I figured out a work around for using biplot to plot pca results of a dataset that contains 4 samples within the dataset and plot the centroids with errorbars on the centroids. First transformed the pca results (coeff and score) with the same transformation biplot would do, creating a new matrix. The centroids (taking the mean) were calculated with new matrix, and the associated error bars.
The original pca data was plotted using biplot function, then centroid and error bars plotted using plot function and ploterr function. I used code found at stackoverflow, url referenced. And the ploterr function from file exchange.
I have double checked a lot of things here and believe the figure represents the data accurately.
Code: %%%%%%%%%%%%%%%%%%%%% % http://stackoverflow.com/questions/5045494/plot-data-with-matlab-biplot-with-more-than-1-color
xxx = coeff(:,1:2);
yyy= score(:,1:2);
%Taken from biplot.m; This is alter the data the same way biplot alters data - having the %data fit on grid axes no larger than 1.**
[n,d2] = size(yyy);
[p,d] = size(xxx); %7 by 3
[dum,maxind] = max(abs(xxx),[],1);
colsign = sign(xxx(maxind + (0:p:(d-1)*p)));
xxx = xxx .* repmat(colsign, p, 1);
yyy= (yyy ./ max(abs(yyy(:)))) .* repmat(colsign, 163, 1);
nans = NaN(n,1);
ptx = [yyy(:,1) nans]';
pty = [yyy(:,2) nans]';
% ptz = [yyy(:,3) nans]';
%I grouped the pt matrices for my benefit**
plotdataholder(:,1) = ptx(1,:);
plotdataholder(:,2) = pty(1,:);
% plotdataholder(:,3) = ptz(1,:);
% %my original score matrix is 42x3 - wanted each 14x3 to be a different color**
scatter(plotdataholder(1:45,1),plotdataholder(1:45,2),'marker', 'o');
hold on;
scatter(mean(plotdataholder(1:45,1)),mean(plotdataholder(1:45,2)),'marker', '.');
scatter(plotdataholder(46:83,1),plotdataholder(46:83,2),'marker', 'd') ;
scatter(mean(plotdataholder(46:83,1)),mean(plotdataholder(46:83,2)),'marker', 'd') ;
scatter(plotdataholder(84:125,1),plotdataholder(84:125,2),'marker', '^') ;
scatter(mean(plotdataholder(84:125,1)),mean(plotdataholder(84:125,2)),'marker', '^') ;
scatter(plotdataholder(126:163,1),plotdataholder(126:163,2),'marker', 's') ;
scatter(mean(plotdataholder(126:163,1)),mean(plotdataholder(126:163,2)),'marker', 's') ;
xlabel('Principal Component 1');
ylabel('Principal Component 2');
% zlabel('Principal Component 3');
Now for the final part: a1=plotdataholder(1:45,1);b1=plotdataholder(1:45,2); a2=plotdataholder(46:83,1);b2=plotdataholder(46:83,2); a3=plotdataholder(84:125,1);b3=plotdataholder(84:125,2); a4=plotdataholder(126:163,1);b4=plotdataholder(126:163,2); n1=length(a1); n2=length(a2); n3=length(a3); n4=length(a4); x1=mean(a1);y1=mean(b1); x2=mean(a2);y2=mean(b2); x3=mean(a3);y3=mean(b3); x4=mean(a4);y4=mean(b4); sema1=std(a1)/n1; semb1=std(b1)/n1; sema2=std(a2)/n2; semb2=std(b2)/n2; sema3=std(a3)/n3; semb3=std(b3)/n3; sema4=std(a4)/n4; semb4=std(b4)/n4;
%%This is the pca all stream code for creating a biplot figure
% load pcasolution.mat
figure
hp=biplot(coeff(:,1:2),'Scores',score(:,1:2),'VarLabels',{'DO' 'K' 'TOM' 'dh' 'N'},...
'Marker','s','MarkerEdgeColor','g','MarkerSize', 9);
legend([hp(16,:) hp(61,:) hp(99,:) hp(141,:)], 'Coal Kiln','Machipongo',...
'Parkers','Phillips','Location','NorthWest');
hold on
plot(x1,y1,x2,y2,x3,y3,x4,y4,'or')
ploterr(x1,y1,sema1,semb1)
ploterr(x2,y2,sema2,semb2)
ploterr(x3,y3,sema3,semb3)
ploterr(x4,y4,sema4,semb4)
