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lecture8 - Pattern Classication Examples Spam detection 6...

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e62: lecture 8 11/10/10 Pattern Classification 1 e62: lecture 8 11/10/10 Examples Spam detection Face recognition Medical diagnosis 2 0 3 6 what ... Nigeria wire funds ... email data sample label photo 1 photo 2 data sample label e62: lecture 8 11/10/10 Hyperplanes 3 S = { z | x T z = α } where x N , α x S S x α x T x x e62: lecture 8 11/10/10 A hyperplane defines two half spaces Goal Positive samples in first half space Negative samples in second half space nothing on the boundary Linear Separation of Data 4 x { z | x T z α } and { z | x T z α }
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e62: lecture 8 11/10/10 Linear Program for Separable Data Data Positive samples Negative samples Linear program What if the data is inseparable? 5 u 1 , . . . , u M N v 1 , . . . , v K N min 0 min 0 min 0 s . t . - x T u m + α + 1 0 m = 1 , . . . , M x T v k - α + 1 0 k = 1 , . . . , K “violations” (if positive) e62: lecture 8 11/10/10 Inseparable Data Minimize number of misclassifications? NP-complete Heuristic approximation Violations: Minimize sum of violations
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