K-Means Clustering of random numbers in Matlab - matlab

I have a program that generates 10 fixed points and 3 random points when run. I would like the 10 fixed points to use K-means clustering but don't know where to begin. My code is below
function TESTING (re_point)
%***********************NOTE*************************************
% if re_point = 0 [default]
% points generated for xtemp and y_temp remain fixed
% if re_point = 1
% new points are generated for x_temp and y_temp
% Variable definitions for tags and figure window
persistent xtemp ytemp hFig
% Initialisiation of re_point
if nargin<1
re_point = 0; % If 0, the points are fixed, if 1 they move
end
A1 = 30; % area defined as 30 X 30 grid
N = 10;
R = 3; % 3 readers
s = rng; % fixed tags does not change position when simulated repatedly
rng(s)
if (isempty(xtemp) && isempty(xtemp)) || re_point == 1
% Generate x and y position of tags
xtemp = A1*rand(1,N);
ytemp = A1*rand(1,N);
end
if isempty(hFig)
hFig = figure;
end
% Generate x and y position of red points
xtemp_2 = A1*rand(1,R);
ytemp_2 = A1*rand(1,R);
% plot data
plot(xtemp,ytemp,'.',xtemp_2,ytemp_2,'rs','LineWidth',1,'MarkerEdgeColor','k','MarkerFaceColor','r','MarkerSize',14);
% Labelling of the red markers
for iter = 1:numel(xtemp_2)
text(xtemp_2(iter),ytemp_2(iter), num2str(iter),...
'FontSize',8,'HorizontalAlignment','center',...
'Color','White','FontWeight','bold');
end
grid on
hold off
axis([0 A1 0 A1])
% Tag formatting
xoffset = 0;
yoffset = -1;
fsize = 8;
temp_str = mat2cell(num2str([xtemp(:) ytemp(:)], '(%.2f,%.2f)'), ones(1,N));
text(xtemp+xoffset, ytemp+yoffset, temp_str,'fontsize', fsize)
% distance function calculator
cDistance = distanceCalc()
function S = distanceCalc
S = size(numel(xtemp),numel(xtemp_2));
for ri = 1:numel(xtemp)
for fi = 1:numel(xtemp_2)
S(ri,fi) = pdist([xtemp(ri),ytemp(ri);...
xtemp_2(fi),ytemp_2(fi)],...
'euclidean');
end
end
end
end
This particular snippet from the block above generates the 10 fixed points that need to be clustered
if (isempty(xtemp) && isempty(xtemp)) || re_point == 1
% Generate x and y position of tags
xtemp = A1*rand(1,N);
ytemp = A1*rand(1,N);
end


It's not clear at all from your question what you want to do with kmeans, for instance how many clusters are you looking for? I recommend looking at the first example in the MATLAB ref guide
For your data you can try e.g.
X = [xtemp(:) ytemp(:)];
Nclusters = 3;
[idx,C] = kmeans(X,Nclusters);
For plotting something like the following should work:
figure, hold on
plot(X(idx==1,1),X(idx==1,2),'b*')
plot(X(idx==2,1),X(idx==2,2),'g*')
plot(X(idx==3,1),X(idx==3,2),'r*')
to get started. This will attempt to classify your random points into 3 clusters. The cluster into which each point has been classified is defined in idx.

Related

Looping my algorithm to plot for a different parameter value on the same graph(MATLAB)

I've implemented an algorithm for my physics project which does exactly what I want. The problem that I'm stuck which is not the Physics content itself hence I think it might be somewhat trivial to explain what my code does. I'm mainly stuck with the way MATLAB's plotting works if I was to loop over the same algorithm to produce similar graphs with a slight change of a value of my parameter. Here's my code below:
clear; clc; close all;
% Parameters:
z_nn = 4; % Number of nearest-neighbour in lattice (square = 4).
z_nnn = 4; % Number of next-nearest-neighbours in lattice (square = 4).
Lx = 40; % Number of sites along x-axis.
Ly = 40; % Number of sites along y-axis.
sigma = 1; % Size of a site (defines our units of length).
beta = 1.2; % Inverse temperature beta*epsilon.
mu = -2.53; % Chemical potential mu/epsilon.
mu_2 = -2.67; % Chemical potential mu/epsilon for 2nd line.
J = linspace(1, 11, 11);%J points for the line graph plot
potential = zeros(Ly);
attract = 1.6; %wall attraction constant
k = 1; %wall depth
rho_0 = 0.4; % Initial density.
tol = 1e-12; % Convergence tolerance.
count = 30000; % Upper limit for iterations.
alpha = 0.01; % Mixing parameter.
conv = 1; cnt = 1; % Convergence value and counter.
rho = rho_0*ones(Ly); % Initialise rho to the starting guess(i-th rho_old) in Eq(47)
rho_rhs = zeros(Ly); % Initialise rho_new to zeros.
% Solve equations iteratively:
while conv>=tol && cnt<count
cnt = cnt + 1; % Increment counter.
% Loop over all lattice sites:
for j=1:Ly
%Defining the Lennard-Jones potential
if j<k
potential(j) = 1000000000;
else
potential(j) = -attract*(j-k)^(-3);
end
% Handle the periodic boundaries for x and y:
%left = mod((i-1)-1,Lx) + 1; % i-1, maps 0 to Lx.
%right = mod((i+1)-1,Lx) + 1; % i+1, maps Lx+1 to 1.
if j<k+1 %depth of wall
rho_rhs(j) = 0;
rho(j) = 0;
elseif j<(20+k)
rho_rhs(j) = (1 - rho(j))*exp((beta*((3/2)*rho(j-1) + (3/2)*rho(j+1) + 2*rho(j) + mu) - potential(j)));
else
rho_rhs(j) = rho_rhs(j-1);
end
end
conv = sum(sum((rho - rho_rhs).^2)); % Convergence value is the sum of the differences between new and current solution.
rho = alpha*rho_rhs + (1 - alpha)*rho; % Mix the new and current solutions for next iteration.
end
% disp(['conv = ' num2str(conv_2) ' cnt = ' num2str(cnt)]); % Display final answer.
% figure(2);
% pcolor(rho_2);
figure(1);
plot(J, rho(1:11));
hold on;
% plot(J, rho_2(1,1:11));
hold off;
disp(['conv = ' num2str(conv) ' cnt = ' num2str(cnt)]); % Display final answer.
figure(3);
pcolor(rho);
Running this code should give you a graph like this
Now I want to produce a similar graph but with one of the variable's value changed and plotted on the same graph. My approach that I've tried is below:
clear; clc; close all;
% Parameters:
z_nn = 4; % Number of nearest-neighbour in lattice (square = 4).
z_nnn = 4; % Number of next-nearest-neighbours in lattice (square = 4).
Lx = 40; % Number of sites along x-axis.
Ly = 40; % Number of sites along y-axis.
sigma = 1; % Size of a site (defines our units of length).
beta = 1.2; % Inverse temperature beta*epsilon.
mu = [-2.53,-2.67]; % Chemical potential mu/epsilon.
mu_2 = -2.67; % Chemical potential mu/epsilon for 2nd line.
J = linspace(1, 10, 10);%J points for the line graph plot
potential = zeros(Ly, length(mu));
gamma = zeros(Ly, length(mu));
attract = 1.6; %wall attraction constant
k = 1; %wall depth
rho_0 = 0.4; % Initial density.
tol = 1e-12; % Convergence tolerance.
count = 30000; % Upper limit for iterations.
alpha = 0.01; % Mixing parameter.
conv = 1; cnt = 1; % Convergence value and counter.
rho = rho_0*[Ly,length(mu)]; % Initialise rho to the starting guess(i-th rho_old) in Eq(47)
rho_rhs = zeros(Ly,length(mu)); % Initialise rho_new to zeros.
figure(3);
hold on;
% Solve equations iteratively:
while conv>=tol && cnt<count
cnt = cnt + 1; % Increment counter.
% Loop over all lattice sites:
for j=1:Ly
for i=1:length(mu)
y = 1:Ly;
MU = mu(i).*ones(Ly)
%Defining the Lennard-Jones potential
if j<k
potential(j) = 1000000000;
else
potential(j) = -attract*(j-k).^(-3);
end
% Handle the periodic boundaries for x and y:
%left = mod((i-1)-1,Lx) + 1; % i-1, maps 0 to Lx.
%right = mod((i+1)-1,Lx) + 1; % i+1, maps Lx+1 to 1.
if j<k+1 %depth of wall
rho_rhs(j) = 0;
rho(j) = 0;
elseif j<(20+k)
rho_rhs(j) = (1 - rho(j))*exp((beta*((3/2)*rho(j-1) + (3/2)*rho(j+1) + 2*rho(j) + MU - potential(j)));
else
rho_rhs(j) = rho_rhs(j-1);
end
end
end
conv = sum(sum((rho - rho_rhs).^2)); % Convergence value is the sum of the differences between new and current solution.
rho = alpha*rho_rhs + (1 - alpha)*rho; % Mix the new and current solutions for next iteration.
disp(['conv = ' num2str(conv) ' cnt = ' num2str(cnt)]); % Display final answer.
figure(1);
pcolor(rho);
plot(J, rho(1:10));
end
hold off;
The only variable that I'm changing here is mu. I would like to loop my first code so that I can enter an arbitrary amount of different values of mu and plot them on the same graph. Naturally I had to change all of the lists dimension from (1 to size of Ly) to (#of mu(s) to size of Ly), such that when the first code is being looped, the i-th mu value in that loop is being turned into lists with dimension as long as Ly. So I thought I would do the plotting within the loop and use "hold on" encapsulating the whole loop so that every plot that was generated in each loop won't be erased. But I've been spending hours on trying to figure out the semantics of MATLAB but ultimately I can't figure out what to do. So hopefully I can get some help on this!

hold on only applies to the active figure, it is not a generic property shared among all figures. What is does is changing the value of the current figure NextPlot property, which governs the behavior when adding plots to a figure.
hold on is equivalent to set(gcf,'NextPlot','add');
hold off is equivalent to set(gcf,'NextPlot','replace');
In your code you have:
figure(3); % Makes figure 3 the active figure
hold on; % Sets figure 3 'NextPlot' property to 'add'
% Do some things %
while conv>=tol && cnt<count
% Do many things %
figure(1); % Makes figure 1 the active figure; 'hold on' was not applied to that figure
plot(J, rho(1:10)); % plots rho while erasing the previous plot
end
You should try to add another hold on statement after figure(1)
figure(1);
hold on
plot(J, rho(1:10));

Line fitting using RANSAC

I am doing a project in image processing, basically to Vectorise hand drawn images using image processing techniques.
I am using RANSAC in my project. The challenge that I am facing is that the algorithm does not perform the best fit as required but
it uses any two random points and draws a line that joins them as shown in the image below.
RANSAC results
In my algorithm to Vectorise hand drawn images, I also did Grey-scaling, Image thresholding (Image Binarization),
and Skeletonization using Morphological Operators.
I am using MATLAB for my project.
The following is the code I have done so far
% Line fitting using RANSAC
[x, y] =size(skeleton_image);
point =[];
count =1;
% figure; imshow(~data); hold on
for n =1:x
for m =1:y
if skeleton_image(n,m)==1
point(count,1)=m;
point(count,2)=n;
count= count+1;
end
end
end
data = point';
number = size(data,2); % Total number of points
X = 1:number;
iter=100; num=2; thresh = 1000;count_inlines=103; best_count=0; best_line=[];
for i=1:iter
% Randomly select 2 points
ind = randi(number,num); % randperm(number,num);
rnd_points= data(:,ind);
% Fitting line
Gradient = (rnd_points(2,2)-rnd_points(2,1))/(rnd_points(1,2)-rnd_points(1,1));
Constant = rnd_points(2,1)-Gradient*rnd_points(1,1);
Line = Gradient*X+Constant; [j,k]=size(Line);
% How many pixels are in the line?
for i=1:number
Distance = sqrt((Line(:,i)-data(1,i)).^2)+(Line(:,i)-data(2,i)).^2);
if Distance<=thresh
inlines = data(:,i);
count_inlines=countinlines+1;
best_line=Line;
end

I think your issue might be in the way you are counting the distance and/or the threshold that is currently 1000. It might choose all the points in any case and just pick the first or the last ransac line.
% Line fitting using RANSAC
%create skeleton_image objects
skeleton_image = zeros(50,50);
% draw a circle
circle_center = [15,15];
radius = 6;
for i=1:50
for j = 1:50
if abs( radius - sqrt( (i-circle_center(1))^2 + (j-circle_center(2))^2 ) ) <0.5 % < controls the thickness of the circle
skeleton_image(i,j) = 1;
endif
end
end
% draw a line
grad=0.5;
dy = 20;
for i=10:50
skeleton_image(ceil(dy + grad*i),i)=1;
if (i < 50)
skeleton_image(ceil(dy + grad*i)+1,i)=1;
endif
end
% a handful of random points to make it more realistic
skeleton_image(20,22)=1;
skeleton_image(30,7)=1;
skeleton_image(18,45)=1;
skeleton_image(10,10)=1;
skeleton_image(20,23)=1;
skeleton_image(31,6)=1;
skeleton_image(19,45)=1;
skeleton_image(9,13)=1;
skeleton_image(20,24)=1;
skeleton_image(31,5)=1;
skeleton_image(18,46)=1;
% [x, y] =size(skeleton_image);
x = 50;
y = 50;
points =[];
count =1;
for n =1:x
for m =1:y
if skeleton_image(n,m)==1
points(count,1)=m;
points(count,2)=n;
count= count+1;
end
end
end
best_line = [];
best_count = 0;
line_point_list = [];
% how close the pixel has to be to the line to be accepted
threshold = 1;
% how many samples are taken
steps = 10;
for i=1:steps
% pick two points
ind1 = randi(number,1);
ind2 = randi(number,1);
point1 = points(ind1,:);
point2 = points(ind2,:);
%auxiliaries
line = [point1;point2];
lpl = []; %line_point_list
count_i = 0;
if point1 != point2
vector1 = point2-point1;
% unit vector
vector1_normalized = vector1 ./ norm(vector1);
% normal direction of the line
normal_of_vector1 = [vector1_normalized(2), -vector1_normalized(1)];
% loop over points
for j = 1:size(points)
% calculate distance
normal_of_vector1;
vector2 = points(j,:) - point1;
distance = abs(dot(vector2, normal_of_vector1));
if ( distance < threshold )
count_i +=1;
lpl(count_i,:) = points(j,:);
endif
end
endif
if ( count_i > best_count)
best_count = count_i;
best_line = line;
line_point_list = lpl;
endif
end
%best_c
%best_l
%line_point_list
% draw found points
for i=1:size(line_point_list)
skeleton_image(line_point_list(i,2),line_point_list(i,1) ) = 0.25;
end
%visualize
figure(1)
imshow(skeleton_image)

Insert random noise in a V slope DEM

With the following code I am generating a V plane with 2 different slopes, 10° and 20° respectively.
% /*
% Assumptions
% */
% resolution [m]
res = 1;
% inclination [deg]
i1 = 10; i2 = 20;
% /*
% DEM -> V shape
% */
% pre-allocate output
testDEM = zeros(513);
% required elevation step [m]
hstep = res*tan(i1*(pi/180));
% elevation start right [m]
k = 513*(2/3)*tan(i1*(pi/180));
% coordinates
q = length(1:513*(2/3));
% initialize
nStep = 0;
for jj = 1:q
testDEM(:,jj) = k-nStep;
nStep = nStep + hstep;
end
% change elevation step
step = res*tan(i2*(pi/180));
% update nStep
nStep = step;
% elevation start left [m]
start = testDEM(end,q);
for jj = q+1:513
testDEM(:,jj) = start + nStep;
nStep = nStep + step;
end
testDEM = testDEM(1:507,1:507);
%//Plot test DEM
f_tSlope = figure();
set(gca,'PlotBoxAspectRatio',[1 1 1]);
surf(testDEM, 'EdgeColor', 'none')
colormap jet;
hb = colorbar('location','eastoutside');
hb.Label.String = '[m]';
hb.Label.Rotation = 0;
hb.Label.HorizontalAlignment = 'Left';
With the following I'm adding noise in every location
sigma = 1;
testDEM = testDEM + sigma*randn(size(testDEM));
But what I'd like instead is to add random noise in random location, not everywhere. How can I do it?
Thanks in advance

How about this:
N_locations = 100; % no. of locations to add random noise
% randomize 'N_locations' linear indecies in 'testDEM':
noise_location = randi(numel(testDEM),N_locations,1);
% add the noise:
testDEM(noise_location) = testDEM(noise_location)+sigma*randn(N_locations,1);
This will randomize N_locations random locations on the map, and apply different random noise to each of them.
If you prefer to add the same noise to all random locations, just write sigma*randn, without the parenthesis after it.
For small N_locations this should suffice. However, if you want to make sure you don't pick the same location twice, or N_locations is large, you can set noise_location like this:
noise_location = randperm(numel(testDEM),N_locations);
so you'll have only non-repeating values of indices in testDEM.

This code adds noise with 0.5 probability
testDEM = testDEM + sigma*randn(size(testDEM)) .* (rand(size(testDEM)) > 0.5);

Regarding visualization of movement of the data points in training of the Self-Organizing Map (SOM) using Simulink

I have implemented the Self-Organizing Map(SOM) algorithm in MATLAB. Suppose each of the data points are represented in 2-dimensional space. The problem is that I want to visualize the movement of each of the data points in the training phase i.e. I want to see how the points are moving and eventually forming clusters as the algorithm is in progress say at every fix duration. I believe that this can be done through Simulation in MATLAB,but I don't know how to incorporate my MATLAB code for visualization?

I developed a code example to visualize clustering data with multiple dimensions using all possible data projection in 2-D. It may not be the best idea for visualization (there are techniques developed for this, as SOM itself may be used for this need), specially for a higher dimension numbers, but when the number of possible projections (n-1)! is not that high it is a quite good visualizer.
Cluster Algorithm 
Since I needed access to the code so that I could save the cluster means and cluster labels for each iteration, I used a fast kmeans algorithm available at FEX by Mo Chen, but I had to adapt it so I could have this access. The adapted code is the following:
function [label,m] = litekmeans(X, k)
% Perform k-means clustering.
% X: d x n data matrix
% k: number of seeds
% Written by Michael Chen (sth4nth#gmail.com).
n = size(X,2);
last = 0;
iter = 1;
label{iter} = ceil(k*rand(1,n)); % random initialization
checkLabel = label{iter};
m = {};
while any(checkLabel ~= last)
[u,~,checkLabel] = unique(checkLabel); % remove empty clusters
k = length(u);
E = sparse(1:n,checkLabel,1,n,k,n); % transform label into indicator matrix
curM = X*(E*spdiags(1./sum(E,1)',0,k,k)); % compute m of each cluster
m{iter} = curM;
last = checkLabel';
[~,checkLabel] = max(bsxfun(#minus,curM'*X,dot(curM,curM,1)'/2),[],1); % assign samples to the nearest centers
iter = iter + 1;
label{iter} = checkLabel;
end
% Get last clusters centers
m{iter} = curM;
% If to remove empty clusters:
%for k=1:iter
% [~,~,label{k}] = unique(label{k});
%end
Gif Creation
I also used #Amro's Matlab video tutorial for the gif creation.
Distinguishable Colors
I used this great FEX by Tim Holy for making the cluster colors easier to distinguish.
Resulting code
My resulting code is as follows. I had some issues because the number of clusters would change for each iteration which would cause scatter plot update to delete all cluster centers without giving any errors. Since I didn't noticed that, I was trying to workaround the scatter function with any obscure method that I could find the web (btw, I found a really nice scatter plot alternative here), but fortunately I got what was happening going back to this today. Here is the code I did for it, you may feel free to use it, adapt it, but please keep my reference if you use it.
function varargout=kmeans_test(data,nClusters,plotOpts,dimLabels,...
bigXDim,bigYDim,gifName)
%
% [label,m,figH,handles]=kmeans_test(data,nClusters,plotOpts,...
% dimLabels,bigXDim,bigYDim,gifName)
% Demonstrate kmeans algorithm iterative progress. Inputs are:
%
% -> data (rand(5,100)): the data to use.
%
% -> nClusters (7): number of clusters to use.
%
% -> plotOpts: struct holding the following fields:
%
% o leftBase: the percentage distance from the left
%
% o rightBase: the percentage distance from the right
%
% o bottomBase: the percentage distance from the bottom
%
% o topBase: the percentage distance from the top
%
% o FontSize: FontSize for axes labels.
%
% o widthUsableArea: Total width occupied by axes
%
% o heigthUsableArea: Total heigth occupied by axes
%
% -> bigXDim (1): the big subplot x dimension
%
% -> bigYDim (2): the big subplot y dimension
%
% -> dimLabels: If you want to specify dimensions labels
%
% -> gifName: gif file name to save
%
% Outputs are:
%
% -> label: Sample cluster center number for each iteration
%
% -> m: cluster center mean for each iteration
%
% -> figH: figure handle
%
% -> handles: axes handles
%
%
% - Creation Date: Fri, 13 Sep 2013
% - Last Modified: Mon, 16 Sep 2013
% - Author(s):
% - W.S.Freund <wsfreund_at_gmail_dot_com>
%
% TODO List (?):
%
% - Use input parser
% - Adapt it to be able to cluster any algorithm function.
% - Use arrows indicating cluster centers movement before moving them.
% - Drag and drop small axes to big axes.
%
% Pre-start
if nargin < 7
gifName = 'kmeansClusterization.gif';
if nargin < 6
bigYDim = 2;
if nargin < 5
bigXDim = 1;
if nargin < 4
nDim = size(data,1);
maxDigits = numel(num2str(nDim));
dimLabels = mat2cell(sprintf(['Dim %0' num2str(maxDigits) 'd'],...
1:nDim),1,zeros(1,nDim)+4+maxDigits);
if nargin < 3
plotOpts = struct('leftBase',.05,'rightBase',.02,...
'bottomBase',.05,'topBase',.02,'FontSize',10,...
'widthUsableArea',.87,'heigthUsableArea',.87);
if nargin < 2
nClusters = 7;
if nargin < 1
center1 = [1; 0; 0; 0; 0];
center2 = [0; 1; 0; 0; 0];
center3 = [0; 0; 1; 0; 0];
center4 = [0; 0; 0; 1; 0];
center5 = [0; 0; 0; 0; 1];
center6 = [0; 0; 0; 0; 1.5];
center7 = [0; 0; 0; 1.5; 1];
data = [...
bsxfun(#plus,center1,.5*rand(5,20)) ...
bsxfun(#plus,center2,.5*rand(5,20)) ...
bsxfun(#plus,center3,.5*rand(5,20)) ...
bsxfun(#plus,center4,.5*rand(5,20)) ...
bsxfun(#plus,center5,.5*rand(5,20)) ...
bsxfun(#plus,center6,.2*rand(5,20)) ...
bsxfun(#plus,center7,.2*rand(5,20)) ...
];
end
end
end
end
end
end
end
% NOTE of advice: It seems that Matlab does not test while on
% refreshdata if the dimension of the inputs are equivalent for the
% XData, YData and CData while using scatter. Because of this I wasted
% a lot of time trying to debug what was the problem, trying many
% workaround since my cluster centers would disappear for no reason.
% Draw axes:
nDim = size(data,1);
figH = figure;
set(figH,'Units', 'normalized', 'Position',...
[0, 0, 1, 1],'Color','w','Name',...
'k-means example','NumberTitle','Off',...
'MenuBar','none','Toolbar','figure',...
'Renderer','zbuffer');
% Create dintinguishable colors matrix:
colorMatrix = distinguishable_colors(nClusters);
% Create axes, deploy them on handles matrix more or less how they
% will be positioned:
[handles,horSpace,vertSpace] = ...
createAxesGrid(5,5,plotOpts,dimLabels);
% Add main axes
bigSubSize = ceil(nDim/2);
bigSubVec(bigSubSize^2) = 0;
for k = 0:nDim-bigSubSize
bigSubVec(k*bigSubSize+1:(k+1)*bigSubSize) = ...
... %(nDim-bigSubSize+k)*nDim+1:(nDim-bigSubSize+k)*nDim+(nDim-bigSubSize+1);
bigSubSize+nDim*k:nDim*(k+1);
end
handles(bigSubSize,bigSubSize) = subplot(nDim,nDim,bigSubVec,...
'FontSize',plotOpts.FontSize,'box','on');
bigSubplotH = handles(bigSubSize,bigSubSize);
horSpace(bigSubSize,bigSubSize) = bigSubSize;
vertSpace(bigSubSize,bigSubSize) = bigSubSize;
set(bigSubplotH,'NextPlot','add',...
'FontSize',plotOpts.FontSize,'box','on',...
'XAxisLocation','top','YAxisLocation','right');
% Squeeze axes through space to optimize space usage and improve
% visualization capability:
[leftPos,botPos,subplotWidth,subplotHeight]=setCustomPlotArea(...
handles,plotOpts,horSpace,vertSpace);
pColorAxes = axes('Position',[leftPos(end) botPos(end) ...
subplotWidth subplotHeight],'Parent',figH);
pcolor([1:nClusters+1;1:nClusters+1])
% image(reshape(colorMatrix,[1 size(colorMatrix)])); % Used image to
% check if the upcoming buggy behaviour would be fixed. I was not
% lucky, though...
colormap(pColorAxes,colorMatrix);
% Change XTick positions to its center:
set(pColorAxes,'XTick',.5:1:nClusters+.5);
set(pColorAxes,'YTick',[]);
% Change its label to cluster number:
set(pColorAxes,'XTickLabel',[nClusters 1:nClusters-1]); % FIXME At
% least on my matlab I have to use this buggy way to set XTickLabel.
% Am I doing something wrong? Since I dunno why this is caused, I just
% change the code so that it looks the way it should look, but this is
% quite strange...
xlabel(pColorAxes,'Clusters Colors','FontSize',plotOpts.FontSize);
% Now iterate throw data and get cluster information:
[label,m]=litekmeans(data,nClusters);
nIters = numel(m)-1;
scatterColors = colorMatrix(label{1},:);
annH = annotation('textbox',[leftPos(1),botPos(1) subplotWidth ...
subplotHeight],'String',sprintf('Start Conditions'),'EdgeColor',...
'none','FontSize',18);
% Creates dimData_%d variables for first iteration:
for curDim=1:nDim
curDimVarName = genvarname(sprintf('dimData_%d',curDim));
eval([curDimVarName,'= m{1}(curDim,:);']);
end
% clusterColors will hold the colors for the total number of clusters
% on each iteration:
clusterColors = colorMatrix;
% Draw cluster information for first iteration:
for curColumn=1:nDim
for curLine=curColumn+1:nDim
% Big subplot data:
if curColumn == bigXDim && curLine == bigYDim
curAxes = handles(bigSubSize,bigSubSize);
curScatter = scatter(curAxes,data(curColumn,:),...
data(curLine,:),16,'filled');
set(curScatter,'CDataSource','scatterColors');
% Draw cluster centers
curColumnVarName = genvarname(sprintf('dimData_%d',curColumn));
curLineVarName = genvarname(sprintf('dimData_%d',curLine));
eval(['curScatter=scatter(curAxes,' curColumnVarName ',' ...
curLineVarName ',100,colorMatrix,''^'',''filled'');']);
set(curScatter,'XDataSource',curColumnVarName,'YDataSource',...
curLineVarName,'CDataSource','clusterColors')
end
% Small subplots data:
curAxes = handles(curLine,curColumn);
% Draw data:
curScatter = scatter(curAxes,data(curColumn,:),...
data(curLine,:),16,'filled');
set(curScatter,'CDataSource','scatterColors');
% Draw cluster centers
curColumnVarName = genvarname(sprintf('dimData_%d',curColumn));
curLineVarName = genvarname(sprintf('dimData_%d',curLine));
eval(['curScatter=scatter(curAxes,' curColumnVarName ',' ...
curLineVarName ',100,colorMatrix,''^'',''filled'');']);
set(curScatter,'XDataSource',curColumnVarName,'YDataSource',...
curLineVarName,'CDataSource','clusterColors');
if curLine==nDim
xlabel(curAxes,dimLabels{curColumn});
set(curAxes,'XTick',xlim(curAxes));
end
if curColumn==1
ylabel(curAxes,dimLabels{curLine});
set(curAxes,'YTick',ylim(curAxes));
end
end
end
refreshdata(figH,'caller');
% Preallocate gif frame. From Amro's tutorial here:
% https://stackoverflow.com/a/11054155/1162884
f = getframe(figH);
[f,map] = rgb2ind(f.cdata, 256, 'nodither');
mov = repmat(f, [1 1 1 nIters+4]);
% Add one frame at start conditions:
curFrame = 1;
% Add three frames without movement at start conditions
f = getframe(figH);
mov(:,:,1,curFrame) = rgb2ind(f.cdata, map, 'nodither');
for curIter = 1:nIters
curFrame = curFrame+1;
% Change label text
set(annH,'String',sprintf('Iteration %d',curIter));
% Update cluster point colors
scatterColors = colorMatrix(label{curIter+1},:);
% Update cluster centers:
for curDim=1:nDim
curDimVarName = genvarname(sprintf('dimData_%d',curDim));
eval([curDimVarName,'= m{curIter+1}(curDim,:);']);
end
% Update cluster colors:
nClusterIter = size(m{curIter+1},2);
clusterColors = colorMatrix(1:nClusterIter,:);
% Update graphics:
refreshdata(figH,'caller');
% Update cluster colors:
if nClusterIter~=size(m{curIter},2) % If number of cluster
% of current iteration differs from previous iteration (or start
% conditions in case we are at first iteration) we redraw colors:
pcolor([1:nClusterIter+1;1:nClusterIter+1])
% image(reshape(colorMatrix,[1 size(colorMatrix)])); % Used image to
% check if the upcomming buggy behaviour would be fixed. I was not
% lucky, though...
colormap(pColorAxes,clusterColors);
% Change XTick positions to its center:
set(pColorAxes,'XTick',.5:1:nClusterIter+.5);
set(pColorAxes,'YTick',[]);
% Change its label to cluster number:
set(pColorAxes,'XTickLabel',[nClusterIter 1:nClusterIter-1]);
xlabel(pColorAxes,'Clusters Colors','FontSize',plotOpts.FontSize);
end
f = getframe(figH);
mov(:,:,1,curFrame) = rgb2ind(f.cdata, map, 'nodither');
end
set(annH,'String','Convergence Conditions');
for curFrame = nIters+1:nIters+3
% Add three frames without movement at start conditions
f = getframe(figH);
mov(:,:,1,curFrame) = rgb2ind(f.cdata, map, 'nodither');
end
imwrite(mov, map, gifName, 'DelayTime',.5, 'LoopCount',inf)
varargout = cell(1,nargout);
if nargout > 0
varargout{1} = label;
if nargout > 1
varargout{2} = m;
if nargout > 2
varargout{3} = figH;
if nargout > 3
varargout{4} = handles;
end
end
end
end
end
function [leftPos,botPos,subplotWidth,subplotHeight] = ...
setCustomPlotArea(handles,plotOpts,horSpace,vertSpace)
%
% -> handles: axes handles
%
% -> plotOpts: struct holding the following fields:
%
% o leftBase: the percentage distance from the left
%
% o rightBase: the percentage distance from the right
%
% o bottomBase: the percentage distance from the bottom
%
% o topBase: the percentage distance from the top
%
% o widthUsableArea: Total width occupied by axes
%
% o heigthUsableArea: Total heigth occupied by axes
%
% -> horSpace: the axes units size (integers only) that current axes
% should occupy in the horizontal (considering that other occupied
% axes handles are empty)
%
% -> vertSpace: the axes units size (integers only) that current axes
% should occupy in the vertical (considering that other occupied
% axes handles are empty)
%
nHorSubPlot = size(handles,1);
nVertSubPlot = size(handles,2);
if nargin < 4
horSpace(nHorSubPlot,nVertSubPlot) = 0;
horSpace = horSpace+1;
if nargin < 3
vertSpace(nHorSubPlot,nVertSubPlot) = 0;
vertSpace = vertSpace+1;
end
end
subplotWidth = plotOpts.widthUsableArea/nHorSubPlot;
subplotHeight = plotOpts.heigthUsableArea/nVertSubPlot;
totalWidth = (1-plotOpts.rightBase) - plotOpts.leftBase;
totalHeight = (1-plotOpts.topBase) - plotOpts.bottomBase;
gapHeigthSpace = (totalHeight - ...
plotOpts.heigthUsableArea)/(nVertSubPlot);
gapWidthSpace = (totalWidth - ...
plotOpts.widthUsableArea)/(nHorSubPlot);
botPos(nVertSubPlot) = plotOpts.bottomBase + gapWidthSpace/2;
leftPos(1) = plotOpts.leftBase + gapHeigthSpace/2;
botPos(nVertSubPlot-1:-1:1) = botPos(nVertSubPlot) + (subplotHeight +...
gapHeigthSpace)*(1:nVertSubPlot-1);
leftPos(2:nHorSubPlot) = leftPos(1) + (subplotWidth +...
gapWidthSpace)*(1:nHorSubPlot-1);
for curLine=1:nHorSubPlot
for curColumn=1:nVertSubPlot
if handles(curLine,curColumn)
set(handles(curLine,curColumn),'Position',[leftPos(curColumn)...
botPos(curLine) horSpace(curLine,curColumn)*subplotWidth ...
vertSpace(curLine,curColumn)*subplotHeight]);
end
end
end
end
function [handles,horSpace,vertSpace] = ...
createAxesGrid(nLines,nColumns,plotOpts,dimLabels)
handles = zeros(nLines,nColumns);
% Those hold the axes size units:
horSpace(nLines,nColumns) = 0;
vertSpace(nLines,nColumns) = 0;
for curColumn=1:nColumns
for curLine=curColumn+1:nLines
handles(curLine,curColumn) = subplot(nLines,...
nColumns,curColumn+(curLine-1)*nColumns);
horSpace(curLine,curColumn) = 1;
vertSpace(curLine,curColumn) = 1;
curAxes = handles(curLine,curColumn);
if feature('UseHG2')
colormap(handle(curAxes),colorMatrix);
end
set(curAxes,'NextPlot','add',...
'FontSize',plotOpts.FontSize,'box','on');
if curLine==nLines
xlabel(curAxes,dimLabels{curColumn});
else
set(curAxes,'XTick',[]);
end
if curColumn==1
ylabel(curAxes,dimLabels{curLine});
else
set(curAxes,'YTick',[]);
end
end
end
end
Example
Here is an example using 5 dimensions, using the code:
center1 = [1; 0; 0; 0; 0];
center2 = [0; 1; 0; 0; 0];
center3 = [0; 0; 1; 0; 0];
center4 = [0; 0; 0; 1; 0];
center5 = [0; 0; 0; 0; 1];
center6 = [0; 0; 0; 0; 1.5];
center7 = [0; 0; 0; 1.5; 1];
data = [...
bsxfun(#plus,center1,.5*rand(5,20)) ...
bsxfun(#plus,center2,.5*rand(5,20)) ...
bsxfun(#plus,center3,.5*rand(5,20)) ...
bsxfun(#plus,center4,.5*rand(5,20)) ...
bsxfun(#plus,center5,.5*rand(5,20)) ...
bsxfun(#plus,center6,.2*rand(5,20)) ...
bsxfun(#plus,center7,.2*rand(5,20)) ...
];
[label,m,figH,handles]=kmeans_test(data,20);

How can I modify the colors on MATLAB's colorbar

I am plotting the azimuth and elevation of some satellites, where the color of each trajectory represents the S4 index, from low (blue) to high (red). I would like however, to be able to format the colors and corresponding values, so that more of the lower effects of scintillation can actually be distinguished. This is because the high end of scintillation (red) only shows one or two points. Here is a picture of the trajectory and the code.
clc; close all; clear all
load combo_323_full
circular_plot
x = [];
y = [];
for s = 1:samples
% plot each satellite location for that sample
for sv = 1:sats
% check if positive or negative elevation
if (elevation((s - 1) * sats + sv) < 0)
elNeg = 1;
else
elNeg = 0;
end
% convert to plottable cartesian coordinates
el = elevation((s - 1) * sats + sv);
az = azimuth((s - 1) * sats + sv);
x = [x;(pi/2-abs(el))/(pi/2).*cos(az-pi/2)];
y = [y;-1*(pi/2-abs(el))/(pi/2).*sin(az-pi/2)];
% check for final sample
% if (s == samples)
% plot(x,y,'r*');
% text(x,y+.07,int2str(SVs(sv)), ...
% 'horizontalalignment', ...
% 'center','color','r');
% else
% check for +/- elevation
% if (elNeg == 0)
% plot(x,y,'.','color',rgb('DarkBlue'));
% else
% plot(x,y,'g.');
% % end
% end
end
end
z = combo(:,5);
for j = 1:10
% hold on
% circular_plot
lRef = length(x);
l1 = floor(lRef*(1/100));
l2 = floor(l1*j);
x_time = x(1:l2);
y_time = y(1:l2);
zr = z(1:l2);
navConstants;
% find out from 'plotMat' if plotting satellite locations or trajectories in
% addition determine how many satellites are being tracked and how many
% samples for each satellite (# samples / satellite must always be equal)
gpsTime = combo(1,2);
i = 1;
t = gpsTime;
while ((i ~= size(combo,1)) & (t == gpsTime))
i = i + 1;
t = combo(i,2);
end
if (t == gpsTime)
sats = i;
else
sats = i - 1;
end;
samples = size(combo,1) / sats;
SVs = combo(1:sats,1);
elevation = combo(:,20).*pi/180;
azimuth = combo(:,19).*pi/180;
% initialize polar - plotting area
figure(j);
axis([-1.4 1.4 -1.1 1.1]);
axis('off');
axis(axis);
hold on;
% plot circular axis and labels
th = 0:pi/50:2*pi;
x_c = [ cos(th) .67.*cos(th) .33.*cos(th) ];
y_c = [ sin(th) .67.*sin(th) .33.*sin(th) ];
plot(x_c,y_c,'color','w');
text(1.1,0,'90','horizontalalignment','center');
text(0,1.1,'0','horizontalalignment','center');
text(-1.1,0,'270','horizontalalignment','center');
text(0,-1.1,'180','horizontalalignment','center');
% plot spoke axis and labels
th = (1:6)*2*pi/12;
x_c = [ -cos(th); cos(th) ];
y_c = [ -sin(th); sin(th) ];
plot(x_c,y_c,'color','w');
text(-.46,.93,'0','horizontalalignment','center');
text(-.30,.66,'30','horizontalalignment','center');
text(-.13,.36,'60','horizontalalignment','center');
text(.04,.07,'90','horizontalalignment','center');
scatter(x_time,y_time,3,zr)
colorbar
axis equal
end

You can make your own colormap, it's just a N by 3 matrix where the columns are the red, green and blue components respectively.
The default colormap is jet. If you type for instance
>>> jet(16)
you will get a 16 by 3 matrix and you can see how it is made.
Then use colormap(your_own_colormap) to change it.