METU Informatics Institute Min720 Pattern Classification with Bio-Medical Applications Part 9: Review.

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METU Informatics Institute Min720 Pattern Classification with Bio-Medical Applications Part 9: Review

Optimum Classification : Bayes Rule Feature vector Categories Discriminant functions one per category A pattern recognizer Optimum classifier discriminant functions (minimum error/ minimum risk) X max g1g1 gcgc g2g2 Action : or reject

for minimum error a posteriori probability Special Cases: Gaussian and Binary Decision Boundaries: divide the feature space into regions Gaussian= Boundaries are quadratic in general, linear for special cases. Binary= Boundaries are linear. Ex: The decision boundary is circular.

Parameter Estimation Given the form of, we want to estimate its parameters using the samples from a given category. Maximum Likelihood Estimation: Maximize the likelihood function Find that will cause for Ex: if Then,

Nearest Neighbor Classification -Density Estimation -1-NN, k-NN -Shown to approach Bayes Rate in error, but computationaly heavy burden. Reduce computational problems with editing algorithms. Reducing the number of features -to remove the redundancies and obtain statistically independent features: use PCA (Principle Component Analysis) -To obtain features with good separating ability- Fisher’s linear discriminant Linear and Generalized Discriminant Functions Decision Boundary : Linear How to find the parameters of hyperplanes that separate best.

-Iterative methods: Use gradient descent: Perceptron learning – minimizes the misclassified samples -Non-iterative methods- minimum squared error (Widrow-Hoff) -Support vector machines- Dimension is increased so that samples are separable. Generalized Discriminant Functions: -Functions like quadratic may be used to generalize. -Multi-category problems. Example: a)Is the problem linearly separable? b)Obtain 3 weight vectors using perceptron algorithm

We need to W 10, W 20, W 30 W2W2 W1W1 W3W3 To solve, apply the algorithm with multicategory extension. augmented

Augment the samples: Iterate the algorithm starting with a randomly selected sample. if so