使用C＃检测嘈杂数据集中的峰值

Question

I would like to find a specific set of maximum points in a collection of data I create. Visually it looks something like this: Where the blue points are my data, the green line is the plot, and in yellow I have marked which max points I want to find.

So far I have tried to "smooth" the function via local average and a rolling window but that modifies the max values and does not quite smooth it out enough to see each of those noisy peaks as one single max value.

Is there some transform I could do in code to this array of number to allow for easier extraction of such values?

I am writing in C#. The closest posts I could find to what I am looking for were for R which I know nothing about unfortunately.

Answer 1

Really naive but efficient approach w/oa statistics package: If you want to find all local maxima for a continuous function, they correspond with changes in the 'direction' of the function (ascending or descending). Whenever it goes from asc-->desc you have a local maxima.

Something like this: https://dotnetfiddle.net/4YPz2A

This will give you more 'yellow' matches than you want; but you could get to the 'right' amount by smoothing the dataset (for example by averaging every 3 consecutive data points first).