CSE803 Fall 2015 1

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

CSE803 Fall 2015 2

Feature Vector Representation n  X=[x1, x2, … , xn], each xj

a real number n  Xj may be object

measurement n  Xj may be count of object

parts n  Example: object rep.

[#holes, Area, moments, ]

CSE803 Fall 2015 3

Possible features for char rec.

CSE803 Fall 2015 4

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

CSE803 Fall 2015 5

Classification paradigms

CSE803 Fall 2015 6

Discriminant functions n  Functions f(x, K)

perform some computation on feature vector x

n  Knowledge K from training or programming is used

n  Final stage determines class

CSE803 Fall 2015 7

Decision-Tree Classifier n  Uses subsets of

features in seq. n  Feature extraction

may be interleaved with classification decisions

n  Can be easy to design and efficient in execution

CSE803 Fall 2015 8

Decision Trees #holes

moment of inertia #strokes #strokes

best axis direction #strokes

- / 1 x w 0 A 8 B

0 1

2

< t ≥ t

2 4

0 1

0 60

90

0 1

CSE803 Fall 2015 9

Classification using nearest class mean

n  Compute the Euclidean distance between feature vector X and the mean of each class.

n  Choose closest class, if close enough (reject otherwise)

n  Low error rate at left

CSE803 Fall 2015 10

Nearest mean might yield poor results with complex structure

n  Class 2 has two modes

n  If modes are detected, two subclass mean vectors can be used

CSE803 Fall 2015 11

Another problem for nearest mean classification n  If unscaled, object X

is equidistant from each class mean

n  With scaling X closer to left distribution

n  Coordinate axes not natural for this data

n  1D discrimination possible with PCA

CSE803 Fall 2015 12

Scaling coordinates by std dev

CSE803 Fall 2015 13

Receiver Operating Curve ROC n  Plots correct

detection rate versus false alarm rate

n  Generally, false alarms go up with attempts to detect higher percentages of known objects

CSE803 Fall 2015 14

Confusion matrix shows empirical performance

CSE803 Fall 2015 15

Bayesian decision-making

CSE803 Fall 2015 16

Normal distribution n  0 mean and unit

std deviation n  Table enables us to

fit histograms and represent them simply

n  New observation of variable x can then be translated into probability

CSE803 Fall 2015 17

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

CSE803 Fall 2015 18

Parametric models