Proper similarity measure for clustering I have problems in finding a proper similarity measure for clustering. I have around 3000 arrays of sets, where each set contains features of certain domain (e.g., number, color, days, alphabets, etc). I'll explain my problem with an example.
Lets assume i have only 2 arrays(a1 & a2) and I want to find the similarity between them. each array contains 4 sets (in my actual problem there are 250 sets (domains) per array) and a set can be empty.
a1: {a,b}, {1,4,6}, {mon, tue, wed}, {red, blue,green}
a2: {b,c}, {2,4,6}, {}, {blue, black}

I have come with a similarity measure using Jaccard index (denoted as J):
sim(a1,a2) = [J(a1[0], a2[0]) + J(a1[1], a2[1]) + ... + J(a1[3], a2[3])]/4

note:I divide by total number of sets (in the above example 4) to keep the similarity between 0 and 1. 
Is this a proper similarity measure and are there any flaws in this approach. I am applying Jaccard index for each set separately because I want compare the similarity between related domains(i.e. color with color, etc...)
I am not aware of any other proper similarity measure for my problem.
Further, can I use this similarity measure for clustering purpose?
 A: A good reference for different similarity measures and distances (metrics) is
"Encyclopedia of Distances" (You can find a copy of it online using Google).
In your question you are asking for:
1. What alternative similarity measures there are except Jaccard-Index, for example 
     s(A,B) = |A intersection B| / (max(|A|,|B|) ('set accurracy')
2. If you have (different) similiartiy measures, then how to combine them into one similarity measure.
Those questions are answered in the above mentioned book. 
The second question is answered at the beginning.
Furthermore, if you want to cluster, most algorithms assume, that you have distances between your points.
That is, you could change from similarity to distance by the formula
distance = sqrt(1-similarity^2)
A: Jaccard index is very suitable when comparing similarities between subsets of any set since it has good interpretation (ratio of their overlap to their union). Note that there is large amount of similar coefficients, see for example this work, where is very comprehensive list of them. You can also find there that most of indices can be classified into 4 groups and coefficients from the same group have equivalent properties so no mather which of them you use.
