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Pattern Recognition Concepts

Pattern Recognition Concepts. Chapter 4: Shapiro and Stockman How should objects be represented? Algorithms for recognition/matching * nearest neighbors * decision tree * decision functions * artificial neural networks How should learning/training be done?.

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Pattern Recognition Concepts

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  1. CSE803 Fall 2013 Pattern Recognition Concepts • Chapter 4: Shapiro and Stockman • How should objects be represented? • Algorithms for recognition/matching * nearest neighbors * decision tree * decision functions * artificial neural networks • How should learning/training be done?

  2. CSE803 Fall 2013 Feature Vector Representation • X=[x1, x2, … , xn], each xj a real number • Xj may be object measurement • Xj may be count of object parts • Example: object rep. [#holes, Area, moments, ]

  3. CSE803 Fall 2013 Possible features for char rec.

  4. CSE803 Fall 2013 Some Terminology • Classes: set of m known classes of objects (a) might have known description for each (b) might have set of samples for each • Reject Class: a generic class for objects not in any of the designated known classes • Classifier: Assigns object to a class based on features

  5. CSE803 Fall 2013 Classification paradigms

  6. CSE803 Fall 2013 Discriminant functions • Functions f(x, K) perform some computation on feature vector x • Knowledge K from training or programming is used • Final stage determines class

  7. CSE803 Fall 2013 Decision-Tree Classifier • Uses subsets of features in seq. • Feature extraction may be interleaved with classification decisions • Can be easy to design and efficient in execution

  8. CSE803 Fall 2013 Decision Trees #holes 0 2 1 moment of inertia #strokes #strokes  t < t 1 0 best axis direction #strokes 0 1 4 2 0 90 60 - / 1 x w 0 A 8 B

  9. CSE803 Fall 2013 Classification using nearest class mean • Compute the Euclidean distance between feature vector X and the mean of each class. • Choose closest class, if close enough (reject otherwise) • Low error rate at left

  10. CSE803 Fall 2013 Nearest mean might yield poor results with complex structure • Class 2 has two modes • If modes are detected, two subclass mean vectors can be used

  11. CSE803 Fall 2013 Scaling coordinates by std dev

  12. CSE803 Fall 2013 Another problem for nearest mean classification • If unscaled, object X is equidistant from each class mean • With scaling X closer to left distribution • Coordinate axes not natural for this data • 1D discrimination possible with PCA

  13. CSE803 Fall 2013 Receiver Operating Curve ROC • Plots correct detection rate versus false alarm rate • Generally, false alarms go up with attempts to detect higher percentages of known objects

  14. CSE803 Fall 2013 Confusion matrix shows empirical performance

  15. CSE803 Fall 2013 Bayesian decision-making

  16. CSE803 Fall 2013 Normal distribution • 0 mean and unit std deviation • Table enables us to fit histograms and represent them simply • New observation of variable x can then be translated into probability

  17. CSE803 Fall 2013 Cherry with bruise • Intensities at about 750 nanometers wavelength • Some overlap caused by cherry surface turning away

  18. CSE803 Fall 2013 Parametric models

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