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Neural Networks 16 (2003) 601–607
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2003 Special issue
Developments in understanding neuronal spike trains and functional
specializations in brain regions
Roberto A. Santiagoa, James McNamesb, Kim Burchielc, George G. Lendarisa,*
b
a
NW Computational Intelligence Laboratory, System Science, Portland State University,1 USA
Biomedical Signal Processing Laboratory, Electrical and Computer Engineering, Portland State University,2 USA
c
Department of Neurological Surgery, Oregon Health Sciences University,3 USA
Abstract
Understanding information processing at the neuronal level would provide valuable insights to computational intelligence research and
computational neuroscience. In particular, understanding constraints on neuronal spike trains would provide indication about the type of
syntactic rules used by neurons when processing information. A recent discovery, reported here, was made through analyzing microelectrode
recordings (MER) made during surgical procedure in humans. Analysis of MERs of extracellular neuronal activity has gained increasing
interest due to potential improvements to surgical techniques involving ablation or placement of deep brain stimulators, done in the treatment
of advanced Parkinson’s disease. Important to these procedures is the identification of different brain structures such as the globus pallidus
internus from the spike train being recorded from the intracranial probe tip during surgery. Spike train data gathered during surgical
procedure from multiple patients were processed using a novel feature extraction method reported here. Distinct structures within the spike
trains were identified and used to build an effective brain region classifier. The extracted features upon analysis provide some insight into the
‘syntactic’ constraint on spike trains.
q 2003 Elsevier Science Ltd. All rights reserved.
Keywords: Microelectrode recordings; Globus pallidus internus; Spike trains
1. Introduction
Analysis of microelectrode recordings (MERs) of
extracellular neuronal activity has importance from both a
neurosurgical and neuroscience perspective. For neurosurgery, MER analysis offers potential benefits to surgical
techniques involving ablation or placement of deep brain
stimulators as in the treatment of Parkinson’s disease. From
the neuroscience perspective, in vivo recordings of neurons
provide an opportunity to analyze the patterns of spike trains
and the interactions of neurons in near normal operational
conditions. Fundamental to either of these pursuits understands the connection between the spike trains recorded in
MERs and the neurons from which they are being recorded.
Unlike in vitro experimentation, the cell type producing the
recorded spike train is much harder to determine. From the
neurosurgical perspective it would be of great advantage to
* Corresponding author.
E-mail address: [email protected] (G.G. Lendaris).
1
www.nwcil.pdx.edu
2
www.bsp.pdx.edu
3
www.ohsu.edu
have real time algorithms that would reliably translate
MERs into cell source classifications, which in turn could be
used to provide accurate estimation and confirmation of
intracranial probe placement. The work reported here was
done for this end purpose but with the knowledge that any
success on this front would also be important for
computational neuroscience and for computational intelligence research.
From the neuroscience perspective, the ability to identify
cell types from recorded spike trains in vivo would provide
some data about the unique information processing
happening in a given brain region. Moreover, it would
also provided some guidance for modifying current
neuronal models such that they capture the information
processing specializations found within specific brain
regions. Much of the literature studying biological spiking
behavior simultaneously treats dendritic processing as
highly complex and treats spiking behavior as characterized
by a distribution of spike intervals (Koch & Segev, 1989).
Many of the spiking neuron models from computational
intelligence research use many variations of integrate and
fire models for connecting the dendritic processing to
0893-6080/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved.
doi:10.1016/S0893-6080(03)00123-0
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R.A. Santiago et al. / Neural Networks 16 (2003) 601–607
spiking behavior (Maass & Bishop, 1999). Other alternatives exist to integrate and fire, which are inspired both from
the biology as well as mathematics (Gerstner & Kistler,
2002). Missing between these two approaches is the ability
to ground the computational models onto the biological
models such that the characteristics of information processing could be understood. More specifically, in order to get
agreement between the computational intelligence models
and computational neuroscience models it would be
advantageous to estimate the type of distributions that not
only correspond to biologically observed spike trains but
that also provide some indication of the ‘syntactic’
constraint placed on the creation of spike trains from the
computational perspective. Such distributions would take
on the form of joint or conditional probability tables. In the
research reported here this type of analysis is done to spike
trains and is the source of the information for accurate
identification of brain region from the spike train.
In next few sections, the details of the spike train feature
extraction algorithm are explained. This is followed a by a
review of results on unseen data. In Section 5 the discussion
returns to the connections between the feature of spike trains
and functional specialization of brain regions.
2. Background
The research reported here was performed in a
neurosurgical context. Currently, Oregon Health Science
University performs deep brain stimulation procedures. This
procedure involves the use of a probe, which is slowly
inserted into the patient’s brain in a stepwise manner. At
each step a reading is taken from the probe, which is
sensitive to the spiking of neurons within the local vicinity
of the probe tip. The signal from the probe is then sampled
and translated into an audio signal as well as visual
presentation on an oscilloscope, which the surgeon uses to
confirm the brain structure in which the probe tip is located.
The insertion path is mapped out presurgically using
magnetic resonance imaging. This process is very precise.
As such, the signal from the probe is used only for
confirmatory information. Still, at time of surgery, the only
information available to the surgeon is the intracranial
position of the probe tip and the signal recorded by the
probe. As such, automated methods to translate this signal
into useful information about the brain structures surrounding the probe tip would add another level of consistency and
accuracy to deep brain stimulation procedures.
Because of the speed and affordability of digital
processing equipment, it now seems feasible to support
and improve this surgical procedure. In order to do this, the
probe data must first be digitally sampled and filtered for
noise. Because this resultant digital signal is of several
neurons firing simultaneously, it must undergo processing to
isolate spike trains from individual neurons. Surgical
recordings were processed postsurgically through a source
separation algorithm to be detailed in McNames (2003).
This algorithm not only separated the signals from each
neuron but also identified spike occurrences. Thus the
resulting individual spike train signal was an array of clock
times with millisecond or better resolution indicating when
a spike was detected. For this research there were a total of
140 spike trains each containing from 2 to 5 s worth of spike
train recording. The set of data used was gathered during
surgical procedure from 26 patients. These data came in two
groupings nominally referred to as the Dirty Data Set (DDS)
and the Starr Data Set (SDS). The DDS contained 93 spike
trains from several patients which were randomly broken
into two subsets, the training DDS (47 spike trains) and the
test DDS (46 spike trains). The test DDS was isolated and
used to test the effectiveness of the resulting algorithm
developed from the training DDS and the Starr DDS. The
reason for the label ‘Dirty’ is due to the unfortunate fact that
the data from the DDS was labeled postsurgically; that is,
the expert opinion about the brain structure source for each
spike train was captured outside the context of the actual
surgery. This method for labeling spike train data has the
disadvantage of not having the depth and spatial location of
the probe to assist with identification. The SDS was
gathered under ideal conditions and represents ‘perfect’
examples of spike trains from individual neurons in the
brain regions of interest. There were four major brain
structures of interest: Globus Palidus Externus (GPE),
Globus Palidus Internus (GPI), the Border (BRD) regions
between GPE and GPI, and finally Tremor cells (TRM).
This last area, TRM, is not a distinct brain structure but
instead describes regions inside the GPI, where the cells fire
in a tremor like manner and are linked to the physical
tremoring common to Parkinson’s disease. Both data sets
contained a large amount of spike trains from neurons in
GPE. Exact numbers are reported in Section 6.
3. Approach
Spike train analysis has been done for many reasons
ranging from understanding the biology of single neurons to
the type of medical application motivating this research.
Spike train research, regardless of motivation, has the
underlying presupposition that the characteristic of spike
trains tell us something about the neuron, its operation
and/or the information it processes. Most often, this type of
research is done in settings, where both input and output of a
neuron can be isolated. From this vantage point it is easy to
gain a better understanding of the type of information
processing being done by a single neuron. Understanding
neuron processing involves understanding the mechanisms
by which incoming signal is integrated and the process by
which a new signal is created and transmitted to other
neurons. Historically, these sub-processes have been understood by means of a rate-coding model. That is, a model,
where neuronal processing is only concerned with the rate
R.A. Santiago et al. / Neural Networks 16 (2003) 601–607
of spike arrival defined over some finite window. Unfortunately, simple rate coding models are not sufficient to
explain fast response characteristics of many neuronal
circuits, particularly those involved with visual processing
(Koch, 1999). Put simply, there is significant presence of
neuronal processing that involves dependency only on
single spikes or on the time interval between spikes. This
latter point is critical since it indicates that the time between
spikes, the inter-spike interval (ISI), may contain useful
information. This insight has fueled research into understanding methods by which neurons may encode and decode
information in these ISIs (Koch, 1999; McNames, 2003).
The models from this research are commonly referred to as
temporal coding or correlation coding. More complex
models have also been developed that describe information
encoded across the spikes of more than one neuron. These
models are commonly referred to as population coding and
pulse coding which each have correlated and non-correlated
forms (Koch, 1999).
While these latter coding models are not of much use for
single spike train analysis, the entire body of coding
research provides information about where to look for
information in the spike train of individual neurons
(hereafter referred to as single spike trains). The use of
coding research in this context is aimed at understanding the
timeframe in which the physical properties of a neuron
could contribute discernable information in an individual
spike train. At the lower end, research supporting rate
coding models for neuronal information processing have an
upper end of 5– 10 ms as the effective length for information
encoding/decoding. By way of explanation, since rate coded
models rely essentially on counting the number of spikes
that arrive during a time period, the critical time factor is the
rate at which a spike signal decays on the neuronal
membrane of the receiving neuron. As it turns out, the
upper bound for the decay in this signal is around 10 ms
(Koch, 1999). So assuming that rate coding is at least a
partially correct model for neuronal processing, any
contribution that an individual neuron makes to this process
would be most discernable above this 10 ms threshold.
Below this threshold, the spike train behavior is most
attributable to the input signal being received from the
dendrites. Finding an upper bound is very difficult in light of
work in temporal and correlation coding. Precise firing
patterns over 200 ms in length have been observed in the
visual processing systems of the macaque monkey (Koch,
1999). Moreover, in laboratory setting, neurons can be
stimulated to produce firing patterns that are precise and
regular for almost indefinite periods. The period of these
patterns are as short as 20 ms and as long as 300 ms. The
structures involved in these spiking patterns involve both
single spikes and sets of spikes separated by very small time
intervals, known as bursts. Analysis of single spike and
bursting patterns in vivo seem to indicate that 200 ms is the
upper bound for discerning any real correlated pattern to
spike times (Koch, 1999). In many contexts, though,
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the nature of the spike train seems random with ISIs
exhibiting a Poisson distribution. Some research indicates
strongly that the stochastic nature of neuronal processing is
far from stationary and may be highly dependent on input
stimulus. Again, with the lack of neuronal input data,
200 ms is the apparent upper bound for pattern recognition
in just the output spike train. So for the research reported
here a window of 10– 200 ms was used for analyzing spike
trains.
Returning to the surgical context, an important clue was
taken from the existing method of train source identification, listening. In terms of description, the sound
produced by the MER from the surgical probe is roughly
like static with much popping and whirring. Individual spike
trains when converted to sound also have a similar
characteristic. Discernable are regular patterns of popping
intensity; roughly speaking, one can hear bursts and changes
in spike frequency. This last comment seems to support
research into spike bursting which seeks to isolate and
characterize burst events. Given these clues it was
hypothesized that within the 10– 200 ms window, there
should exist discernable patterns of spiking that would
happen repeatedly and ultimately would be the source of the
characteristics discernable when listening to MER data. As
a note, the search for a novel approach to feature extraction
was motivated by the lack of strong results from research
involving single statistics, power spectrums, smoothing,
averaging and histogram approaches (McNames, 2003).
These approaches have similar insights and motivations as
the research presented here. Moreover, none of these
approaches have been able to yield sufficient feature
information from individual spike trains to provide a
reliable automated spike source identification algorithm.
4. Feature extraction method
The majority of the effort for the present research project
was spent analyzing spike trains using a 10– 200 ms moving
window. This analysis focused on developing a visualization technique for behavior in the moving window. In
essence, the research sought features that made visually
distinguishing different neuron types very easy. After many
attempts only one feature extraction method worked very
well and is described here. The method involved the use of
two moving windows across a digital spike train (DST). The
DST breaks up the duration of a spike train into fixed width
intervals with each interval represented by a one or zero.
One indicates a spike occurred during that time interval
while a zero indicates no spike occurred during that interval.
Two adjacent moving windows counted the number of ones
in each window, producing a pair of integers. These pairs of
integers were used to create a two dimensional histogram.
This histogram was used to produce a surface plot, which
revealed visually distinguishable features to each of the
different types of neurons of interest. Figs. 1 – 4 are
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R.A. Santiago et al. / Neural Networks 16 (2003) 601–607
Fig. 1. Example of GPI 2-D histogram.
Fig. 3. Example of BRD 2-D histogram.
representative examples of the type of histograms produced
by this method. These particular histograms were produced
using a sampling rate of 100 Hz and with window sizes of 9
bits. These were not the histograms that were ultimately
used for the classification algorithm but because of
resolution limitations these histograms demonstrate the
types of features that were found and indicated that this
method would be useful in the context of classification. It is
important to note that while there is much symmetry in each
graph, the localization of histogram activity for each type is
unique. Moreover, these differing localizations and presence
of asymmetries is what inspired looking at these histograms
as estimates of joint and conditional distribution and the
subsequently as possible indication of syntactic constraints
which will be discussed later.
Before moving on, a more detailed explanation of the
algorithm is now provided
Fig. 2. Example of GPE 2-D histogram.
1. The spike train is converted to a binary digital signal.
This involves setting up an array of zeros, where each
element represents a time interval. End to end these
elements represent the duration length of a given spike
train. So for example, each element of the array could
represent 1 ms (i.e. the temporal spike train is sampled at
1000 Hz). If a spike train of 5.7 s were being analyzed,
this would indicate that the array would have to be 5700
units in length. The array is initialized with all zeros.
Continuing with the example, the first spike might occur
at 0.1189 s. Translated into milliseconds this time would
mean that the first spike of the spike train came after a
118.9 ms pause. Rounding up this number to 119, the
119th element of the array is changed to a one.
2. The binary digital signal is then sampled with two
adjacent moving windows of finite length. So for
example, a window length of 8 would gather all pairs
of 8 bit binary words that occur in the DST.
Fig. 4. Example of TRM 2-D histogram.
R.A. Santiago et al. / Neural Networks 16 (2003) 601–607
3. The number of ones in each binary word is counted
converting each pair of binary 8 bit words into a pair of
decimal integers. So for example if a pair of eight digit
words were 01110101 and 10011001, this would be
converted to the decimal integer pair of 5 and 4.
4. These integer pairs are then binned together to create a
two dimensional histogram.
5. The 0,0 entry in the histogram is then removed. This was
done because the most common binary word pairs were
all zeros, which yielded no information about the spike
train. Additionally the histogram was normalized by
dividing by the number of entries and doing a natural
logarithmic conversion. This last step was used to avoid
problems with histograms generated from different spike
trains of significantly different durations. In some cases
spike trains were as short as 2 s in duration.
What bears mentioning is the nature of the features seen
in the visualization of the histogram. In early experimentation, one dimensional histograms were created using a
single moving window. These histograms did not provide
enough information for visual identification. The one
dimensional histogram is equivalent to looking at the
distribution of spike rates. We recall that one of the models
of neuron to neuron communication is a rate model that only
cares about the number of spikes that occur during a finite
time window. The one dimensional histogram essentially
analyzes the spike train from that perspective. The two
dimensional histogram analyzes the change in the rate of
spike arrivals. Although not fully a temporal coding model it
does reveal common changes in firing rate.
So for example, a histogram created from a GPE spike
train sampled at 1000 Hz with window size of 20 bits may
have large numbers associated with the 4,18 and 10,10 bins.
This would indicate that if four spikes occur in a 20 ms
period it is very likely that it will be followed by 18 spikes in
the next 20 ms period. Likewise if 10 spikes occur in a
20 ms period it is likely to be followed by the same rate of
spiking. Again, in essence the two dimensional histogram
analyzes the changes in spike rate. What it reveals is that
changes in spike rate can uniquely characterize the spike
trains of different neurons. More analysis is needed to
understand all the information revealed in these histograms.
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classifiers do not provide any easy methods for predicting
performance on unseen test data.
Unlike linear methods that provide characterizations
associated with bias and variance, neural networks do not
have any analog to these informative statistics. Neural
networks were applied to this problem and were found to
generalize very poorly. Instead, a support vector machine
was employed. Support vector machines have gained much
popular acclaim. In essence, they provide a method for
calculating optimal hyperplanes for separating points in
feature space. In the context of this project, the feature space
is the set of values from the histogram. Returning to the
example of the histogram created using 1000 Hz sampling
rate and 20 bit window, each histogram has 21 £ 21 ¼ 441
values. These 441 values form a single point in the feature
space into which the support vector machine will place
hyperplanes to draw boundaries between the points
representing GPI, GPE, BRD and TRM cells. More detailed
discussion on the operation of support vector machines for
classification can be found in Haykin (1999). The
application of support vector machines was very successful
as will be discussed in Section 6. A set of support vector
MATLAB libraries from Ohio State University were used
(Ma, Zhao & Ahalt, 2002).
6. Results
Because the test DDS was held separate, early results
were generated using a leave one out cross validation
method. The support vector classifier was computationally
very efficient making this form of testing possible. The first
cross validation was performed with the SDS. The spike
trains from the SDS were sampled at 400 Hz to create spike
trains and a 20 bit window size was used. Table 1 shows a
confusion matrix summarizing the results from the cross
validation. The results are perfect. As stated before, the SDS
was collected under ideal conditions and represents a
‘perfect’ set of spike train recordings. As such this result
indicates that enough features are extracted in the rate
change histogram to perform accurate classification in ideal
circumstances.
Next, the same cross validation was performed with the
training DDS. This data was not gathered under ideal
5. Application of support vector machines
The algorithm just described performs well at the task of
feature extraction. In order to make this feature extraction
applicable to the surgical context it was necessary to choose
some form of classifier. Many linear and non-linear
classifiers exist. Among the most popular non-linear
classifiers that exist are neural networks. While neural
networks are effective in many contexts, they often fall short
in being able to generalize, or generalize in predictable
manners. What is meant by this is that neural network
Table 1
Results of leave one out cross validation testing with the dirty data set
Actual
Predicted
GPE
GPE
GPI
BRD
TRM
31
1
2
2
GPI
BRD
TRM
2
2
1
5
1
606
R.A. Santiago et al. / Neural Networks 16 (2003) 601–607
Table 2
Results from test of classification algorithm on unseen data
Actual
GPE
GPI
BRD
TRM
Predicted
GPE
GPI
30
2
6
BRD
TRM
2
3
3
conditions and it is known that at least one of the spike trains
is labeled incorrectly. Still, the DDS has some characteristics of data that would be encountered in the surgical
context. As such it provides a good bench mark with respect
to robustness of this classification method with respect to
noise. Table 1 is a confusion matrix summarizing the results
of this cross validation.
Finally, the training DDS was used to create a support
vector classifier that was applied to the testing DDS. Again,
this data set was held independently and was not accessible
during the development of the feature extraction algorithm
and the subsequent development of the support vector
classifier. The confusion matrix describing the classification
results with the testing DDS is provided in Table 2. It is
important to emphasize that the results in Table 2 are the
result of a single pass through the unseen testing data. It is
not a leave one out cross validation test as is shown in
Tables 1 and 3.
After cross validation, it seemed like the algorithm was
performing in a consistent and accurate manner. As a final
test, a set of completely unseen data was presented to the
classifier. The classifier was ‘trained’ using data from both
the Starr and the Dirty sets. The unseen data set was held by
a separate person and was never seen by the researchers
prior to the final testing. The classifier was only allowed one
single attempt to classify this unseen data. The results of this
final test are summarized in Table 2.
It seems apparent that the rate change histogram
provides efficient and effective feature extraction for
spike trains. The ability to visually identify the different
types of neurons was a strong indicator that it would be
effective in an automated classification context. The
application of support vector machines seems to support
Table 3
Results of leave one out cross validation testing with the starr data set
Actual
Predicted
GPE
GPE
GPI
BRD
TRM
GPI
BRD
TRM
13
9
7
8
this conclusion. The cross validation results from the
training DDS and the final results from the testing DDS
strongly indicate the feature extraction is fairly resistant to
noise but that additional work is needed to cope with
irregularities in recorded data, the source of many of the
misclassifications. These irregularities are caused by many
conditions that are encountered during the surgical
procedure. Overall, though, the preliminary results are
strong enough to warrant much additional work in further
developing this feature extraction technique.
7. Discussion
Returning to the neuroscience perspective, it is important
to seek an explanation as to why this type of classification
should even be possible. While it seems that the underlying
cellular mechanisms for actions potentials (spikes) are well
understood, what is not understood is their role in the
processing of information beyond the most general
description as a method to transmit information from one
cell to another. By way of analogy, understanding the
significance of neuron spiking is like trying to understand
the significance of transistor switching in digital microprocessors without having an understanding of digital
computing theory. More to the point, what these regular
patterns indicate about the cells of interest is very
ambiguous.
Along these lines there seem to be two general
hypothesis that could be explored. First, it might be possible
that neurons by their physiology have a specific spiking
pattern, which is activated when the membrane potential
reaches a threshold. This is slightly different that the
standard integrate and fire models of neurons since it
includes the ability of neurons to not just simply fire but to
fire specific temporal patterns that show conditional
statistical regularity. This would provide a foundation for
why the histogram visualization shown before should have
such consistency.
This model fails, though, to take into account any
significant sensitivity to incoming signal. If the recorded
spike trains represent primarily the effect of incoming
signals, then it implies that regions of the brain have the
ability to consistently produce spiking patterns, which are
common among all the cells within a region. If this model is
true then it would also suggest that the recorded spike trains
represent functional specialization within a region. But this
model, in the extreme, would suggest functional specialization independent of cell physiology which seems unlikely
given what is known about the cell types studied here.
Not enough data exists yet to firmly conclude that either
of these models (or some other form in between) is truly
correct. This in turn points to deeper research issues
surrounding both the nature of what MERs represent and
how ablation and stimulation is actually affecting circuits in
the brain as understood from a systemic neurophysiological
R.A. Santiago et al. / Neural Networks 16 (2003) 601–607
level and not just a behavioral model perspective. The fact
that such regular patterns can be discerned in these recorded
spike trains indicates that it might be possible to develop
neuronal population models that more closely described and
explain the functioning of these brain regions.
Further research will look to extend this algorithm to cell
types found in the substantia nigra which are much more
challenging to recognize. Related research will seek to
move these and other source identification techniques into
the surgical context to asses their impact on the effectiveness of ablation and deep brain stimulation procedures. Still,
further research will also seek to ground these methods in
the physiology of neuron populations in search of a clearer
understanding of these spike train patterns.
Finally, after studying the types of histograms as shown
in Figs. 1 – 4 it seemed reasonable to conclude that if these
histograms are indeed unique to brain region then they
indeed did characterize the types of spiking patterns
inherent to the information processing occurring in that
brain region. In turn, if this were true then these same
histograms could be looked at as conditional distributions.
Assuming that spike trains are essentially binary digital
communication between neurons then the proper syntactic
input and output of the neurons within a given region is
characterized by this estimated distribution. Returning to
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the idea of studying digital processors without understanding digital computing theory, the uniqueness of the
spike train syntax provides an indication of the type of
instruction sets that are encoded into the operation of the
neuron. This is a loose hypothesis but the current results
seem to significantly support the feasibility of this type of
analysis which is one of the foci of the continuing research.
References
Gerstner, W., & Kistler, W. (2002). Spiking neuron models. Cambridge,
UK: Cambridge University Press.
Haykin, S. S. (1999). Neural networks: A comprehensive foundation. Upper
Saddle River, NJ: Prentice Hall.
Koch, C. (1999). Biophysics of computation: Information processing in
single neurons. New York, NY: Oxford University Press.
Koch, C., & Segev, I. (1989). Methods in neuronal modeling: From
synapses to networks. Cambridge, MA: MIT Press.
Ma, J., Zhao, Y., Ahalt, S (2002). OSU SVM Classifier Matlab Toolbox
(ver. 3.00). http://eewww.eng.ohiostate.-edu/maj/osu_svm/
Maass, W., & Bishop, M. (1999). Pulsed neural networks. Cambridge, MA:
MIT Press.
McNames, J. (2003). Microelectrode signal analysis techniques for
improved localization. Microelectrode recordings in movement disorder surgery. New York, NY: Thieme Medical Publishers.