1 Pattern Recognition Concepts How should objects be represented? Algorithms for recognition/matching * nearest neighbors * decision tree * decision functions.

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Pattern Recognition Concepts 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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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, ]

Moment is, loosely speaking, a quantitative measure of the shape of a set of points. Second moment", for example, is widely used and measures the "width" of a set of points in one dimension

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Possible features for char rec.

Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion.

Strokes are the individual pen movements that are required to draw a character.

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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: Assign object to a class based on features

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Classification paradigms

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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

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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

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Decision Trees

#holes

moment ofinertia

#strokes #strokes

best axisdirection

#strokes

- / 1 x w 0 A 8 B

01

2

< t t

2 4

0 1

060

90

0 1

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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

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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

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Scaling coordinates by std dev

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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

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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

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Confusion matrix shows empirical performance

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Bayesian decision-making

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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

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Parametric Models can be used