Design Considerations for a Social Network-Based Recommendation System (SNRS) - Community-Built Databases: Research and Development - page 102

Dining

Asian Food

European Food

Thai Food Chinese Food Japanese Food French Food Italian Food

Fig. 4.10 A TAH for relaxation of food styles

similarity between category C and category T . Thus, homophily effects among
friends U and V can be estimated as,

Hist W CT ð ð R UI R VI Þ Þ I 2 I ð U Þ\ I ð V Þ (4.12)

Equation (4.12) counts U' sand V' s rating differences on all of their commonly
reviewed items. But for each item I that they both reviewed, the contribution of
the rating difference on I to the final histogram is multiplied by a factor of W CT
which is the similarity between the categories to which the target item and item
I belong.
Given two categories C and T , the value of W CT can be decided based on the
following two observations. First, let us define D ( C , T ) as the distance from
categories C and T to their lowest common ancestor LCA( C , T ) in the TAH.
(Note that C and T are the leaf nodes in the same depth.) The smaller the distance,
the closer C and T are in the domain space; thus, they are more closely related.
Second, categories in a specific domain are more strongly related to one another
than in general domains. We use

j

LCA( C , T )

j

as the number of all the leaf nodes
under LCA( C , T ) to measure its generalities. The larger

j

LCA( C , T )

j

, the more
general the domain space that both C and T belong to. Following these observa-
tions, we propose to measure W CT as in (4.13).

(

1

if C ¼ T

;
otherwise

W CT ¼ (4.13)

:

D ð C T Þ

log 2 ðj

ð C T Þj þ Þ

; LCA ; 1

1
log 2 4 ¼

Therefore, the similarity between Thai food and Chinese food is 0 5

: ;

1
2log 2 6 ¼

while the similarity between Thai food and Italian food is 0 19 Since

: :

0.19 is less than 0.5, it is consistent with our intuition. Note that similar intuitions
have been used to estimate the similarity between two concepts in a TAH [ 29 ]. The
difference in our work is that we estimate the similarity between leaf nodes in a
TAH, while [ 29 ] has no such a restriction. In addition, (4.13) assumes a linear decay
model of W CT in D ( C,T ), which is arguable. Future work can be made on selecting a
better model to fit a specific domain.
Once we obtain W CT , the homophily of a pair of users can be quantified [as
shown in (4.12)]. By doing so, even though these two users may not have enough