EFFECTS OF SPIKE SORTING ERROR ON INFORMATION CONTENT
IN MULTI-NEURON RECORDINGS
Deborah S. Won, David Y. Chong, and Patrick D. Wolf
Department of Biomedical Engineering, Duke University, Durham, NC 27708
Methods
Problem
In multi-neuron recording applications, more
than one neuron is detected on an electrode.
Results
s
r
IAF
Spike sorters make errors.
The effects of this error on the ability to decode
the neural responses have not been studied.
•Error tolerance:
IAF
1
s
r1
•to maintain 80% information - < 2%
r-
+
e/2 FN
r2
•to maintain 50% information - < 13-14%
r¢
•Omission and insertion of an erroneous spike
are equally detrimental to information content
spike sorter should aim to optimize for
both sensitivity and selectivity.
r+
+
1-e/2 FN
FP
γ
FN
•If spike sorter can not meet error tolerance,
alternative schemes for computational
analysis on neural population responses,
should be considered – e.g., using multi-unit
signals of 2-3 neurons, which can be
accurately detected from microelectrodes.
Figure 2)
 IAF – integrate-and-fire neuron with variable threshold
electrode
 s – input stimulus
 r - neural unit’s spike train.
unit 2
unit 1
Figure 1) The current prototype for multi-neuron acquisition and
processing systems involves sorting the multi-unit signal on each
channel into single-unit signals before most of the data is
discarded and only the onset times of action potentials from each
unit are retained. The goal is to retain as much of the relevant
information as possible in the original spike trains. The
information may be about the stimulus that elicited the response
or the behavior that was to be elicited by the neural activity..
Ideally, the spike output from the neurons are reproduced at the
output of the acquisition system, and the information transmitted
to the computational decoders remains unchanged. However,
spike sorting does not exactly replicate the spike trains due to the
error inevitably associated with spike sorting.
Goals
ε - spike sorting percent error. False positives (FP) and false negatives (FN)
 ( r - r )
were added at a percent error rate of e  100
r
2 types of error
• Misdetection: random spikes added and deleted (top).
% error, ε
•Misclassification: spikes generated by local neurons but misclassified as part
of a neighboring neuron’s spike train (bottom).
s, r'
WienerHopf
Filter
shat
Shannon
information
% error, ε
Figure 5) Effect of false positive (x’s) and false negative (dots) misdetection error
on information rate (top)coding fraction (middle), and average firing rate (bottom).
.
Figure 7) Comparing effect of error on
information rate (bottom) when average firing rate
(top) is kept constant and when it is changing
linearly.
I(s, shat)
1
  log 21 + SNR( f ) df
2
Summary of results
s
•Information rate İ as a function of percent spike
sorting error ε decreases in an exponential
fashion, both with misdetection error and
misclassification error.
Figure 3) The optimal linear estimate of the stimulus was computed by applying the
Wiener-Hopf filter to ρ(t) [4]. From the error between s and ŝ, the signal-to-noise
ratio (SNR) was computed and İ(s, ρ) was estimated by İ(s, ŝ). Coding fraction was
also calculated from the mean square error and standard deviation of the stimulus,
 sˆ - s 
2
The aim of this investigation is to quantify the
effects of incorrectly discriminated spikes on
encoded information so as to set tolerable limits
on sorting error and glean insight into the
necessity of sorting. To address how sorting error
affects the ability to decode the multi-neuron
response, spike trains were simulated with
random detection error and with classification
error and changes in the Shannon information
content were observed.
according to   1 -
s
.
•Above 2% error, average decay constant over
ten trials is roughly 8.6 for misclassification and
11.3 for misdetection. İ decays even more
quickly below 2% errors.
γ
% error, ε
Figure 6) Misclassification error. Exponential curve (solid) fit to data to model
İ(s,ŝ) (top) and coding fraction (bottom) as a function of total percent spike sorting
error. Dashed lines demarcate where error causes information rate to fall by half its
information rate (top) and where coding fraction crosses 0 (bottom).
Methods
To compute the information
transmission rate İ(s, ρ) and coding fraction γ,
we utilize a signal-reconstruction paradigm
commonly used in information-theoretic
analysis [1]-[3]. Average values were found for
results from 10 unique input signals.
multi-neuron
•Accuracy of spike sorter is crucial to
retaining information in single-unit responses.
e
IAF
2
spike
sorter
r¢
+
Necessity of spike sorting has been taken for
granted without studying its effects.
Implications
for
recording applications
Figure 4) Stimulus signal s(t) (top solid) is input into IAF neuron which
outputs a spike train. The spike train is contaminated by random sorting
error. Output with no error is shown in bottom panel. The spike train is
then input into an optimal reconstruction filter to yield stimulus estimate
ŝ(t) (top dashed).
Information rate is fit well by exponential curve for percent errors > roughly 2%
(R2 > .9). For smaller percent errors, the decay rate is steeper. At percent errors
greater than 17% misdetection and 19% misclassification, the coding fraction γ
drops below 0. Since γ provides a measure of how much of the stimulus variance
is accounted for by the estimate variance, the error at which γ becomes less than 0
is the point beyond which spikes act as completely random occurrences,
uncorrelated with the stimulus input. Information per spike also changed similarly
to information rate starting at 0.8-0.9 bits/spike and decreasing to an asymptotic
value of 0.1-0.2 bits/spike. Figures display results for one trial.
•İ is expected to decrease to half its maximum
value at only 10.5% detection error and 13.3%
classification error.
•False positives and false negatives have
indistinguishable effects.
•Average firing rate does not affect response to
error. There is no significant difference between
İ(ε) with constant firing rate and with linearly
changing firing rate.
•Coding fraction γ reaches 0 at 17% misdetection
and 19% misclassification error; i.e., by 19%
error, a computational decoder on a single-unit
response can do no better than random guessing.
Conclusions
•Mutual information İ(s, ρ) between a
stimulus signal and the resulting single-unit
response was found to decrease exponentially
with random misdetections and classification
error.
•This dependence on error is regardless of
being false negative or false positive.
•On average, 10.5% detection error or 13.3%
classification error could be tolerated before
the information content dropped to half the
information transmitted by the original spike
train. Since spike sorters can reasonably be
expected to perform with 10% error [5],[6], it
is not unreasonable to expect spike sorting to
degrade a neuron’s response to half its
original information content.
References
[1] Y. Tock and G. Inbar, Modern Techniques in
Neuroscience Research, Springer-Verlag, 1999.
[2] F. Rieke, D.A. Bodnar, and W. Bialek, Proceedings of
the Royal Society London B (1995) 262: 259-265.
[3] R. Wessel, C. Koch, and F. Gabbiani, Journal of
Neurophysiology (1996) 75: 2280-2293.
[4] S. Seung, http://hebb.mit.edu/courses/9.29/lectures/
lecture02.html.
[5] K. D. Harris, D. A. Henze, J. Csicsvari, H. Hirase, and
G. Buzsaki, Journal of Neurophysiology (2000) 84: 401414.
[6] B. Wheeler and W. Heetderks, IEEE Trans on
Biomedical Engineering (1982).
Acknowledgments
Funding provided by National Science Foundation and
DARPA contract #N66-001-02-C-8022.