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In order to clustering data to reduce the noise, we can use the simple k-means clustering algorithm. The idea of k-means is quite simple. Here is the step of the k-means algorithm. 1. Randomly pick samples (depending on how many groups we want to cluster) as the references. 2. Compute the distance between each data point and references. 3. Comparing the distance to each reference, grouping the data points from the shortest distance. 4. Compute the centroid of each group as the new reference. 5. Repeat 2-4, until the centroids are the same with the previous result. Here is the Matlab code: ======================================= % An example for k-means clustering % % Renfong 2018/12/19 % % create test data % There are 3 types of sigal % 1-20, 36-70, 91-100 are the group 1 % 21-35 are group 2 % 71-90 are group 3 xx=0:1:1024; cen=[120, 360, 780]; amp=[100, 60, 55]; sig=[50, 10, 30]; % peak 1+3 for i=1:20     sp(i,:)=amp(1)*exp((-...

MLLS stands for  multiple linear least squares fitting, which is the common strategy for the solving EELS edge overlapping and which is also built-in the GMS software. The target spectrum Y and the reference spectrum X Y = A * X Assuming Y is 1*256 matrix and we have three reference spectrums, ie, X is 3*256 matrix. So A is 1*3 matrix. The target is to solve A. If Y and X are n*n matrices, we can use the simple formula Y * inv(X) = A * X * inv(X), ie., A = Y * inv(X). However, Y and X are not n*n  matrices, it is necessary to have some trick to solve it. We can multiply the transpose matrix to produce n*n matrix. Y * X' = A * X * X'  (ps X' means the transpose matrix of X) so A = Y * X' * inv(X * X') Here is the Matlab code: =========  % create target spectrum x=0:256; c=[90,120,155]; sig=[5,10,8]; int=[5,10,8]; xn=zeros(size(x)); ref=zeros(length(c),length(x)); factor=rand(size(c))'; for i=1:length(c)     xn=xn+int(i)*ex...