1. Linking non-binned spike train kernels to several existing spike train metrics
27 April ESANN 2006
Benjamin Schrauwen and Jan Van Campenhout
Electronics and Information Systems Department
Ghent University

2. Overview Spike train processing Non-binned spike train kernel
Linking to existing spike train metrics
Toy application
Conclusion

3. Spike train processing
Spike train = a set of events
Types of spike train processing:
Physiological data:
Classification/clustering used for better understanding of biological neural systems
Information coding and representation
Neural man-machine interface
‘Engineering’ spike trains
SNN more powerful than ANN [Maass]
But representing information and training networks is still difficult
stimulus
biological neural
system
detect stimulus
Need for state of the art classification techniques that can operate on spike trains

4. Non-binned spike train kernel
Linear discriminant solution can be written in inner-product form: h(x)=iiyi(xitx)+b
Can be easily made non-linear by mapping to feature space:
: X → F with x = (x1, x2, ... xn) → (1(x), 2(x), ... N(x))
h(x) = iiyi((xi)t(x))+b = iiyiK(xi,x)+b
Feature space  does not need to be explicit: Mercer kernels: K(xi,x) implicitly defines 
Many classification/clustering techniques can be written in inner-product form: can be easily ‘kernelised’: SVM (kernel maximum-margin linear classifier), kernel PCA, kernel k-means, ...

5. Non-binned spike train kernel
Classic techniques first convert set of events to vector by binning: based on rate coding hypothesis
Recently much physiological evidence of temporal coding: exact spike times do matter
So spike trains stay sets of events and not vectors
Need for (kernel) techniques that are able to cope with sets

6. Non-binned spike train kernel
Kernels for spike trains: based on sets, not vectors
Compare all to all set elements using an exponential measure:
x=(t1,t2,..,ti,..,tN), z=(t1,t2,..,tj,..,tM)
λ sets the kernel 'width'
Can easily be proved to be a Mercer kernel
Fast implementation possible for λ » 1

7. Linking to existing spike train metrics
Spike train algebra
L2-norm for Gaussian filtered spike trains
Spike train metric spaces

8. Linking to existing spike train metrics
Spikernel
Alignment score kernel

9. Toy application detect original template 1 2
Fact 1: Acquiring physiological data is expensive
So: Neurobiology departments don’t give away their datasets
Fact 2: Our department is not neurobiology
So: Our only option: use artificial data
detect original template 1 2
‘Toy’ application:
Jittered spike train template matching
Generate a small set of random spike trains and call them templates
Generate large set of training/test data by randomly jittering spikes of templates
Try to detect the original templates

10. Toy application SNN learning rule [Booij2005]
1 s templates, 10 Hz Poisson firing rate, 500 training, 200 testing
Soft margin SVM (C=10)
Laplacian and Gaussian very similar because
Biologically realistic value:
equals a membrane potential of 10 ms
SNN learning rule [Booij2005]
LSM based template classification [Maass2002]

11. Conclusions
Two kernels that operate on spike trains have been presented
These kernels are very related to several existing spike train metrics (which all embody the natural spike train variability)
Due to this, the presented kernels are also biologically relevant
The applicability of the kernels is demonstrated on an artificial spike train classification problem
Future work:
Test this technique on physiological data
Spike based post-processing for the Liquid State Machine
Make technique based on ISIs to solve preprocessing problems