Transcript Introduction to Chronux

Chronux Tutorial: Part I
Hemant Bokil
Cold Spring Harbor Laboratory
People
Hemant Bokil
Catherine Loader
Partha Mitra
Peter Andrews
Contributors
Dan Hill
Chris Fall Samar Mehta
Hirak Parikh Andrew Sornborger
Outline
 Introduction to Chronux
► Aim
► Website
● Download
● Documentation
► Key functions
 Analysis of LIP data - Example 2 of the previous talk :
rates, spike and LFP spectra and coherences,
coherences between cells
 Analysis protocol
 F-test for line noise
Chronux: Aim
To provide a comprehensive set of
tools for the analysis of neurobiological
time series data
Current version
Spectral analysis
MATLAB®
Toolboxes
Locfit
local regression and likelihood based analyses
Spike sorting
 Univariate and multivariate time series data.
 Continuous data (e.g. LFPs) and point process data (e.g.
spikes).
 Multiple modalities: Image data (examples in Chris Fall’s talk)
 Extensive online and within-Matlab help
 GUI under active development, release in a few months
Website (www.chronux.org)
Documentation
Key routines for continuous processes
Denoising
Slow variations (e.g. movements
50/60 Hz line noise
of a patient for EEG data)
locdetrend.m: Loess method
rmlinesc.m
rmlinesmovingwinc.m
Spectra, Coherences etc
Fourier transforms using multiple tapers: mtfftc.m
Spectrum: mtspectrumc.m
Coherency:mtcoherencyc.m
Spectrogram: mtspecgramc.m
Coherogram:mtcohgramc.m
Local regression and likelihood
Regression and likelihood: locfit.m
Plotting the fit: lfplot.m
Plotting local confidence bands: lfband.m
Plotting global confidence bands: scb.m
Chronux data format

Continuous/binned point process data
matrices with dimension time x channels/trials
e.g. 1000 x 10 dimensional matrix
interpreted as 1000 samples
10 channels/trials

Spikes times
struct array with dimension = number of channels/trials
e.g. data(1).times=[0.3 0.35 0.42 0.6]
data(2).times=[0.2 0.22 0.35]
2 spike trains with 4 and 3 spikes
Important parameter in mulitple Chronux functions
params: structure with multiple fields
 Fs: sampling frequency (slightly different interpretation for spike times
 tapers: controls the number of tapers
 pad: controls the padding
 fpass: frequency range of interest
 err: controls error computation
 trialave: controls whether or not to average over trials
Example II: Spike rates, spectra
and coherence (from the previous lecture)
• Simultaneous two-cell recording from Macaque
area LIP – dataset DynNeuroLIP.mat
Cue
Delay
Reach and
Saccade
Reach
and
Saccade
Task
Pesaran et al (Unpublished)
Example II
3 local field potentials (LFP) and 2 single units, LFP
sampled at 1 kHz
 Trial: 3 seconds of data for 9 trials to one of the
directions:
1 s (Baseline), 2 s (Delay + post movement)
 Baseline: 1 second of data for 74 trials (pooled
across all directions)
Tasks
Compute the following for the Memory trials
 Spike rates
 LFP and spike spectra
 Spike-field coherence
 Spike-Spike coherence
Compare spike-spike coherence during the
memory period and the baseline period.
The main script for this tutorial
lip_master_script.m
Calls other scripts to run
through the various analyses
The main script for this tutorial
lip_master_script.m
Calls other scripts to run
through the various analyses
Spike rate: 1 trial
Basic locfit usage (rate estimate)
>> fit=locfit(data,'family','rate');
>> lfplot(fit);
>> lfband(fit);
Density estimate:
replace
'rate‘ by ‘dens’
Regression
>> fit=locfit(x,y);
Setting the bandwidth –fixed (h), nearest neighbor (nn)
h: fixed/absolute
bandwidth e.g. h=1
is interpreted as 1 s if
data is in seconds
nn: fixed fraction of
the total number of
points e.g. nn=0.3
takes the 30%
closest points to a
given point
Default: nn=0.7, h=0
>> fit=locfit(data,'family','rate‘,’nn’,0.3);
>> lfplot(fit);
>> lfband(fit);
Multiple trials
pool the spikes and compute fit
rescale fits and confidence intervals
LFP spectrum : mtspectrumc.m
>>[S,f]=mtspectrumc(data);
>> plot(f,10*log10(S))
S: spectrum
f: frequency
Sampling frequency
Set params.Fs
>>params.Fs=1000;
>>[S,f]=mtspectrumc(data,params); Default = 1
>> plot_vector(S,f);
plot_vector:
Allows plotting
errors and choice
of color and scale
(default: log scale
for S)
>> plot_vector(S,f,’n’);
%Uses linear scale for S
Restricting frequencies of interest
Set params.fpass
Default = [0 params.Fs/2]
>>params.Fs=1000;
>>params.fpass=[0 100];
>>[S,f]=mtspectrumc(data,params);
>> plot_vector(S,f)
Changing the padding
Set params.pad
Default=0
Allowed values: -1
0
1
2 ...
For N=500, NFFT: 500 512 1024 2048 …
Default: 0
>> params.pad=2;
>>[S,f]=mtspectrumc(data,params);
>> plot_vector(S,f)
Smoothing (changing the bandwidth)
Set params.tapers : of the form
[TW K]
Default = [3 5]
 TW: time-bandwidth product
 K<2TW: well concentrated
Slepian sequences
>>params.tapers=[5 9];
>>[S,f]=mtspectrumc(data,params);
>> plot_vector(S,f,[],[],’r’)
Averaging over trials
Set params.trialave=1
>> params.trialave=1;
>>[S,f]=mtspectrumc(data,params);
>> plot_vector(S,f)
Note: computing the spectrum separately for each trial and averaging
will work for the spectrum, but not for the Jackknife error bars
Errors
params.err = [1 p]:  
Set params.err
params.err=[2 p]: Jackknife
Serr: (1-p)% confidence
interval of S
>>p=0.05;
>>params.err=[1 p];
>>[S,f,Serr]=mtspectrumc(data,params);
>>plot_vector(S,f,[],Serr);
>> hold on
>>p=0.05;
>>params.err=[2 p];
>>[S,f,Serr]=mtspectrumc(data,params);
>>plot(f,10*log10(Serr(1,:)),’r’);
>>plot(f,10*log10(Serr(2,:)),’r’);
Spike spectrum
mtspectrumpt.m
>>params.err=[1 p];
>>[S,f,R,Serr]=mtspectrumpt(data,params);
Spectrogram: mtspecgramc
Set duration and step size of moving window:movingwin
>> movingwin=[0.5 0.05];
>> [S,t,f]=mtspecgramc(data,movingwin,params);
Spike spectrogram
mtspecgrampt.m
>>[S,t,f,R]=mtspecgrampt(data,movingwin,params);
Coherence between LFP and spikes
coherencycpt.m
>>params.err=[1 p];
>>[C,phi,S12,S1,S2,f,zerosp,confC,phistd]=coherencycpt(datalfp,
datasp,params);
C: coherence
Phi: phase
confC:
Probability(C>confC)=p
phistd:
asymptotic
standard deviation of
phase
Coherence between cells
coherencypt.m
>> params.err=[2 p];
>> [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencypt(datasp1,…
datasp2,params);
Phistd: Jackknifed standard
deviation of the phase
Cerr: (1-p)% confidence
intervals for C
Comparison of coherences and
spectra
• Two experimental conditions with unequal number of
trials
•
Coherence and spectral estimates are biased and the
bias depends on sample size
•
Would like a simple hypothesis test with a
corresponding p value
Bokil et al., J Neurosci Methods. 2006 Aug 28
Comparison of coherences and
spectra
If z=tanh-1 (C)
• E(z)=tanh-1(Cpop)+1/(2m-2)
• V(z)=’(m)
For two coherence estimates
C1,C2 define test statistic
z1  z2
z 
V z1   V z2 
Null hypothesis: C1,pop=C2,pop  z~N(0,1)
Bokil et al., J Neurosci Methods. 2006 Aug 28
Chronux code for comparing coherences
[dz,vdz,Adz]=two_group_test_coherence(J1c1,J2c1,J1c2,J2c2,p,'y',f);
Fourier transforms
Bokil et al, 2006
Electrophysiology Analysis Protocol
Electrophysiolgy: Data Conditioning
Removing 50/60 Hz
N samples: X1, X2, …, XN
Model: X(t)=a cos(2f0t+)+(t)
Potential Method: Least squares
N

X


min
{a , f 0 , }
n 1
 a cos2f 0 nt   
2
n
 (t) is non-white in general
 non-linear in f0 and 
Thomson’s F test
Idea: Equation can be transformed to a
linear regression in frequency
Notice
e e
cos(x) 
2
ix
i 2f 0t
X (t )  e
 ix
* i 2f 0t
 e
 (t )
Thomson’s F test
 Multiply both sides by kth
Slepian sequence ukn and
Fourier transform
Data
Slepian
At f=f0
Noise
~
*
~ (f)
X k ( f )  Uk ( f  f 0 )   Uk ( f  f 0 ) 
k
where k=1,2,…, 2TW-1
~
X k  f0    f0 Uk 0 ~k  f0 
yk  axk   k
Thomson’s F-test
K 1
  f0  
~
X
 k  f 0 U k 0
k 1
K 1
U 0
2
k 1
F2, 2 K  2 
k
K  1   f 0  2
K

k 1
~
X k  f 0     f 0 U k 0 
2
N
2
2
x


i N
Normal variables
i 1
 N
 FN ,M
 M
2
N
2
M
Used in touch-tone phones to detect the key