I am reading SimRank paper by Jeh and Widom which tries to find the similarity between objects based on the relationships between them. Effectively, SimRank is a measure that says "two objects are similar if they are related to similar objects."

Let us denote the similarity between objects a and b by $s(a, b) \in [0, 1]$. Following the earlier motivation, a recursive equation is written for $s(a, b)$. If $a = b$ then $s(a, b)$ is defined to be 1. Otherwise,

$s(a, b) = \frac{C}{\left|I(a)\right| \left|I(b)\right|} \sum_{i=1}^{\left|I(a)\right|}\sum_{j=1}^{\left|I(b)\right|} s(I_i(a), I_j(b))$

where $C$ is a constant between 0 and 1.

I was wondering about whether we can incorporate any prior information about objects(Taking a semi-supervised approach). By prior information, I mean that we have similarities between some pair of objects(which may be rough/inconsistent). I tried to change the initialization in the process but proved later that the system of equations is independent of the initialization. Any thoughts on the same.



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