How to get cluster more than 2 if i have :

Y1 = mvnpdf(X,mu1,sigma1); 
Y2 = mvnpdf(X,mu2,sigma2); 
Y3 = mvnpdf(X,mu3,sigma3);
Cluster1 = Y1 > Y2; 
Cluster2 = ~Cluster1; 
Cluster3 = ??????

[Image Analyst]

Original question

How to get cluster more than 2 if i have :

Y1 = mvnpdf(X,mu1,sigma1); 
Y2 = mvnpdf(X,mu2,sigma2); 
Y3 = mvnpdf(X,mu3,sigma3);
Cluster1 = Y1 > Y2; 
Cluster2 = ~Cluster1; 
Cluster3 = ??????

Answer 1

[Walter Roberson]

Cluster1 = Y1 > Y2 & Y1 > Y3 & Y2 > Y3
Cluster2 = Y1 > Y2 & Y1 > Y3 & Y2 <= Y3
Cluster3 = Y1 > Y2 & Y1 <= Y3           %Y2 < Y3 by transitive
Cluster4 = Y1 <= Y2 & Y1 > Y3           %Y2 > Y3 by transitive
Cluster5 = Y1 <= Y2 & Y1 <= Y3 & Y2 > Y3
Cluster6 = Y1 <= Y2 & Y1 <= Y3 & Y2 <= Y3

Or use kmeans() with the number of clusters that you want.

Caution: kmeans will always return the number of clusters you ask for, even if it does not make sense for the data.

[Steven Pranata]

If i just want 3 clusters? Its same?

[Walter Roberson]

Pick any three of those.

Note that there is a difference between finding three clusters, versus finding three meaningfull clusters.

If your mu* values are well separated, you could probably use the mu* values as the locations around which clusters would be expected to form. If you were to sort the mu values, ms1, ms2, ms3, then you could form clusters "value <= (ms1+ms2)/2, (ms1+ms2)/2 <= value < (ms2+ms3)/2, value >= (ms2+ms3)/2 . These would, however, not necessarily represent equal areas.

[Walter Roberson]

I doubt that you want to be comparing Y1 to Y2 or Y3. I think you want to be throwing all of the values into one basket, [Y1, Y2, Y3] and then trying to form clusters that can distinguish which of the three sources the values came from.

Answer 2

[Image Analyst]

Just define Cluster3 to be something. What would you want it to be? It could be virtually anything you direct it to be.