How to find a point in a dataset at which graph is changing (aka whole graph derivative)

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Madina Makhmutova
Madina Makhmutova 2018-9-11
评论： Image Analyst 2018-9-11
Pretty trivial problem from someone not strong in math:) I hava a dataset with intensity values over time. At a certain point intensity starts increasing. I want to find the time point at which intensity starts increasing. Due to the nature of the data there is some fluctuation in the baseline, therefore graph is not a smooth line. I tried finding the first derivative:
data = [1 2 1 3 1 2 4 7 8 15 6 4 3 1 2 1];
time = [1:16]
dydx = diff(data)./diff(time)
end
but this returns the derivative for every single datapoint. How do I find the tangent point for the whole graph, and not just for a single point?
I tried approaching it from another angle by doing the following:
S = std(data(1:5)
logic = data > S
I take the first few points as the baseline and calculate the standard deviation of the baseline. And later I create a logical array where 1 is any value 1 SD above the baseline. This is pretty accurate, the instance where '0 1 0 0 1' changes into a continuous '1 1 1 1 1' indicates the point that I need, but I don't know how to extract an index of this changing point.
Attached is an image of a sample graph.
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jonas
jonas 2018-9-11
findchangepts has loads of input arguments whereas ischange is a bit more limited. However, both functions comes with the optional threshold value to limit the "sensitivity to noise".
Image Analyst
Image Analyst 2018-9-11
Is there some number of points at the beginning where you are assured that they are the initial, flat, non-increasing values that we can use as a threshold? If so I'd smooth the signal with sgolayfilt() and then just threshold at the proper value.

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jonas
jonas 2018-9-11
编辑：jonas 2018-9-11
findchangepts has a number of optional inputs . Try this for example:
% change in std
findchangepts(data(:,3),'statistic','std')
% constant segments
findchangepts(data(:,3),'statistic','mean','minthreshold',2e4)
% linear segments
findchangepts(data(:,3),'statistic','linear','minthreshold',2e4)
To get the index, you simply specify the output arguments
[idx] = findchangepts(data(:,3),'statistic','linear','minthreshold',2e4)
Ideally, the first value in idx is your point of interest. You have to play around with the input arguments to find the best method for this. I would go for one of the above. Perhaps its better to remove minthreshold and use maxnumchanges instead.

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