Stockman CSE803 Fall 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 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 Possible features for char rec.

Stockman CSE803 Fall 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 Classification paradigms

Stockman CSE803 Fall 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 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 Decision Trees #holes moment of inertia #strokes best axis direction #strokes - / 1 x w 0 A 8 B < t  t

Stockman CSE803 Fall 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 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 Scaling coordinates by std dev

Stockman CSE803 Fall 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 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 Confusion matrix shows empirical performance

Stockman CSE803 Fall Bayesian decision-making

Stockman CSE803 Fall 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 Parametric Models can be used

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