I am identifying the maximum Y value of a subset a of set of values such that the subset is a contiguous block of values above the mean of the entire set. The data set is a bit like the sum of a sine wave at a low frequency plus a wave with a higher frequency and a much lower amplitude. The result is like a ripply sine wave. So the points I am identifying are those at the peak of each section that is above the mean (zero in the case of two sine waves in my example). They do happen to be local maxima, but other local maxima are ignored.
Is there an established mathematical term for finding a maximum that is not a local maximum, and not an absolute maximum, but a maximum within a given subset of the entire set? I would coin the phrase “regional maximum” but I don’t know if that phrase is already used for something else.
You can name it how you choose… you are naming each of your data sets sections,
so each maximum is the maximum in the section…
The reason the local maxima have a specific name is that they are where d/dx = 0 … Are you ignoring parts of the curve where d/dx not equal zero, eg at the very left or very right of the section ? you are ignoring anything not a local maxima ? because they’d be on a peak which was a local maxima in a different section ?
you wouldn’t be the first to investigate the properties of a regional max. That is the term I thought of when I read your OP. I don’t have a cite right now, but it seems to me to be a common term. Though I would think of the points above the trend-line as opposed to the mean of the entire data set, but I guess the mean could be used.
I wouldn’t use the term regional maximum as this has a very specific meaning in image processing.
Each one of those high points may be a local maximum, as all a local maximum is the highest in a given range. Although the range is often for the entire data set, it doesn’t have to be. If your sections are definable than the local maximum is the point you’ve circled given the range of that section. Assuming I’m understanding what you’re asking for properly.
For example, the first circle for the range of 0 <= x <= 5. And the second circle for 5 <= x <= 10. and so on.
I would agree with this if you’d change the word “local” to “absolute.”
If the two circled points in the example are at the same height, they’d both count as points where the graph reaches an absolute (or global) maximum. Even if they weren’t the same height, each could be the absolute maximum within a specified interval/domain. A local (or relative) maximum just has to be higher than all points in its immediate neighborhood, and there are many such local maxima in the example graph.
I certainly wouldn’t use the word “absolute” to describe these. “Absolute” would likely be interpreted as the largest realization of the absolute value.
Your own cite supports that “absolute maximum” is defined over the function’s entire domain, not over a subset of the domain.
The OP’s goal is to divide his data in a semi-regular fashion into a collection of individually disjoint but collectively all-covering subsets and then capture the maximum within each such subset/interval.
I have no idea if there is a formal term of art for this. But I like “regional maxima” or “subset maxima”. I’d favor the former if we’re dealing with a continuous function and the latter if we’re dealing with collections of discrete data points. As I understand the OP, the latter holds and “subset maxima” would be my vote.
IMO, YMMV, void where prohibited, etc.
The one thing we know for sure is the relevant term isn’t “local maxima” or “absolute maxima”.
