I'm a biologist by origin, and I'm asking this question to the math community to learn from the vast knowledge that I don't posses myself but is out there in the math field.
Edit: This question was originally posted on mathoverflow but moved to CrossValidated based on suggestions in the comments: enter link description here
This is a very general question, I know, but I'm also mostly seeking general, inspirational answers and clues to steer me in a new direction. (I'm pretty sure the moderators will have comments about this post, let's hope they are constructive, and perhaps suggestions on what tags to add).
Perhaps this is a bit of a wide net that I'm throwing, but I am not sure in what other way to start a thought process towards possible tracking down existing knowledge on the topic described below. Looking around on google and scientific literature has left me a bit lost as I stumble into too many information that is not what I'm actually looking for.
The question is the following: I am wondering if there are effective ways to compare particle data in the form of signal pulse scans, specifically to separate them into groups of particle types.
For each particle, the full pulse of 6 channels is recorded.
Pulses have a wide range in length (nr of datapoints) as particles can be between 0.2 and 2000 um, and pulses are recorded at a speed that comes down to ~10 points + 1 point for every 0.5 um length
Pulses have a wide range in amplitude. Of the 6 signals, all can vary over several orders of magnitude in maximum value, and high values in 1 signal don't necessarily mean high values in others.
or pretty much anything in between.
Currently I have done extensive work on clustering algorithms working on derived summary parameters of the pulses such as: Maximum (height) Total (area under the curve) length inertia centre of gravity etc.
This gives quite decent results, but looking at the pulses grouped within one cluster, very often there is still variation in pulses present in the clusters, such as the image below, and hence I wonder if there are ways to do cluster analysis on the actual full pulse shapes.