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ECE471-571 – Pattern Recognition Lecture 4 – Parametric Estimation

ECE471-571 – Pattern Recognition Lecture 4 – Parametric Estimation. Hairong Qi, Gonzalez Family Professor Electrical Engineering and Computer Science University of Tennessee, Knoxville http://www.eecs.utk.edu/faculty/qi Email: hqi@utk.edu. Pattern Classification. Statistical Approach.

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ECE471-571 – Pattern Recognition Lecture 4 – Parametric Estimation

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  1. ECE471-571 – Pattern RecognitionLecture 4 – Parametric Estimation Hairong Qi, Gonzalez Family Professor Electrical Engineering and Computer Science University of Tennessee, Knoxville http://www.eecs.utk.edu/faculty/qi Email: hqi@utk.edu

  2. Pattern Classification Statistical Approach Non-Statistical Approach Supervised Unsupervised Decision-tree Basic concepts: Baysian decision rule (MPP, LR, Discri.) Basic concepts: Distance Agglomerative method Syntactic approach Parameter estimate (ML, BL) k-means Non-Parametric learning (kNN) Winner-takes-all LDF (Perceptron) Kohonen maps NN (BP) Mean-shift Support Vector Machine Deep Learning (DL) Dimensionality Reduction FLD, PCA Performance Evaluation ROC curve (TP, TN, FN, FP) cross validation Stochastic Methods local opt (GD) global opt (SA, GA) Classifier Fusion majority voting NB, BKS

  3. Bayes Decision Rule Maximum Posterior Probability If , then x belongs to class 1, otherwise, 2. Likelihood Ratio Discriminant Function Case 1: Minimum Euclidean Distance (Linear Machine), Si=s2I Case 2: Minimum Mahalanobis Distance (Linear Machine), Si = S Case 3: Quadratic classifier , Si = arbitrary

  4. Multivariate Normal Density

  5. Calculate m, S Estimating Normal Densities

  6. Covariance

  7. *Why? – Maximum Likelihood Estimation Compare “likelihood”

  8. *Derivation

  9. * Derivative of a Quadratic Form

  10. **Why? – Baysian Estimation • Maximum likelihood estimation • The parameters are fixed • Find value for q that best agrees with or supports the actually observed training samples – likelihood of q w.r.t. the set of samples • Baysian estimation • Treat parameters as random variable themselves

  11. ** The pdf of the parameter (m) is Gaussian

  12. ** Derivation

  13. ** mn and sn Our best guess for m after observing n samples Measures our uncertainty about this guess • Behavior of Bayesian learning • The larger the n, the smaller the sn – each additional observation decreases our uncertainty about the true value of m • As n approaches infinity, p(m|D) becomes more and more sharply peaked, approaching a Dirac delta function. • mn is a linear combination between the sample mean and m0

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