Classification_and_Discriminant_Analysis

Classification_and_Discriminant_Analysis - Classification...

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1/21/2009 1 Classification and Discriminant Analysis Kwok Leung Tsui Industrial & Systems Engineering Georgia Institute of Technology
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1/21/2009 2 Learning Methods Supervised Learning • Statistical data mining techniques creating a functions from a training dataset. • Prediction or classification for unknown datasets. Unsupervised Learning Statistical data mining techniques grouping or partitioning datasets. • Visualization or variable reduction. • Association rules or correlation analysis.
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1/21/2009 3 Supervised Learning Methods X Y Continuous Categorical Regression Classification
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1/21/2009 4 Datasets Training Set Testing Set Dataset used for creating classifiers Dataset used for validating classifier obtained from training set.
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1/21/2009 5 Training error Test error Model Complexity Low High Prediction Error Prediction or Classification Error Overfitting
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1/21/2009 6 Email spam Normal Emails Spam Method, Classifier, Learner … New emails Normal emails Spam Known Unknown Example of Classification Problem
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1/21/2009 7 Basic Approaches to Prediction / Classification ± Linear methods ² Regression (Prediction): Linear Regression ² Classification: Linear Discriminant Analysis (LDA) Logistic Regression ± K Nearest neighbor (KNN) ² Regression (Prediction) ² Classification
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1/21/2009 8 Bayes Decision Theory () ( ) ( ) x P P x P x P j j j ω | | = Posterior probability from Bayes Formula: ( ) j P Class probabilities (Prior) Conditional density of X: ( ) j x P | ( ) = = n j j j P x P x P 1 | ωω Unconditional density of X Review of Basic Bayes Theory
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1/21/2009 9 Bayes Classifier ( ) ( ) 11 2 2 For a given , if | ( ) | ( ), then is classified to class 1, otherwise, class 2. xP x p P x p x ωω ω > ± The basic idea of Bayesian classification: Find the maximum posterior probability !!
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1/21/2009 10 Bayes Classifier ± Classification Methods Based on Bayes Classifiers: ± Naïve Bayes Classifiers assuming conditional independent dist. on inputs ± Linear and quadratic discriminant analysis using Gaussian class conditional dist.
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This note was uploaded on 11/13/2010 for the course ISE 680 taught by Professor Santanu during the Spring '10 term at Purdue University Calumet.

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Classification_and_Discriminant_Analysis - Classification...

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