I have a transaction matrix like this:
"u1" "u10" "u2" "u3" ...
_____________________________________
"A", | 1 0 1 1 ...
"B", | 0 1 0 0
"u10"| 0 0 0 0 .
"u11"| 0 0 0 0 .
"u2" | 0 0 0 0 .
"u4" | 0 0 0 0
. .
. .
. .
And I am trying to determining the lift of the each pair (i, j), eg., lift(u1, A), in that matrix using R first I tried to use the apriori algorithm of the arules package, but I am not interested in rules. Then, I came to this implementation, but this only works for symmetric matrix. I would like some idea of how can do that or if there is some implementation of this in any R package that do this.
Many thanks!
I guess what you want is something like the following:
My first assumption is, the matrix you start with is not a user-item transaction matrix, rather an item-item co-occurrence matrix, where the entry i,j represents # transactions where the item i was bought given item j was brought. Here is a small co-occurrence matrix C. In this matrix each row i represents the # transactions where the i th item was bought.
C
I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13 I14 I15 I16 I17 I18 I19 I20
I1 2 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0
I2 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
I3 0 0 9 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1
I4 0 0 0 5 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0
I5 0 0 1 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
I6 0 0 0 0 0 3 0 0 0 1 0 0 0 0 0 0 0 1 1 0
I7 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 1 0
I8 1 0 1 1 0 0 0 6 2 0 0 0 0 0 0 2 0 1 0 1
I9 0 0 1 1 0 0 1 2 9 0 1 1 0 0 0 1 1 2 1 0
I10 1 0 0 0 0 1 0 0 0 4 0 0 0 0 0 0 0 0 1 0
I11 0 0 1 0 0 0 0 0 1 0 2 0 0 0 0 0 1 0 0 0
I12 0 0 0 0 0 0 0 0 1 0 0 6 0 0 0 1 1 1 1 1
I13 0 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0
I14 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 1 0 0 0 0
I15 0 0 0 1 0 0 0 0 0 0 0 0 0 0 5 0 0 0 1 0
I16 1 0 0 0 0 0 0 2 1 0 0 1 0 1 0 4 1 1 1 0
I17 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 5 0 1 0
I18 0 0 0 0 0 1 0 1 2 0 0 1 0 0 0 1 0 9 0 0
I19 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 7 0
I20 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 6
Now lift of an item A given an item B is P(A|B) / P(A).
items.probs <- rowSums(C) / sum(C)
cond.probs <- C / rowSums(C)
lifts <- round(cond.probs / items.probs,2)
lifts
I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13 I14 I15 I16 I17 I18 I19 I20
I1 0.90 0.90 0.45 1.79 1.79 1.35 1.79 0.90 0.00 1.79 1.79 1.35 0.45 0.45 0.45 0.00 0.90 0.45 1.35 0.45
I2 2.42 1.82 1.21 1.82 1.21 0.61 0.00 1.21 2.42 0.00 1.21 0.00 0.61 1.82 1.21 1.21 0.61 1.82 0.00 1.21
I3 0.66 0.99 0.66 0.99 0.99 0.99 1.33 0.00 0.99 0.99 0.33 0.99 0.33 0.99 0.66 1.33 1.33 0.66 0.99 0.33
I4 2.18 0.55 0.55 0.55 0.55 0.00 2.18 0.00 0.55 1.64 2.18 2.18 0.55 1.09 0.55 0.55 1.09 0.55 2.18 1.64
I5 0.00 0.00 0.00 1.35 2.71 2.03 2.03 0.68 0.00 2.03 2.03 0.68 2.03 0.68 2.71 0.00 2.03 0.00 2.03 0.68
I6 0.68 2.71 0.00 0.00 0.00 2.03 2.71 0.68 0.00 2.71 2.71 1.35 1.35 1.35 0.00 1.35 0.00 2.03 0.68 1.35
I7 0.69 1.38 0.69 0.69 1.04 1.38 1.38 0.35 0.00 0.35 0.69 1.38 1.38 1.04 0.35 0.69 0.35 1.38 0.35 1.38
I8 1.04 1.38 0.00 0.00 1.38 1.04 0.35 1.38 1.38 0.35 1.04 1.04 1.04 0.69 1.04 0.35 1.04 0.69 1.04 0.69
I9 0.00 1.97 1.97 0.00 2.96 1.97 0.99 1.97 0.99 1.97 0.00 0.00 0.99 0.99 0.99 1.97 1.97 3.94 2.96 0.00
I10 2.30 1.15 1.15 0.00 1.72 2.30 1.15 0.57 0.00 1.15 1.15 0.00 0.00 1.15 1.15 1.15 2.30 1.15 2.30 0.00
I11 0.59 1.18 0.00 0.30 0.89 0.00 1.18 1.18 0.89 1.18 0.30 1.18 0.00 1.18 0.89 0.89 1.18 0.30 1.18 1.18
I12 0.75 1.13 0.38 0.38 0.00 0.38 1.13 1.13 0.00 1.13 0.38 1.13 1.13 1.50 1.50 1.50 0.38 1.50 0.75 1.50
I13 1.50 1.50 0.38 1.13 1.13 1.50 1.50 0.75 0.00 0.38 1.13 0.75 0.00 1.13 1.50 0.75 1.50 0.00 0.38 0.75
I14 1.88 0.94 0.47 0.94 0.00 1.88 0.00 0.47 0.47 0.47 1.41 0.94 0.94 1.88 0.94 0.94 0.47 1.88 1.88 0.94
I15 0.00 1.04 1.38 1.38 1.38 1.04 1.38 0.35 0.00 1.38 1.04 1.04 1.04 1.38 0.69 1.04 0.00 0.35 0.35 0.69
I16 1.08 1.08 0.72 0.72 1.44 1.08 1.44 1.08 0.00 0.00 0.72 0.00 1.08 1.44 0.72 1.44 0.72 1.44 1.08 0.00
I17 1.97 1.97 2.96 0.00 0.00 0.99 0.00 1.97 0.00 2.96 0.00 0.00 0.99 0.99 3.94 1.97 1.97 0.99 0.99 3.94
I18 0.00 0.00 0.00 2.42 1.82 0.00 0.00 2.42 1.21 1.21 2.42 2.42 0.00 2.42 1.82 1.82 1.82 0.61 0.00 0.00
I19 1.41 1.41 0.94 1.88 0.47 0.47 1.88 1.88 0.00 0.47 0.00 0.00 1.41 0.00 0.47 0.94 0.94 1.41 1.88 1.88
I20 0.00 0.00 3.45 0.86 0.00 2.59 0.86 0.86 0.86 1.73 0.86 2.59 1.73 1.73 3.45 0.00 1.73 0.00 2.59 0.86