algorithm - Data Set Manipulation -

i need reverse engineer data set original form. original data set derived process multiple users have multiple characteristics enter room , click on button. column variables in indicator form user click on button or have characteristic recorded 1 , don't it's indicated zero. data set transformed in form characteristic types observations represented 2 characteristic variables. new data set shows users have 2 characteristics, amount of them, , button clicks. encompasses users. explanation might not clearest here image might might explanation

i'm thinking of using type of algorithm solve not might efficient.

unfortunately, in general, not able unambiguously reverse engineer data set. ignoring moment action column, consider following 2 data sets:

data set 1:

a b c 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 

data set 2:

a b c 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 

unless i'm mistaken, these 2 data sets show same number of users under each pair of characteristics:

a 5 b 2 c 2 b b 5 b c 2 c c 5 

now, might tempted think: "hey, first data set has 10 users second data set has 9. if i'm able total number of users, solve problem?" answer no. if have 3 or fewer characteristics, answer yes (see: inclusion-exclusion principle). however, if have more 3 characteristics, answer no. can construct ambiguous examples total number of users same.