---
# System prepended metadata

title: Reciprocal Recommendation

---

# Reciprocal Recommendation

![](https://i.imgur.com/AXzeKdZ.png)


## Content-based filtering

![](https://i.imgur.com/8jj1y4n.png)

![](https://i.imgur.com/DRSCYHa.png)

![](https://i.imgur.com/ra45KAe.png)

![](https://i.imgur.com/rz2LCAs.png)

![](https://i.imgur.com/CXHVk9Z.png)

![](https://i.imgur.com/OuizT5n.png)


![](https://i.imgur.com/qI1YReH.png)


## Collaborative-based filtering

![](https://i.imgur.com/XmeLuOz.png)

![](https://i.imgur.com/AXzeKdZ.png)

![](https://i.imgur.com/zdi3WLG.png)
![](https://i.imgur.com/eWT9OGf.png)
![](https://i.imgur.com/EEcX8Bd.png)


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):
    
![](https://i.imgur.com/6czLDoM.png)
    
    = 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):
    
![](https://i.imgur.com/6czLDoM.png)
    
    = 2 / ((1/12)**-1 + (1/4)**-1)
    = 0.125