right now I have a 3d scatter plot with peaks that I need to find the volumes for. My data is from an image, so the x- and y- values indicate the pixel positions on the xy-plane, and the z value is the pixel value for each pixel.
Here's my scatter plot:
scatter3(x,y,z,20,z,'filled')
I am trying to find the "volume" of the peaks of the data, like drawn below:
I've tried findpeaks() but it gives me many local maxima without the the two prominent peaks that I'm looking for. In addition, I'm really stuck on how to establish the "base" of my peaks, because my data is from a scatter plot. I've also tried the convex hull and a linear surface fit, and get this:
But I'm still stuck on how to use any of these commands to establish an automated peak "base" and volume. Please let me know if you have any ideas or code segments to help me out, because I am stumped and I can't find anything on Stack Overflow. Sorry in advance if this is really unclear! Thank you so much!
Here is a suggestion for dealing with this problem:
Define a threshold for z height, or define in any other way which points from the scatter are relevant (the black plane in the leftmost figure below).
Within the resulted points, find clusters on the X-Y plane, to define the different regions to calculate. You will have to define manually how many clusters you want.
for each cluster, perform a Delaunay triangulation to estimate its volume.
Here is an example code for all that:
[x,y,z] = peaks(30); % some data
subplot 131
scatter3(x(:),y(:),z(:),[],z(:),'filled')
title('The original data')
th = 2.5; % set a threshold for z values
hold on
surf([-3 -3 3 3],[-4 4 -4 4],ones(4)*th,'FaceColor','k',...
'FaceAlpha',0.5)
hold off
ind = z>th; % get an index of all values of interest
X = x(ind);
Y = y(ind);
Z = z(ind);
clustNum = 3; % the number of clusters should be define manually
T = clusterdata([X Y],clustNum);
subplot 132
gscatter(X,Y,T)
title('A look from above')
subplot 133
hold on
c = ['rgb'];
for k = 1:max(T)
valid = T==k;
% claculate a triangulation of the data:
DT = delaunayTriangulation([X(valid) Y(valid) Z(valid)]);
[K,v] = convexHull(DT); % get the convex hull indices
% plot the volume:
ts = trisurf(K,DT.Points(:,1),DT.Points(:,2),DT.Points(:,3),...
'FaceColor',c(k));
text(mean(X(valid)),mean(Y(valid)),max(Z(valid))*1.3,...
num2str(v),'FontSize',12)
end
hold off
view([-45 40])
title('The volumes')
Note: this code uses different functions from several toolboxes. In any case that something does not work, first make sure that you have the relevant toolbox, there are alternatives to most of them.
Having already a mesh, maybe you could use the process described in https://se.mathworks.com/matlabcentral/answers/277512-how-to-find-peaks-in-3d-mesh .
If not, making a linear regression on (x,z) or (y,z) plane could make a base for you to find the peaks.
Out of experience in data with plenty of noise, selecting the peaks manually is often faster if you have small set of data to make the analysis. Just plot every peak with its number from findpeaks() and select the ones that are relevant to you. An interpolation to a smoother data can help to solve the problem in the long term (but creates a problem by itself).
Other option will be searching for peaks in the (x,z) and (y,z) planes, then having the amplitude of each peak in an (x) [or (y)] interval and from there make a integration for every area.
Related
I have a piece of code that is not performing as intended (at least in my view) and was hoping if someone could help clarify this issue.
The code plots a histogram of my data and the applies a ksdensity function to smooth the data, finally it runs a findpeaks function to return the max values plotted. However the coordinates for the horizontal axis do not correspond to the graphical representation of the plotted data.
MB(A); %array with the data to be plotted
figure;
histogram(MB(A),25)
[f,xi] = ksdensity(MB(A), 'Bandwidth',10);
figure;
plot(xi,f);
[peaks,loc] = findpeaks(f)
the result from this piece of code are that:
peaks =
0.0232 0.0017
loc =
27 76
however when looking at the graphical representation the coordinates of the peaks (for the horizontal axis) are very different from these values
histogram
smoothed data
I originally thought that might be a problem of over or under fitting but after playing around with the values a little bit the issue remained. Am I just missing some basic concept? Any help would be greatly appreciated. Many thanks
The [loc] location is the index of the point, so you would get the graphical x by:
xi(loc)
see matlab help for info on the returned variables:
[PKS,LOCS]= findpeaks(Y) also returns the indices LOCS at which the
peaks occur.
The figure shown above is the plot of cumulative distribution function (cdf) plot for relative error (attached together the code used to generate the plot). The relative error is defined as abs(measured-predicted)/(measured). May I know the possible error/interpretation as the plot is supposed to be a smooth curve.
X = load('measured.txt');
Xhat = load('predicted.txt');
idx = find(X>0);
x = X(idx);
xhat = Xhat(idx);
relativeError = abs(x-xhat)./(x);
cdfplot(relativeError);
The input data file is a 4x4 matrix with zeros on the diagonal and some unmeasured entries (represent with 0). Appreciate for your kind help. Thanks!
The plot should be a discontinuous one because you are using discrete data. You are not plotting an analytic function which has an explicit (or implicit) function that maps, say, x to y. Instead, all you have is at most 16 points that relates x and y.
The CDF only "grows" when new samples are counted; otherwise its value remains steady, just because there isn't any satisfying sample that could increase the "frequency".
You can check the example in Mathworks' `cdfplot1 documentation to understand the concept of "empirical cdf". Again, only when you observe a sample can you increase the cdf.
If you really want to "get" a smooth curve, either 1) add more points so that the discontinuous line looks smoother, or 2) find any statistical model of whatever you are working on, and plot the analytic function instead.
I couldn't find a solution after trying for a long time.
I have 3 columns of data: x, y, and the stress value (S) at every point (x,y). I want to generate a 2D color plot displaying continuous color change with the magnitude of the stress (S). The stress values increase from -3*10^4 Pa to 4*10^4 Pa. I only have hundreds of data points for an area, but I want to see the stress magnitude (read from the color) at every location (x, y). What Matlab command should I use?
I want to make a 2D color plot showing stress magnitude (S) at every location (x, y) based on continuous color change using limited data points
I'd use patch with interpolated coloring:
% some data, x/y are random
N = 50;
x = rand(N,1);
y = rand(N,1);
S = sin(2*x)+y;
% plotting
tr = delaunay(x,y);
trisurf(tr,x,y,zeros(N,1),S,'FaceColor','interp');
view (2)
Take a look at surf and mesh in the MATLAB documentation
To further contribute on Gunther Struyf answer; assuming it is a FEM analysis you may already have a connectivity matrix say 'M' and 'x' 'y' column vectors with node coordinates. Stress values at the nodes may be contained in a column vector 'S'; then you may use the patch function as stated above:
patch('faces',M,'vertices',[x(:) y(:)],'facevertexcdata',S(:),'FaceColor','interp');
and you will have a 2D plot of your data similar to the one posted by Gunther Struyf.
I 'm having a problem with creating a joint density function from data. What I have is queue sizes from a stock as two vectors saved as:
X = [askQueueSize bidQueueSize];
I then use the hist3-function to create a 3D histogram. This is what I get:
http://dl.dropbox.com/u/709705/hist-plot.png
What I want is to have the Z-axis normalized so that it goes from [0 1].
How do I do that? Or do someone have a great joint density matlab function on stock?
This is similar (How to draw probability density function in MatLab?) but in 2D.
What I want is 3D with x:ask queue, y:bid queue, z:probability.
Would greatly appreciate if someone could help me with this, because I've hit a wall over here.
I couldn't see a simple way of doing this. You can get the histogram counts back from hist3 using
[N C] = hist3(X);
and the idea would be to normalise them with:
N = N / sum(N(:));
but I can't find a nice way to plot them back to a histogram afterwards (You can use bar3(N), but I think the axes labels will need to be set manually).
The solution I ended up with involves modifying the code of hist3. If you have access to this (edit hist3) then this may work for you, but I'm not really sure what the legal situation is (you need a licence for the statistics toolbox, if you copy hist3 and modify it yourself, this is probably not legal).
Anyway, I found the place where the data is being prepared for a surf plot. There are 3 matrices corresponding to x, y, and z. Just before the contents of the z matrix were calculated (line 256), I inserted:
n = n / sum(n(:));
which normalises the count matrix.
Finally once the histogram is plotted, you can set the axis limits with:
xlim([0, 1]);
if necessary.
With help from a guy at mathworks forum, this is the great solution I ended up with:
(data_x and data_y are values, which you want to calculate at hist3)
x = min_x:step:max_x; % axis x, which you want to see
y = min_y:step:max_y; % axis y, which you want to see
[X,Y] = meshgrid(x,y); *%important for "surf" - makes defined grid*
pdf = hist3([data_x , data_y],{x y}); %standard hist3 (calculated for yours axis)
pdf_normalize = (pdf'./length(data_x)); %normalization means devide it by length of
%data_x (or data_y)
figure()
surf(X,Y,pdf_normalize) % plot distribution
This gave me the joint density plot in 3D. Which can be checked by calculating the integral over the surface with:
integralOverDensityPlot = sum(trapz(pdf_normalize));
When the variable step goes to zero the variable integralOverDensityPlot goes to 1.0
Hope this help someone!
There is a fast way how to do this with hist3 function:
[bins centers] = hist3(X); % X should be matrix with two columns
c_1 = centers{1};
c_2 = centers{2};
pdf = bins / (sum(sum(bins))*(c_1(2)-c_1(1)) * (c_2(2)-c_2(1)));
If you "integrate" this you will get 1.
sum(sum(pdf * (c_1(2)-c_1(1)) * (c_2(2)-c_2(1))))
I have a Matlab figure I want to use in a paper. This figure contains multiple cdfplots.
Now the problem is that I cannot use the markers because the become very dense in the plot.
If i want to make the samples sparse I have to drop some samples from the cdfplot which will result in a different cdfplot line.
How can I add enough markers while maintaining the actual line?
One method is to get XData/YData properties from your curves follow solution (1) from #ephsmith and set it back. Here is an example for one curve.
y = evrnd(0,3,100,1); %# random data
%# original data
subplot(1,2,1)
h = cdfplot(y);
set(h,'Marker','*','MarkerSize',8,'MarkerEdgeColor','r','LineStyle','none')
%# reduced data
subplot(1,2,2)
h = cdfplot(y);
set(h,'Marker','*','MarkerSize',8,'MarkerEdgeColor','r','LineStyle','none')
xdata = get(h,'XData');
ydata = get(h,'YData');
set(h,'XData',xdata(1:5:end));
set(h,'YData',ydata(1:5:end));
Another method is to calculate empirical CDF separately using ECDF function, then reduce the results before plotting with PLOT.
y = evrnd(0,3,100,1); %# random data
[f, x] = ecdf(y);
%# original data
subplot(1,2,1)
plot(x,f,'*')
%# reduced data
subplot(1,2,2)
plot(x(1:5:end),f(1:5:end),'r*')
Result
I know this is potentially unnecessary given MATLAB's built-in functions (in the Statistics Toolbox anyway) but it may be of use to other viewers who do not have access to the toolbox.
The empirical CMF (CDF) is essentially the cumulative sum of the empirical PMF. The latter is attainable in MATLAB via the hist function. In order to get a nice approximation to the empirical PMF, the number of bins must be selected appropriately. In the following example, I assume that 64 bins is good enough for your data.
%# compute a histogram with 64 bins for the data points stored in y
[f,x]=hist(y,64);
%# convert the frequency points in f to proportions
f = f./sum(f);
%# compute the cumulative sum of the empirical PMF
cmf = cumsum(f);
Now you can choose how many points you'd like to plot by using the reduced data example given by yuk.
n=20 ; % number of total data markers in the curve graph
M_n = round(linspace(1,numel(y),n)) ; % indices of markers
% plot the whole line, and markers for selected data points
plot(x,y,'b-',y(M_n),y(M_n),'rs')
verry simple.....
try reducing the marker size.
x = rand(10000,1);
y = x + rand(10000,1);
plot(x,y,'b.','markersize',1);
For publishing purposes I tend to use the plot tools on the figure window. This allow you to tweak all of the plot parameters and immediately see the result.
If the problem is that you have too many data points, you can:
1). Plot using every nth sample of the data. Experiment to find an n that results in the look you want.
2). I typically fit curves to my data and add a few sparsely placed markers to plots of the fits to differentiate the curves.
Honestly, for publishing purposes I have always found that choosing different 'LineStyle' or 'LineWidth' properties for the lines gives much cleaner results than using different markers. This would also be a lot easier than trying to downsample your data, and for plots made with CDFPLOT I find that markers simply occlude the stairstep nature of the lines.