1. CSE803 Fall 2014 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?

2. CSE803 Fall 2014 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, ]

3. CSE803 Fall 2014 3 Possible features for char rec.

4. CSE803 Fall 2014 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

5. CSE803 Fall 2014 5 Classification paradigms

6. CSE803 Fall 2014 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

7. CSE803 Fall 2014 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

8. CSE803 Fall 2014 8 Decision Trees #holes moment of inertia #strokes best axis direction #strokes - / 1 x w 0 A 8 B 0 1 2 < t  t 2 4 01 0 60 90 0 1

9. CSE803 Fall 2014 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

10. CSE803 Fall 2014 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

11. CSE803 Fall 2014 11 Scaling coordinates by std dev

12. CSE803 Fall 2014 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

13. CSE803 Fall 2014 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

14. CSE803 Fall 2014 14 Confusion matrix shows empirical performance

15. CSE803 Fall 2014 15 Bayesian decision-making

16. CSE803 Fall 2014 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

17. CSE803 Fall 2014 17 Cherry with bruise Intensities at about 750 nanometers wavelength Some overlap caused by cherry surface turning away

18. CSE803 Fall 2014 18 Parametric models