1. Radoslav Forgáč, Igor Mokriš Pulse Coupled Neural Network Models for Dimension Reduction of Classification Space Institute of Informatics Slovak Academy of Sciences Bratislava, Slovakia WIKT 2006, 28.11. – 29.11.2006, Bratislava

2. 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

3. Goal of our research Goal of our research Dimension reduction of feature space d << D Class 1Class 2Class X Feature generationClassification Input image Feature selection Dimension space of input image D n; n << D d; d < n D d Dimension reduction of classification space Minimization the number of iteration steps by O-PCNN Minimization of the number of iteration steps by O-PCNN Dimension of classification space d

4. Why we use PCNN?  Invariant to geometrical transformations  Fixed structure of neural network  Learning – free  Minimal set of image etalons, i.e. only one etalon for every class PCNN Properties 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

5.  One-layer, two dimension NN  Lateral connection of weights  The PCNN structure is the same as the structure of the input object matrix S Introduction to PCNN

6. Structure of PCNN neuron  Primary and Linking input  Linking part  Pulse generator

7. Feeding input: Linking input Input part Internal activity of neuron: Linking part Output: Threshold potential: Pulse generator image pixel intensity iteration step W1, W2: weight matrix V L, V F,, V  :coefficients of potentials  L,  F : decay coefficients linking coefficient activated neuron non-activated neuron Mathematical model of PCNN neuron

8. Feature generation by PCNN PCNN output input image PCNN output in 3. iteration step vector of generated features generated feature in 28. iteration step

9. 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

10. 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)

11. OM-PCNN vs. ICM neuron ICM neuron OM-PCNN neuron

12. Thank you for your attention