CS558 Project

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CS558 Project

• Local SVM Classification based on triangulation
  (on the plane)
• Glenn Fung

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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

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Classification Problem in
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SAMPLING 1000 randomly sampled points
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ORDERING Clustering

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

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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.

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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.

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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

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What are Support Vector Machines Used For?

• Classification
• Regression Data Fitting
• Supervised Unsupervised Learning

(Will concentrate on classification)
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Support Vector MachinesMaximizing the Margin
between Bounding Planes
A
A-
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The Nonlinear Classifier

• Where K is a nonlinear kernel, e.g.

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Reduced Support Vector Machine AlgorithmNonlinear
Separating Surface
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How to Choose in RSVM?
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(No Transcript)
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Obtained Bizarre Checkerboard
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Optimization More sampled points Training
parameters adjusted
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Result Improved Checkerboard
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Nonlinear PSVM Spiral Dataset94 Red Dots 94
White Dots
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NextBascom Hill
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Some Questions

• Would it work for BW pictures (regression
  instead of classification?

• Aplications?