Lab improvement with Matlab

Ori

Response

Ori

SF

d16

Ori

SF

d16

SF

d16

Physiological Signs

Posters, PapersThesis

Graduation

Figures

Ori

D16

How things were

Tables

Another MK data

Combined Data

One MK data

Computer

Monkey

Vis

ua

l S

tim

uli

Another MK data

Ori

Response

Ori

SF

d16

Ori

SF

d16

Computer

Monkey

Vis

ua

l S

tim

uli

SF

d16

Physiological Signs

Posters, PapersThesis

Graduation

Tables

Combined Data

Ori

D16

Figures

Problems: slow

One MK dataCommand Driving

Limited Types of Exp

Text File output Not fitted curves

Error-prone table align by copy & paste

Monitoring 1 week experiment; 2-3 week data analysis; 11-12 monkeys/ year

Another MK data

Ori

Response

Ori

SF

d16

Ori

SF

d16

Computer

Monkey

Vis

ua

l S

tim

uli

SF

d16

Physiological Signs

Posters, PapersThesis

Graduation

Tables

Combined Data

Ori

D16

Figures

Possible Solution

One MK data

Graphic User Interface

New visual Stimuli

Instant online plotBetter visualizing

Curve fitting

Automatically generated Database

Eliminate copy & paste

Recording

Improvements

1.New visual stimuli2.Graphic user interface3.Online results plotting and curve fitting 4.Data management5.Physiological signs recording

0 100 200 300 40010

15

20

25

30

35

40

45

0 100 200 300 4000

10

20

30

40

50

PhaseHow to build GUIExample codes: busybox.mOn the web

Online plotting Curve fitting

Fourier analysisAnimal 343HemisphereLUnit 64Exp 4

1 0 30.58 19.622 8 23.48 15.663 16 22.39 7.824 24 17.92 1.585 32 14.21 3.996 40 15.75 8.087 48 21.78 14.768 56 14.21 13.279 64 21.78 25.39

10 72 19.92 34.7311 80 26.26 36.8912 88 35.53 39.2413 96 41.08 36.8914 104 36.91 39.2615 112 37.84 41.9616 120 39.54 30.3517 0 19 12.4418 0 28.11 18.2119 0 14.21 5.31

1. Pick up some model function y_est=fitFun(p,x) the model has to be reasonable, e.g. Gaussian

2. Provide the initial values [100, -80 , 20]

3. Select some algorithm

4. Understand what are you looking for function d= objectiveFun(p, y, x) y_est=fitFun(p,x); d = sqrt( sum( (y_est - y).^2 ) );

Minimize the objective function

0

20

40

60

80

-160 -120 -80 -40 0

Orientation (degree)

Resp

on

se (

sp

ikes/s

ec)

General steps to do curve fitting

Standard error of parametersIf the standard error is small, it means that a small variation in the parameter would produce a curve that fits the data much worse. Therefore, we say that we know the value of that parameter well. If the standard error is large, a relatively large variation of that parameter would not spoil the fit much; therefore, we do not really know the parameter’s value well.

Pearsons R known as the goodness of fit. It is computed as the fraction of the total variation of the Y values of data points that is attributable to the assumed model curve, and its values typically range from 0 to 1. Values close to 1 indicate a good fit.

Chi-squareSum of residual square divided by the number of degrees of freedom (data points -parameter). To reduce the bias caused by the number of parameters. The smaller this value, the better the fit.

How good is the fit?

ResidualRandomly distribution, no clear pattern.

% pick the model, prepare the fitting options, initial values, methods, algorithm fopt = fitoptions('method','NonlinearLeastSquares','Algorithm','Levenberg-Marquardt');coef_guess = [mean(yyvals) 1 0 ]; set(fopt,'Startpoint',coef_guess);ftyp = fittype(’fitFun' ,'dependent',{'y'},'independent',{'x'},'coefficients',{'a', 'b', 'c'});

% do the curve fitting[fitresult,goodness,fitinfo] = fit(xxvals,yyvals,ftyp ,fopt);yyfit=feval(fitresult,xxvals);

% Get the residuals rr=fitinfo.residuals;

% chisquarejj=fitinfo.Jacobian; [nd np]=size(jj); dfe1=nd-np; chisqr=rr'*rr/dfe1;

% parameter standard errorvar_cov=inv(jj' * jj); se=sqrt(diag(var_cov))*chisqr;

% pearsons Rmeasdiff=(yyvals-mean(yyvals)); modeldiff=(yyfit-mean(yyfit));pr1=measdiff' * modeldiff; pr2=measdiff' * measdiff; pr3=modeldiff' * modeldiff;pearsons=pr1/(sqrt(pr2)*sqrt(pr3));

Use Curve Fitting Toolbox for unconstrained fit

Modified from Hope’s codes

fmincon

p = [ p1 p2 p3 p4 ]; %initial guess

A = [1 0 -1 0]; B = [0]; %A*p’<B; in this case:%1*p1+0*p2+(-1)*p3+0*p4<0;%p1-p3<0; %p1<p3;

Aeq = [ ]; Beq = [ ]; %Aeq*p’=Beq; this case, none

LB = [0 0 0 0]; %lower boundaryUB = [ 10 200 40 10]; %upper boundary

opts = optimset('fmincon');

p = fmincon('ObjFun', p, A, B, Aeq, Beq, LB, UB, [ ], opts, y, x);fitX=[0:0.1:12]; fitY=sizeFun(p,fitX);

use optimization toolbox for constrained fitParameters follow certain relation. e.g. p1<p3

Size (degree)

Resp

onse

(sp

ikes/

sec)

A Matlab figure is worth thousands of words

3

4

5

6

7

8

9

10

0 50 100 150 200 250 300 350

Res

pons

e (s

pike

s/se

c)

Phase (degree)

m = x: [16x1 double]response: [16x1 double]std: [16x1 double]rightOnly: 6.6410rightOnlyStd: 1.4200leftOnly: 5.2510leftOnlyStd: 1.4230noise: 1.2360noiseStd: 0.4490index: [1x1 struct]fit: [6.35 2.79 30.45]

m.index= RMS: 2.4606

BII: 0.3575 SN: 0.8684 mean: 6.35 amplitude: 2.79 optPhase: 30.45 DOM: 6.6410 meanBM: 0.9000 peakBM: 1.2218 maxBM: 1.6744 minBM: 0.5120

h=hgload(figurename), m=get(h, ‘userdata’);

h=gcfset(h, ‘userdata’, m);hgsave(h, figurename);

•newEmptyMK to create an empty data structure, which holds many units•feedMKWithFigures to go through each figure and fill up this empty data structure •getRoutineFigures to make routine figures across the units (30-40 figures in one click)•getparam to get any combination of parameters to make figure or export into a text file•Combine different monkeys data, Mkcombined=[Mk343;Mk300;Mk299];

MK343

unit #1

unit # n-2 .......exp_GeneralscDepth_absDepth_relativeV1orV2unitNo.

exp_BoriFitDomEyepeakFire_m1preferDir_m2std_m3oriBWType

exp_D16RMS:BIISN:betterMono:MeanOverMono:MaxOverMono:MinOverMono:noise:realBetterMono:

exp_Size:RpeakSize:RpeakFire:RflatSize:RflatFire:LpeakSize:LpeakFire:LflatSize:LflatFire:Type:

GeneralInfo #2 #m#m-1

exp_cstc_m1c_m2c_m3I_m1I_m2I_m3X_m1X_m2Xm3

exp #1

-160 -140 -120 -100 -80 -60 -40 -20 0 20 400

10

20

30

40

50

60

Orientation (degree)

Response (spikes/sec)

343d09301F0

0 50 100 150 200 250 300 350 4000

5

10

15

20

25

30

35

Spatial Phase (degree)

Response (spikes/sec)

343d05904F0

BII= 0.39 peakBM= 0.85

1 2 5 10 20 50 800

5

10

15

20

25

30

35

40

45

Contrast of Center Stimuli (%)

Response (spikes/sec)

343d02808. F0

0 2 4 6 8 10 120

10

20

30

40

50

Size (degree)

Response (spikes/sec)

343d02803F0

Each Monkey has N unitsEach unit has M experimentsEach experiment has one figureEach figure contains many measurements

Post-experiment data management

Mk343.mat is NxM cell array; Mk343{unitNum}{expNum}.OriBW

No more copy & past, align spread sheet, just call matlab functions

How things are

PostersPapersThesis

Graduation

More time to think and write

Quickergraduation

2-3 weeks analysis1-2 days analysis

Before: 1week, 3-5 exp x 50-60 cells; Now: 1 week, 10-15 exp x 100+ cells;

Computer

Monkey

Response Figures, fitted

Vis

ua

l S

tim

uli

CenterSurround

BasicExps

Timing

Physiological Signs

Binocular

DatabaseAutomatically

Generated

newEmptyMKfeedMKWithFigures

Thanks

Scott for leading me into the doorHope for helping me on many projects

Yiji and lab coworkers for helpful discussion

A small progress opens a new door

Single unit responses correlate to EEG?A, b, wavesDifferent anesthesia drugs effects

If you want to know the actual computing algorithmmore control over the fitting process

1. example code (fitogive)

2. example code (Levenberg-Marquardt)

3. book “Numerical Optimization” (by Jorge Nocedal)