1. Clustering using Spiking Neural Networks

2. Biological Neuron: The Elementary Processing Unit of the Brain

3. Biological Neuron: A Generic Structure Dendrite Soma Synapse AxonAxon Terminal

4. Biological Neuron: Nerve Impulse Transiting Action Potential (Spike) Postsynaptic Potential Membrane Potential Action Potential (Spike) Spike-After Potential

5. Biological Neuron: Soma Firing Behavior Synchrony is the main factor of soma firing

6. Biological Neuron: Information Coding Neurons communicate via exact spike timing Firing rate alone does not carry all the relevant information

7. Neuroscience Models of Neuron: The Hodgkin-Huxley Model Alan Lloyd Hodgkin and Andrew Huxley received the Nobel Prize in Physiology and Medicine in 1963 The Hodgkin-Huxley model is too complicated model of neuron to be used in artificial neural networks

8. Neuroscience Models of Neuron: Leaky Integrate-And-Fire Model or Leaky Integrate-And-Fire model disregards the refractory capability of neuron

9. Neuroscience Models of Neuron: Spike-Response Model Spike-Response model captures the major elements of a biological neuron behavior

10. Biological Neuron – Computational Intelligence Approach: The First Generation The first artificial neuron was proposed by W. McCulloch & W. Pitts in 1943

11. Biological Neuron – Computational Intelligence Approach: The Second Generation Multilayered Perception is a universal approximator

12. Biological Neuron – Computational Intelligence Approach: Artificial Neurons – Too Artificial? spike occurrence spike absence From neurophysiology point of view, y is existence of an output spike Number of spikes Time frame From neurophysiology point of view, y is firing rate Spike timing is not considered at all!

13. Biological Neuron – Computational Intelligence Approach: The Third Generation Spiking neuron model was introduced by J. Hopfield in 1995 Spiking neural networks are - biologically more plausible, - computationally more powerful, - considerably faster than networks of the second generation

14. Spiking Neural Network: Overall Architecture RN is a receptive neuron MS is a multiple synapse SN is a spiking neuron Spiking neural network is a heterogeneous two-layered feed- forward network with lateral connections in the second hidden layer

15. Spiking Neural Network: Population Coding Pool of Receptive Neurons Input spike:

16. Spiking Neural Network: Multiple Synapse Delayed postsynaptic potential: Spike-response function: Total postsynaptic potential: Membrane potential:

17. Spiking Neural Network: Hebbian Learning – WTA and WTM Winner-Takes-All: Winner-Takes-More*: *Proposed for the first time on the 11 th International Conference on Science and Technology “System Analysis and Information Technologies” (Kyiv, Ukraine, 2009) by Ye. Bodyanskiy and A. Dolotov

18. Spiking Neural Network: Image Processing* Original ImageSOM at 50 epochSNN at 4 epoch *In Bionics of Intelligence: 2007, 2 (67), pp. 21-26 by Ye. Bodyanskiy and A. Dolotov

19. Spiking Neuron: The Laplace Transform Basis Thus, transformation of action potential to postsynaptic potential taken into synapse is nothing other than pulse-position – continuous-time transformation, and soma transformation is just reverse one, continuous-time – pulse-position transformation From control theory point of view, action potential (spike) is a signal in pulse- position form:

20. Spiking Neuron Synapse: A 2 nd order critically damped response unit * *Proposed for the first time on the 6 th International Conference “Information Research and Applications” (Varna, Bulgaria, 2009) by Ye. Bodyanskiy, A. Dolotov, and I. Pliss

21. Spiking Neuron: Technically Plausible Description* Incoming Spike:Time Delay: Spike-Response Function: Membrane Potential: Relay:Outgoing Spike: *Proposed for the first time on the 6 th International Conference “Information Research and Applications” (Varna, Bulgaria, 2009) by Ye. Bodyanskiy, A. Dolotov, and I. Pliss

22. Spiking Neuron: Analog-Digital Architecture* * Proposed for the first time in Image Processing / Ed. Yung-Sheng Chen: In- Teh, Vukovar, Croatia, pp. 357-380 by Ye. Bodyanskiy and A. Dolotov, Analog-digital spiking neurons corresponds to spike-response model entirely

23. Fuzzy Receptive Neurons*: *Proposed for the first time in Information Technologies and Computer Engineering: 2009, 2(15), pp. 51-55 by Ye. Bodyanskiy and A. Dolotov Pool of receptive neurons is a linguistic variable, and a receptive neuron within a pool is a linguistic term.

24. Fuzzy Spiking Neural Network: Fuzzy Probabilistic Clustering* *Proposed for the first time in Sci. Proc. of Riga Technical University: 2008, 36, P. 27-33 by Ye. Bodyanskiy and A. Dolotov There is no need to calculate cluster centers!

25. Fuzzy Spiking Neural Network: Fuzzy Possibilistic Clustering* *Proposed for the first time on the 15 th Zittau East-West Fuzzy Colloquium (Zittau, Germany, 2008) by Ye. Bodyanskiy, A. Dolotov, I. Pliss, and Ye. Viktorov

26. Fuzzy Spiking Neural Network: Image Processing* *In Proceeding of the 4 th International School-Seminar “Theory of Decision Making“ (Uzhhorod, Ukraine, 2008) by Ye. Bodyanskiy, A. Dolotov, and I. Pliss Original image Training set FSNN at 4 th epoch SOM at 40 th epoch

27. Fuzzy Spiking Neural Network: Image Processing* *In Proceeding of the 11 th International Biennial Baltic Electronics Conference "BEC 2008“ (Tallinn/Laulasmaa, Estonia, 2008) by Ye. Bodyanskiy and A. Dolotov Original image Training set FSNN at 3 rd epoch FCM at 29 th epoch

28. Fuzzy Spiking Neural Network: Image Processing* *In Image Processing / Ed. Yung-Sheng Chen: In-Teh, Vukovar, Croatia, pp. 357-380 by Ye. Bodyanskiy and A. Dolotov Original image Training set FSNN at 1 st epoch FSNN at 3 rd epoch FCM at 3 rd epoch FCM at 30 th epoch