"Cluster/group by attribute ranges and classification density"
I have a transactional data with 20 attributes a1 to a20 (numerical, nominal, binominal) and 4000 examples. Attribute a20 is classifiaction (binominal with value 1 or 0). I have to group/cluster data in the following way:
1. 3 to 6 groups/clusters (it can be a fixed number, e.g. 5)
2. groups have to be sorted ranges of numeric attribute a1. Values of a1 are between 100 and 10000. (sounds like discretization operators can be used)
3. main criterion is min/max density of negative classified examples (those with value of a20 equal to 0) in a given range.
Example set has roughly 10 % of those classified as negative. One example of a solution would be:
C1, group where a1 €[100,1000], density of negative = 30% (if there were 500 examples, 60 would be negative)
C2, group where a1 €<1000,2000], density of negative = 5% (if there were 100 examples, 50 would be negative)
C3, group where a1 €<2000,3000], density of negative = x (if there were y examples, x*y would be negative)
C4, group where a1 €<3000,6000], density of negative = x (if there were y examples, x*y would be negative)
C5, group where a1 €<6000,10000], density of negative = x (if there were y examples, x*y would be negative)
The goal is to group examples such that there are few groups of a1 and that in each group there are as much or as few negative examples as possible.
Which approach/process could solve this grouping/discretization problem? I have been unsuccesfully trying to cluster it for some time now.
