Clustering multiple variables between multiple subjects

Dear all,

I have a clustering question/problem. I have 15 subjects, and each subject has up to 4 time varying profiles. I would like to see whether there are certain time varying profiles that are common between all subjects or between a few subjects. Now, I can do a cluster analysis between each pair of subjects and try to combine those clusters, but that might not be the right way at it. Is there an algorithm (or can anyone advise me on how to write an algorithm) to handle this?

So, as an example:

t = 0.01:0.01:10;

var1 = sin(2*pi*t);

var2 = sin(4*pi*t);

var3 = cos(2*pi*t);

var4 = cos(4*pi*t);

noise = rand(1,1000).*0.2;

Sub1 = [var1+noise ; var2+noise ; var3+noise ];

Sub2 = [var2+noise ; var4+noise ; var1+noise ; var 3+noise ];

Sub3 = [var1+noise ; var3+noise ; var4+noise ];

Now, all subjects have a few out of the 4 variables, but

1) I do not have predefined variables as I describe here, subjects will just have up to 4 time varying profiles that will be similar between subjects.

2) I do not know which subjects have which variables.

Now my goal is to find out how many general types of similar variables there are (var1-4 in my example) and which subjects have which variables. Could anyone help me?

Best wishes, Carlijn