# Reciprocal Recommendation


## Content-based filtering








## Collaborative-based filtering




interest_similarity(M1, M2):

=(Se(M1) intersect Se(M2) )/(Se(M1) Union Se(M2) )
=((F1,F2) intersect (F1,F3))/(F1,F2) Union (F1,F3) )
= F1/(F1,F2,F3)
= 1/3

attractiveness_similarity(F3,F1):

= (Re(F3) intersect Re(F1) )/(Re(F3) Union Re(F1) )
= ((M2,M3) intersect (M1,M2,M3)) / ((M2,M3) union (M1,M2,M3))
= (M2,M3) / (M1,M2,M3)
= 2/3

Compat(M1, F3):

= interest_similarity(M1, Re(F3))
= 1/2 *(interest_similarity(M1, M2) + interest_similarity(M1, M3))
= 1/2 * (1/3 + 2/4)
= 10/24
= 5/12

Compat(F3, M1):

= attractiveness_similarity(F3, Se(M1))
= 1/2 * (attractiveness_similarity(F3, F1) + attractiveness_similarity(F3, F2))
= 1/2 * (attractiveness_similarity(F3, F1) + attractiveness_similarity(F3, F2))
= 1/2 * (2/3 + 1/3)
= 1/2

Reciprocal_score(M3,F1):


= 2 / ((5/12)**-1 + (1/2)**-1)
= 0.45

Compat(M4, F1):

= interest_similarity(M4, Re(F1))
= 1/3 *(interest_similarity(M4, M1) + interest_similarity(M4, M2) + interest_similarity(M4, M3))
= 1/3 * (0 + 0 + 1/4)
= 1/12

Compat(F1, M4):

= attractiveness_similarity(F1, Se(M4))
= 1/1 * attractiveness_similarity(F1, F4)
= 1/4

Reciprocal_score(M2,F1):


= 2 / ((1/12)**-1 + (1/4)**-1)
= 0.125