlinear classifier.

  8. What is a Support Vector Machine? • An optimally defined surface • Typically nonlinear in the input space • Linear in a higher dimensional space • Implicitly defined by a kernel function

  9. What are Support Vector Machines Used For? • Classification • Regression & Data Fitting • Supervised & Unsupervised Learning (Will concentrate on classification)

  10. Support Vector MachinesMaximizing the Margin between Bounding Planes A+ A-

  11. The nonlinear classifier: : • Gaussian (Radial Basis) Kernel • The represents the “similarity” -entryof of data points and The Nonlinear Classifier • Where K is a nonlinear kernel, e.g.:

  12. of (i) Choose a random subset matrix entire data matrix (ii) Solvethe following problem by the Newton method with corresponding : min (iii) The separating surface is defined by the optimal in step(ii): solution Reduced Support Vector Machine AlgorithmNonlinear Separating Surface:

  13. is a representative sample of the entire dataset • Need not be a subset of • A good selectionof may generate a classifier using very small : • Possible ways to choose random rows from the entire dataset • Choose such that the distance between its rows • Choose exceeds a certain tolerance and as • Use k cluster centers of How to Choose in RSVM?

  14. Obtained Bizarre “Checkerboard”

  15. Optimization: More sampled points Training parameters adjusted

  16. Result: Improved Checkerboard

  17. Nonlinear PSVM: Spiral Dataset94 Red Dots & 94 White Dots

  18. Next:Bascom Hill

  19. Some Questions • Would it work for B&W pictures (regression instead of classification? • Aplications?

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