Finding threshold values for classification

Question

Jimmy Neutron 2021-11-19

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1591144-finding-threshold-values-for-classification

编辑： Jimmy Neutron 2021-11-20

I have been struggling too much on a book question that I know the answer, but cannot find the mathematical solution. The question goes like this:

A device uses a camera which has discovered three spectral peaks that reflect different types of particles. Each spectra follows a normal distribution. The parametric distributions of the three particle classes are N(7,2*2), N(15,5*5), and N(3,5*5). The manufacturers need help to define the thresholds to perform robust classification. They wish to perform a parametric classification of the three classes.

What signal thresholds should they use?

Answer: 4.24 and 10.29

The previous question was similar, but it asked for the minimum distance classification instead of the parametric classification. For this I ploted the peaks as lines and then found the average between those lines and got that the thresholds should be 5 and 11, which is correct:

% N1 = N(7,2*2);
% N2 = N(15,5*5);
% N3 = N(3,5*5);
signal1 = (3+7)/2; % N3-N2
signal2 = (15+7)/2; % N1-N2
figure
hold on
xline(signal2, 'r'); 
xline(signal1, 'r'); 
xline(7)
xline(15)
xline(3)

I have been trying to solve it for the parametric classification, but have no idea how to do it. Could someone please point me in the right direction?