Abrupt changes in data; 'ischange', means, and 'stairs'

I have multiple, large data sets that I need to acertain the means along certain linear regions. The regions are dileneated by relatively abrupt changes, as shown in the figure below that I manually marked up.

Ultimately I want a 7 element array of the means of each of these regions (aka the y-intercepts as shown). Thoughts? Other types of curve fittings that could help?

A sample data set is attached.

The below code not working for me, and I've tried a variety of max number of changes and threshold levels.

[TF,S1] = ischange(a, 'linear','MaxNumChanges',12);
plot(a, '*')
hold on
stairs(S1)

Answer 1

[Matt J]

Here is a method using the Image Processing Toolbox (treating the signal as a 1D image, in other words).

load('dataTest.mat')

w=5000;

b=movmedian(a,w);
cmax=movmax(b,[w,1]);
cmin=movmin(b,[1,w]);

q=cmax-cmin;

lmap=bwlabel(q<0.01);

result = regionprops('table',lmap,b,'MeanIntensity')

plot(a)
hold on
for i=1:size(result,1)
   plot(xlim,result{i,1}*[1,1],'--') 
end
hold off

Answer 2

[Matt J]

Yes, you can use splitapply(@mean,data,G)

https://www.mathworks.com/help/matlab/ref/splitapply.html

with G identifying the regions you wwant grouped together,

https://www.mathworks.com/help/matlab/ref/splitapply.html#butc687-G

[noMathWiz]

I'm not seeing how to do this the way you're describing it. In the examples for using "G," the arrays are like a "true/false" or "male/female," etc. If I'm understanding it, my "G" values would be like the x-values for Avg 1-5? (5 different G values), but in my case I have indices that should not be included (the sloped rigions between average 1 and 2, between 2 and 3, etc.

Can you elaborate?

[Matt J]

So, here is an example where I find the means of the first 4 and last 3 elements of the 1x7 vector data,

>> data=[10,20,30,40,50,60,70], G=[1 1 1 1,2 2 2]

data =

    10    20    30    40    50    60    70


G =

     1     1     1     1     2     2     2

>> splitapply(@mean,data,G)

ans =

    25    60

As you can see, the G vector labels the first 4 elements of data with '1' and the final 3 elements with '2'.

but in my case I have indices that should not be included (the sloped rigions between average 1 and 2, between 2 and 3, etc.

To handle the unincluded regions, either remove them from 'data', or assign them a group label of their own. In the latter case, you can just disregard whatever mean value is calculated for the unwanted regions.

[noMathWiz]

Thanks for your help, but I think this is too much manual work (i.e. it requires me to manually find where the changes in data are, delete the data, then create G vectors of the same length).

[Matt J]

If you were to construct G manually, it would indeed be a lot of work, but the philosophy behind splitapply is that you would find some automated way to construct the group labels. Below is a method that makes use of group1s from the File Exchange.

https://www.mathworks.com/matlabcentral/fileexchange/78008-group1s

load('dataTest.mat')

w=5000;

b=movmedian(a,w);
cmax=movmax(b,[w,1]);
cmin=movmin(b,[1,w]);

q=cmax-cmin;
lmap=group1s(q<0.01);

result = splitapply(@mean, b, findgroups(lmap))
 result(1)=[];

plot(a)
hold on
for i=1:size(result,1)
   plot(xlim,result(i)*[1,1],'--') 
end
hold off