Recently, I have been working on automatically identifying peaks from thousands of curves. I use the prominence to detect a peak in Matlab. However, how prominent a peak needs to be such that we perceive it as a peak (true, rather subjective)? Please feel free to share your opinions. Some background knowledge follows:
The prominence of a peak measures how much the peak stands out due to its intrinsic height and its location relative to other peaks. A low isolated peak can be more prominent than one that is higher but is an otherwise unremarkable member of a tall range.
To measure the prominence of a peak:
- Crosses the signal because there is a higher peak
- Reaches the left or right end of the signal
Assuming we are dealing with acceleration data in time domain and from a geotechnical earthquake engineering perspective, one of the ways in which a peak can be defined would be to look at the incremental increase due to the occurrence of the peak on the cumulative energy (we can cater for negative and positive peaks mathematically). That is of course assuming that the there is no 'drift' in the data. Since cumulative energy yielded by an earthquake correlates well with many structural seismic demand measures, an appreciable increase in the cumulative input energy will be relevant to the structural response. The question is, how big of an increase in the energy warrants it to be called a peak? This might depend on the nature of the application/problem but exceedance of a a certain percentage of the total energy can be a simplistic method to define the relevant criteria.
A very interesting q.
IMHO
1.Your strating point "place a marker on the peak" to me seems
a bit confusing as it implies we have already identified the peak!
2. Would suggest define peaks as
2.1 necessary condition points which are local maximums df/dx=0
2,2 sufficient d2f/dx2 apprx = delta(0) preferably over some range
3. Perhaps WT might help in a more general way as threshold can be set
to label peak points
Good Luck
Cheers
In physics, the concept of full-width at half-maximum (FWHM) is often used to denote the extent of a symmetrical function in a manner that is similar to your problem: https://en.m.wikipedia.org/wiki/Full_width_at_half_maximum
The concept of any peak is tied to the derivative over an interval being zero (with the second derivative test to determine whether minima or maxima). The challenge is that for abundant data, such as time-series financial data for instance, it becomes necessary to set a criterion for what constitutes a local peak. Thus, if the progression is “up-level-down“, the “level“ is the peak by our criterion if the value of the function delta=mag(up minus level) or (level minus up) exceeds our set criterion. Therefore, it is up to us to set a delta that is greater than a least-upper bound, U. Ideally, U should exceed the measurement uncertainty by some predetermined amount. The idea behind FWHM conveys the criterion ”delta” in terms of a Gaussian distribution, which implicitly refers to variance or standard deviation.
It is possible to write a MATLAB code to do such local condition testing, or perhaps there’s already a toolkit for that. I’d prefer to write own code.
Hi, Zhu,
As I understand your query is about peak selection.
The Matlab command "findpeaks" based on prominence algorithm as mention in your question. The first step as "Place a marker on the peak" is subjective as mentioned and depends on application & system characteristics . The peak may be some time enhanced or suppress depends on how the real signal is modulated by many other system parameters and drift in acquisition (It is explained by Dr. Cihan). So it should be decided by application mathematical model.
It is interesting to analyse maxima/minima of a function graphically via MATLAB. Good job!!!
This Link Maybe Useful:
https://www.telegraph.co.uk/news/2020/05/10/what-coronavirus-second-peak-wave-meaning/
Cihan Cengiz Thank you, Cihan. You are right, how big of an increase in amplitude or other forms can be called a peak highly depends on the problem. The optimal threshold might be the one under which peaks automatically picked/unpicked are consistent with experts’ eye. It seems to be unavoidable to have a certain degree of subjectivity. I think there might be something to translate this human perception of a peak into a mathematical language, e.g., prominence/width > threshold.
Narasim Ramesh
Thank you, Narasim. It may be better to put it this way “place a marker on a local maxima point”. There will be several maxima points (df/dx=0) on a curve, however, some maxima are too low to be viewed as peaks. Thus, further screening criteria shall be imposed.
Thank you Richard O. Ocaya The full-width at half-prominence (or normalized by its prominence) is indeed a factor worth considering.
This is a fascinating problem. Very relevant in radar. What is the relative importance of peak height, shape and context? I consider some of these things in
Article Improving the frequency response of Savitzky-Golay filters v...
this link helpful
https://www.mathworks.com/help/signal/ref/findpeaks.html
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