# Unsupervised spike detection and sorting with wavelets and

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```					Unsupervised spike detection
and sorting
Rodrigo Quian Quiroga

This is an updated and expanded version of a talk given at the
32nd annual meeting of the Society for Neuroscience; 2002.
More details can be obtained from:
Unsupervised spike sorting with wavelets and superparamagnetic clustering.
R. Quian Quiroga, Z. Nadasdy and Y. Ben-Shaul
Neural Computation 16, 1661-1687; 2004.
Problem: detect and separate spikes
corresponding to different neurons
Goals:
• Algorithm for automatic detection and sorting of spikes.
• Suitable for on-line analysis.
• Improve both detection and sorting in comparison with
previous approaches.

Outline of the method:
I - Spike detection: amplitude threshold.
II - Feature extraction: wavelets.
III - Sorting: Superparamagnetic clustering.
Ex. 1
Simulated data
Ex. 2
Simulated data
I - Spike detection
• Set an automatic amplitude threshold

 x 
T  4  median         
 0.6745 

• Store 64 data points for each spike.
• Spikes are aligned after interpolation with
cubic splines.
Threshold estimation

The improved estimate decreases the dependence of the threshold on the
firing rate and spike amplitude.
Detection results (in brackets, results
including overlapping spikes).
Example #         Nr. of spikes    Misses       False positives
[noise level]
Ex. 1 [0.05]              3514 (785)      17 (193)          711
[0.10]               3522 (769)       2 (177)           57
[0.15]               3477 (784)     145 (215)           14
[0.20]               3474 (796)     714 (275)           10
Ex. 2 [0.05]              3410 (791)       0 (174)           0
[0.10]               3520 (826)       0 (191)           2
[0.15]               3411 (763)      10 (173)           1
[0.20]               3526 (811)     376 (256)           5
Ex. 3 [0.05]              3383 (767)       1 (210)           63
[0.10]               3448 (810)       0 (191)           10
[0.15]               3472 (812)       8 (203)           6
[0.20]               3414 (790)     184 (219)           2
Ex. 4 [0.05]              3364 (829)       0 (182)           1
[0.10]               3462 (720)       0 (152)           5
[0.15]               3440 (809)       3 (186)           4
[0.20]               3493 (777)     262 (228)           2
et function

II - Feature extraction: wavelets
 = |a|
(t)
1/2
 b 
 a
t
____
ab

69

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Wavelets idea

Clin. Neurophysiol. 110: 643-654 (1999)
Brain Research Protocols 8: 16-24 (2001)
Multiresolution decomposition
20                            20

0                             0
VEP
20                            20
1       0.5   0   0.5   1     1      0.5      0       0.5       1
50                            20

0                             0
D1
50                            20
1       0.5   0   0.5   1     1      0.5      0       0.5       1
50                            20

0                             0

D2
50                            20
1       0.5   0   0.5   1     1      0.5      0       0.5       1
50                            20

0                             0

D3   50                            20
1       0.5   0   0.5   1     1      0.5      0       0.5       1
50                            20

0                             0

D4   50
1       0.5   0   0.5   1
20
1      0.5      0       0.5       1
50                            20

0                             0

D5   50
1       0.5   0   0.5   1
20
1      0.5      0       0.5       1
50                            20

0                             0

50                            20
A5        1    0.5   0   0.5   1        1   0.5      0       0.5       1

Physica D 145: 278-292 (2000)
Clin. Neurophysiol. 114: 376-390 (2003)
• Wavelet Transform: is a time-frequency
decomposition of the signal with optimal
resolution both in time and frequency.

• Key idea: a few wavelet coefficients
will be able to separate the different
spike classes.
Wavelet coefficients
Ex 1

Ex 2
II a - Selection of wavelet coefficients:
KS test of Normality

Distribution of a given
Wavelet coefficient

No separation

Good separation
II a - Selection of wavelet coefficients:
KS test of Normality
Ex 2
Projections into the feature space
Misses                                                                     Ex 2

1/507 (0.2%)                                                     KS criterion

134/507 (26.4%)                                                   STD criterion

32/507 (6.2%)
First 3 PCs

For a more stricking example, see Figure 8 in Neural Computation 16, 1661-1687; 2004.
III – Superparamagnetic clustering

• Automatic clustering algorithm based on
ideas from statistical mechanics.
• It’s based on nearest-neighbor’s
interactions.
• Clusters don’t need to have a well-defined
center, low variance or a Gaussian
distribution.
Toy example
Toy example

Misses

102/2400
Outline of the method
Simulated data
Ex 1
Misses
3/521
Ex. 2
Simulated data
Misses
330/507
32/507
1/507
134/507
Simulation results
Results for all examples
Results are in terms of the number of miss-classifications. In brackets, number of clusters
detected when different from 3. Wavelets combined with SPC do the best job!
Example #       Nr. of                           SPC                                 K-   means

[noise level]   spikes    Wavelets   PCA         Spike shape   Feature set   Wavelets     PCA

Ex. 1 [0.05]    2729         1             1            0         863           0               0

[0.10]     2753         5          17              0         833           0               0

[0.15]     2693         5          19              0       2015 (2)        0               0

[0.20]     2678        12          130            24         614          17            17

[0.25]     2586        64          911            266      1265 (2)       69            68

[0.30]     2629        276        1913            838      1699 (1)       177          220
[0.35]     2702        483       1926 (2)    1424 (2)      1958 (1)       308          515

[0.40]     2645        741       1738 (1)    1738 (1)      1977 (1)       930          733

Ex. 2 [0.05]    2619         3             4            2         502           0               0

[0.10]     2694        10          704            59       1893 (1)        2            53

[0.15]     2648        45        1732 (1)    1054 (2)      2199 (1)       31           336

[0.20]     2715        306       1791 (1)    2253 (1)      2199 (1)       154          740

Ex. 3 [0.05]    2616         0             7            3         619           0               1
[0.10]     2638        41         1781            794      1930 (1)       850          184

[0.15]     2660        81        1748 (1)    2131 (1)      2150 (1)       859          848

[0.20]     2624        651       1711 (1)    2449 (1)      2185 (1)       874          1170

Ex. 4 [0.05]    2535         1         1310            24       1809 (1)       686          212

[0.10]     2742         8        946 (2)      970 (2)      1987 (1)       271          579

[0.15]     2631        443       1716 (2)    1709 (1)      2259 (1)       546          746

[0.20]     2716      1462 (2)    1732 (1)    1732 (1)      1867 (1)       872          1004

Average      2662        232        1092            873       1641          332          371
Human data (from Itzhak Fried’s lab at UCLA.
Human data (from Adam Mamelak’s lab at Huntington
Memorial Hospital)
Another channel…

These two spike shapes are quite overlapping and seem hard to separate!
Monkey data (from Bijan Pesaran at
Richard Andersen’s lab at Caltech.)
Locust data (from Ofer Mazor at Giles Laurent’
lab at Caltech.)

The improved threshold (based on the median) does a better job!
This clustering is done using only Channel 1, however, the other 3 channels will be used later
to check results. This may give some ‘ground truth’ feedback for real data!
Channel 3 shows that Cluster 1 was a multiunit…
Clustering using all channels
Conclusions:
• We presented an unsupervised and fast
method for spike detection and sorting.

• By using a small set of wavelet coefficients
we can focus on localized differences in the
spike shapes of the different units.

• SPC does not require a well-defined mean, low
variance, Normality or non-overlapping
clusters.

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