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?

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Feature Vector Representation

• Xx1, 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,

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Possible features for char rec.
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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
• Assigns 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
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best axis direction
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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

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

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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

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

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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
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Cherry with bruise

• Intensities at about 750 nanometers wavelength
• Some overlap caused by cherry surface turning away