Radoslav Forg

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Institute of Informatics Slovak Academy of
Sciences Bratislava, Slovakia
Pulse Coupled Neural Network Models for Dimension
Reduction of Classification Space

• Radoslav Forgác, Igor Mokriš

WIKT 2006, 28.11. 29.11.2006, Bratislava
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Outline

• Goal of our research
• Why we use Pulse Coupled Neural Network (PCNN)?
• Introduction to PCNN
• Structure of PCNN neuron
• Mathematical model of PCNN neuron
• Feature generation by PCNN
• Purposes of PCNN modification
• Overview of PCNN modifications
• OM-PCNN versus ICM neuron

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Goal of our research
Dimension space of input image D
Input image
D
Dimension reduction of classification
space Minimization of the number of iteration
steps by O-PCNN
n n ltlt D
Dimension reduction of feature space d ltlt D
d d lt n
Dimension of classification space d
d
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Why we use PCNN?
PCNN Properties

• Invariant to geometrical transformations
• Fixed structure of neural network
• Learning free
• Minimal set of image etalons, i.e. only one
  etalon for every class

Properties of Standard Neural Networks

• Generated features are not invariant to
  geometrical transformations
• Problem to set the optimal structure of NN and
  its parameters
• High time consumption especially by gradient
  methods of learning
• Typical learning problems overlearning, looking
  for local minimum of error function

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Introduction to PCNN

• One-layer, two dimension NN
• Lateral connection of weights
• The PCNN structure is the same as the structure
  of the input object matrix S

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Structure of PCNN neuron

• Primary and Linking input
• Linking part
• Pulse generator

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Mathematical model of PCNN neuron
iteration step
Input part
W1, W2 weight matrix
image pixel intensity
aL , aF decay coefficients
VL, VF,, Vq coefficients of potentials
Linking part
Internal activity of neuron
linking coefficient
activated neuron
Pulse generator
Output
non-activated neuron
Threshold potential
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Feature generation by PCNN
input image
PCNN output in 3. iteration step
generated feature in 28. iteration step
PCNN output
vector of generated features
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Purposes of PCNN modification

• reduction the number of generated features
• and high recognition precision preservation
• reduction of PCNN parameters
• optimization of PCNN parameters
• determination of optimal number of iteration
  steps N
• selection of features with the highest
  information value
• increasing the invariance of generated features
  against rotation, dilation and translation of
  images

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Overview of PCNN modifications

• PCNN with modified primary input (M-PCNN)
• Fast linking PCNN
• Feedback PCNN
• PCNN with Linear Decay Threshold
• Intersecting Cortical Model - ICM
• Optimized M-PCNN (OM-PCNN)

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OM-PCNN vs. ICM neuron
OM-PCNN neuron
ICM neuron
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Thank youfor your attention