This GIT respository contains all files needed for an adequate analysis of the gait (6MWT) accelerometer data.
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function [mutM,cummutM,minmuttauV] = MutualInformationHisPro(xV,tauV,bV,flag)
% [mutM,cummutM,minmuttauV] = MutualInformationHisPro(xV,tauV,bV,flag)
% MUTUALINFORMATIONHISPRO computes the mutual information on the time
% series 'xV' for given delays in 'tauV'. The estimation of mutual
% information is based on 'b' partitions of equal probability at each dimension.
% A number of different 'b' can be given in the input vector 'bV'.
% According to a given flag, it can also compute the cumulative mutual
% information for each given lag, as well as the time of the first minimum
% of the mutual information.
% INPUT
% - xV : a vector for the time series
% - tauV : a vector of the delays to be evaluated for
% - bV : a vector of the number of partitions of the histogram-based
% estimate.
% - flag : if 0-> compute only mutual information,
% : if 1-> compute the mutual information, the first minimum of
% mutual information and the cumulative mutual information.
% if 2-> compute (also) the cumulative mutual information
% if 3-> compute (also) the first minimum of mutual information
% OUTPUT
% - mutM : the vector of the mutual information values s for the given
% delays.
% - cummutM : the vector of the cumulative mutual information values for
% the given delays
% - minmuttauV : the time of the first minimum of the mutual information.
%========================================================================
% <MutualInformationHisPro.m>, v 1.0 2010/02/11 22:09:14 Kugiumtzis & Tsimpiris
% This is part of the MATS-Toolkit http://eeganalysis.web.auth.gr/
%========================================================================
% Copyright (C) 2010 by Dimitris Kugiumtzis and Alkiviadis Tsimpiris
% <dkugiu@gen.auth.gr>
%========================================================================
% Version: 1.0
% LICENSE:
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 3 of the License, or
% any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see http://www.gnu.org/licenses/>.
%=========================================================================
% Reference : D. Kugiumtzis and A. Tsimpiris, "Measures of Analysis of Time Series (MATS):
% A Matlab Toolkit for Computation of Multiple Measures on Time Series Data Bases",
% Journal of Statistical Software, in press, 2010
% Link : http://eeganalysis.web.auth.gr/
%=========================================================================
nsam = 1;
n = length(xV);
if nargin==3
flag = 1;
elseif nargin==2
flag = 1;
bV = round(sqrt(n/5));
end
if isempty(bV)
bV = round(sqrt(n/5));
end
bV(bV==0)=round(sqrt(n/5));
tauV = sort(tauV);
ntau = length(tauV);
taumax = tauV(end);
nb = length(bV);
[oxV,ixV]=sort(xV);
[tmpV,ioxV]=sort(ixV);
switch flag
case 0
% Compute only the mutual information for the given lags
mutM = NaN*ones(ntau,nb);
for ib=1:nb
b = bV(ib);
if n<2*b
break;
end
mutM(:,ib)=mutinfHisPro(xV,tauV,b,ioxV,ixV);
end % for ib
cummutM=[];
minmuttauV=[];
case 1
% Compute the mutual information for all lags up to the
% largest given lag, then compute the lag of the first minimum of
% mutual information and the cumulative mutual information for the
% given lags.
mutM = NaN*ones(ntau,nb);
cummutM = NaN*ones(ntau,nb);
minmuttauV = NaN*ones(nb,1);
miM = NaN*ones(taumax+1,nb);
for ib=1:nb
b = bV(ib);
if n<2*b
break;
end
miM(:,ib)=mutinfHisPro(xV,[0:taumax]',b,ioxV,ixV);
mutM(:,ib) = miM(tauV+1,ib);
minmuttauV(ib) = findminMutInf(miM(:,ib),nsam);
% Compute the cumulative mutual information for the given delays
for i=1:ntau
cummutM(i,ib) = sum(miM(1:tauV(i)+1,ib));
end
end % for ib
case 2
% Compute the mutual information for all lags up to the largest
% given lag and then sum up to get the cumulative mutual information
% for the given lags.
cummutM = NaN*ones(ntau,nb);
miM = NaN*ones(taumax+1,nb);
for ib=1:nb
b = bV(ib);
if n<2*b
break;
end
miM(:,ib)=mutinfHisPro(xV,[0:taumax]',b,ioxV,ixV);
% Compute the cumulative mutual information for the given delays
for i=1:ntau
cummutM(i,ib) = sum(miM(1:tauV(i)+1,ib));
end
end % for ib
mutM = [];
minmuttauV=[];
case 3
% Compute the mutual information for all lags up to the largest
% given lag and then compute the lag of the first minimum of the
% mutual information.
minmuttauV = NaN*ones(nb,1);
miM = NaN*ones(taumax+1,nb);
for ib=1:nb
b = bV(ib);
if n<2*b
break;
end
miM(:,ib)=mutinfHisPro(xV,[0:taumax]',b,ioxV,ixV);
minmuttauV(ib) = findminMutInf(miM(:,ib),nsam);
end % for ib
mutM = [];
cummutM=[];
end