PNS toy example

Example of horizontal analysis using PNS

Contents

1. Set up

To make this example work, please first download J. S. Marron's softwares AllMatlab7Combined.zip on http://www.unc.edu/depts/stat-or/miscellaneous/marron/Matlab7Software/ and unzip it. The softwares we need are 'General' and 'Smoothing'. Then, add 'General','Smoothing' and 'SRVF' to your search path. One way to do it is: Click on 'Set Path' -> 'Add with Subfolders', select 'General', 'Smoothing' and 'SRVF', then all these three and their subfolders will be added to the search path.

2. Make data

d = 300;
n = 21;
sig = 0.1;
m = 1;
warpRange = 5;
b = 3;
randn('seed',0);

gamO = zeros(d,n);
a = linspace(-warpRange,warpRange,n+1); a = a(a~=0);
t = linspace(-b,b,d);
m=1;
f = zeros(d,n);
for i = 1:n;
    if a(i)~=0;
        gamO(:,i) = ((2*b)*(exp(a(i)*(t+b)/(2*b))-1)/(exp(a(i))-1)-b);
    else gamO(:,i) = t;
    end;
end;
t = (t+b)/(2*b);
gamO = (gamO+b)/(2*b);
for i = 1:n;
    f(:,i) = normrnd(m,sig) * betapdf(gamO(:,i),6,12)+ ... # 6,12
        normrnd(m,sig) * betapdf(gamO(:,i),12,6);
end;

mycolor = hsvcolmapQY(n); % rainbow color

clf ;
hold on;
for i = 1:n
    plot(t, f(:,i),'color',mycolor(i,:))
end
hold off;

3. Fisher-Rao curve registration

[fn,qn,q0,fmean,mqn,gam,psi,stats]=time_warping_oneplot(f,t',mycolor);

 lambda =   0.0 

Initializing...
Computing Karcher mean of 21 functions in SRVF space...
updating step: r=1
updating step: r=2

4. PNS on the warping functions

inputstruct = struct( 'gam',gam,...
    'meanf',fmean,...
    't',t,...
    'colmap',mycolor, ...
    'plotType',2,...
    'npns',3);

curvepnsLXS(inputstruct);

Message from PNSmain.m; dataset is on 298-sphere.
 .. found null space of dimension 278,to be trivially reduced.
 .. then narrow down to 20-sphere

  (c)  Qunqun Yu, Xiaosun Lu  2015

Published with MATLAB® R2013a