Pattern Recognition Concepts

1. 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? Stockman CSE803 Fall 2009

2. 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, ] Stockman CSE803 Fall 2009

3. Possible features for char rec. Stockman CSE803 Fall 2009

4. 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 Stockman CSE803 Fall 2009

5. Classification paradigms Stockman CSE803 Fall 2009

6. 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 Stockman CSE803 Fall 2009

7. 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 Stockman CSE803 Fall 2009

8. 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 Stockman CSE803 Fall 2009 - / 1 x w 0 A 8 B

9. 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 Stockman CSE803 Fall 2009

10. 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 Stockman CSE803 Fall 2009

11. Scaling coordinates by std dev Stockman CSE803 Fall 2009

12. 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 Stockman CSE803 Fall 2009

13. 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 Stockman CSE803 Fall 2009

14. Confusion matrix shows empirical performance Stockman CSE803 Fall 2009

15. Bayesian decision-making Stockman CSE803 Fall 2009

16. 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 Stockman CSE803 Fall 2009

17. Parametric Models can be used Stockman CSE803 Fall 2009

18. Cherry with bruise • Intensities at about 750 nanometers wavelength • Some overlap caused by cherry surface turning away Stockman CSE803 Fall 2009