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Linear Classification Linear separability Inseparability Real - - PowerPoint PPT Presentation
Linear Classification Linear separability Inseparability Real - - PowerPoint PPT Presentation
Linear Classification Linear separability Inseparability Real world problems: there may not exist a hyperplane that separates cleanly Solution to this inseparability problem: map data to higher dimensional space Called the
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- Real world problems: there may not exist a hyperplane
that separates cleanly
- Solution to this “inseparability” problem: map data to
higher dimensional space
- Called the “feature space”, as opposed to the original “input
space”
- Inseparable training set can be made separable with proper
choice of feature space
Inseparability
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Feature map
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Linear classifier
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Linear classifier
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Good and bad linear classifiers
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Support Vector Machine
Two popular implementations
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Margin
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Margin
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Linear Support Vector Machine
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Inseparable case
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Linear SVM
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Classification vs Regression
Discrete Continuous
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f(x1,x2) =
- r
y = f(x) = 10.5 x1 x2 x y
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Protein structure prediction as regression
3D coordinates and angles
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Linear regression
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Nonlinear regression
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When does linear regression work?
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K nearest neighbor regression
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Nearest neighbor regression
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Nearest neighbor regression
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Filling patches in images
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Linear regression
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Linear Regression
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Linear regression
Squared prediction error