marrayclass14 - Supervised classification Dr. Edgar Acuna...

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Dr. Edgar Acuna Departmento de Matematicas Universidad de Puerto Rico- Mayaguez math.uprrm.edu/~edgar Supervised classification
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Supervised Classification: predicts categorical class labels constructs a model based on the training set and uses it in classifying new data Prediction (Regression): models continuous-valued functions. It can be used to predict unknown or missing values Supervised Classification vs. Prediction
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The Supervised classification problem X 1 X 2 X M y C(x,L) The Learning sample L y*=C(x*,L) The classifier The estimated class P r e d i c t o r s Class
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Supervised Classification—A Two-Step Process Model construction: describing a set of predetermined classes Each tuple/sample is assumed to belong to a predefined class, as determined by the class label attribute The model is represented as classification rules, decision trees, or mathematical formulae Model usage: for classifying future or unknown objects Estimate accuracy of the model The known label of test sample is compared with the classified result from the model. Test set is independent of training set, otherwise over-fitting will occur. Accuracy rate is the percentage of test set samples that are correctly classified by the model
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Supervised classification methods 1 . Linear Discriminant Analysis. 2. Nonlinear Methods: Quadartic Discrimination, Logistic Regression, Projection Pursuit. 3. Decision Trees. 1. k-nearest neighbors 2. Classifiers based on kernel density estimation and gaussian mixtures. 6. Neural Networks: Multilayer perceptron. Radial Basis Function, Kohonen self-organizing map, Linear vector quantification. 7. Support vector machines.
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Linear Discriminant Analysis Y X 1 X 2 X p 1 X 11 X 21 …. X p1 1 X 12 X 22 X p2 .. .. .. .. .. 1 X 1n1 X 2n1 X pn1 2 X 1,n1+1 X 2,n1+1 X p,n1+1 2 X 1,n1+2 X 2,n1+2 X p,n1+2 .. .. .. .. 2 X 1,n1+n2 X 2,n1+n2 X p,n1+n2 Consider the following training sample with p features and two classes (column Y)
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Let be the mean vector of the p features in class 1, and let be the corresponding mean vector for the class 2. Let us consider μ 1 and μ 2 as the mean vector of the respective class populations Let us assume that both populations have the same covariance matrix, ie Σ 1 = Σ 2 = Σ . This is known as the homocedasticity property. For now, we do not need to assume that the random vector of predictor x =(x1,…. .xp) is normally distributed. Linear discrimination is based on the following fact: A object x is assigned to the class C1 if D( x , C1)<D( x ,C2) (2.1) where D( x ,Ci)=(x-u i )’ Σ -1 (x-u i ), for i=1,2, represents the squared Mahalanobis distance of x to the center of the Ci class. 1
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This note was uploaded on 05/12/2010 for the course APPLIED ST 2010 taught by Professor Various during the Spring '10 term at Universidad Nacional Agraria La Molina.

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marrayclass14 - Supervised classification Dr. Edgar Acuna...

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