Ch4 - Insight by Mathematics and Intuition for...

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Unformatted text preview: Insight by Mathematics and Intuition for understanding Pattern Recognition Waleed A. Yousef Faculty of Computers and Information, Helwan University. May 8, 2010 Ch4. Linear Models for Classification Before modeling a linear model for classification, what is the best descision function? Back to Ch2. we find: ln f 1 ( X ) f 2 ( X ) G 1 ≷ G 2 ln π 2 L 21 π 1 L 12 h ( X ) G 1 ≷ G 2 th, (the log-likelihood ratio). If we know f 1 and f 2 the best thing one can do is to use them and estimate their parameters, and h ( X ) is the decision function that decides to which class X belongs, with the decision surface h ( X ) = th . Decision boundary for mltinormal distributions 1 2 x Í Σ- 1 2- Σ- 1 1 x ü ûú ý Quadratic Term- x Í Σ- 1 2 μ 2- Σ- 1 1 μ 1 ü ûú ý Linear Term + 1 2 μ Í 2 Σ- 1 2 μ 2- μ Í 1 Σ- 1 1 μ 1- 1 2 ln | Σ 1 | | Σ 2 | = th Linear Discriminant Analysis (LDA): We assume that...
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Ch4 - Insight by Mathematics and Intuition for...

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