My task is to identify parameters (mean, standard deviation, height) of gaussian peaks in given histogram data with as lowest CV as possible. Number of peaks and approximate means are known (pointed by user).
Standard approach uses regression to fit gaussian mixture to the data. Results are listed below:
I've tryed to employ EM algorithm in the following way:
- At first, I didn't care about heights of peaks (used normalized values) and I was searching only for means and standard deviations using EM.
- Second, I fixed means and standard deviations found by EM and used regression to find height of each gaussian.
- I received following results:
I want to ask:
- If my approach is theoretically correct.
- If those results from second approach could be (by sense) valid. Except the last peak, of cause, which had so few points.
Chi squared result is logically bad for second solution; however, the data could contain outliers.
I would be very happy if those CV values were correct, but I am not sure, if I didn't do something wrong.
I try to explain briefly, why I am so surprised...
These measured data were collected from cytometer and correspond to particle (biological cell) count (y axis) per some fluorescence intensity (x axis)..
This intensity correlates with biological cell size, and the goal is to measure cell size of each examined type of plant (one peak correspond to one type of plant).
It is expected that not all cells of same plant share same size, but we know that these sizes (of one plant) are normally distributed.
During measurement process many outliers and false signals are collected and mixed with the original data (we know that the real CV should be much lower), so we want to reach as lowest CV as possible to be sure about cell-type size.
Cytometric softwares that we tested uses the method that i described first (non-linear least squares regression). I've tryed EM, received low CVs, however received a huge difference between my model and data (can be seen in image or ChiSqr). Now I am wondering, if I didn't missed something, because if my approach was correct, then common cytometric softwares would probably use it.