## TF-IDF Applied to Recommendations

One of the possibilities that Aura is exploring is to leverage an existing TF-IDF implementation in minion.

There are a couple different mappings of the TF-IDF tuples under consideration, but the one considered here is:

TF-IDF Term TF-IDF Variable Aura Mapping Aura Variable Explanation
term t listener listens to music
document d artist a a has created music
corpus $\overline{d}\equiv$

di
tk
c

all artists $\overline{a}\equiv$

ai
k
c

k has listened to ai c times
term frequence $\overline{f}\equiv$

di
tk
f

listener fanaticism $\overline{f}\equiv$

ai
k
f

f percent of the time ai was listened to by k
document frequence $\overline{F}\equiv$

tk
F

listener promiscuity $\overline{F}\equiv$

k
F

k has listened to F percent of the artists
tf-idf $\overline{\mathrm{tfidf}}\equiv$

di
tk
w

dedicated fanaticism $\overline{\mathrm{df}}\equiv$

ai
k
w

The basic reasoning here is: a user who is a big fan of a limited number of artists is more likely to be focused within similar artists.

The cosine similarity is identical since both methods produce the tuples (or vectors) with the same positional meanings. The question is how similar the results will be.