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lec22

# lec22 - Lecture 22 November 8 10 HW5 due Nov 10 Exam 2 Dec...

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USC CS574: Computer Vision, Fall 2010 Copyright 2010, by R. Nevatia 1 Lecture 22: November 8, 10 HW5 due Nov 10 Exam 2, Dec 1, during class time, closed book, closed notes Similar in style to Exam 1 Content: Material from Lec 12 onwards, detailed list will be given later. • Review Principal component analysis (PCA) Linear discriminant analysis (LDA)/Canonical_variates • Today Support Vector Machines Pedestrian detectors

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USC CS574: Computer Vision, Fall 2010 Copyright 2010, by R. Nevatia 2 Support Vector Machine (SVM) Linear classifier (decision surfaces are hyper planes) First, assume that classes are linearly separable SVM chooses a hyperplane that maximizes error margin (minimum distance from each class), see figure 22.19. Plane is defined by a weighted sum of some of the data points (called support vectors) Basic equation is y i ( w . x i + b) > 0; y i is label of sample x i , task is to compute w and b from multiple samples Many solutions are possible, we want to maximize the margin which turns out to be equivalent to minimizing (1/2) w . w subject to y i ( w . x i + b) 0. Problem further transformed to a quadratic optimization using Lagrangian multipliers (these details are not important for the course), formula is given in Algorithm 22.8 Classification rule is simple, see algorithm 22.8. Uses weighted sum of dot product of observed vector and support vectors (these are the closest to the hyperplane and only ones with non-zero values of α i .Thus, classification is efficient even with large training data sets
USC CS574: Computer Vision, Fall 2010 Copyright 2010, by R. Nevatia 3 SVM: Decision Surface

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USC CS574: Computer Vision, Fall 2010 Copyright 2010, by R. Nevatia 4 SVM: Algorithm
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