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It first compares the similarity between the query q + and the user profile P u (i.e., s i m(q +,P u )) against the similarity between the query q + and the profile of fake queries P FQ (i.e., s i m(q +,P FQ )).
The algorithm determines if the similarity distance between the query q + and the user profile P id (i.e., s i m(q +,P id )) is greater than the similarity metric between the query q + and the profile of fake queries P FQ (i.e., s i m(q +,P FQ )).
If we consider first that the adversary does not have this external knowledge, it evaluates if the similarity between the query q + and the user profile P u is greater than a given threshold δ.
It first computes the value c o e f[i] corresponding to the Dice's coefficient [23] between the query q and the query q i stored in P u, the profile of user u (line 2).
The adversary is able to distinguish between fake queries and real ones by comparing the similarity between the query q + and the user profile P id (i.e., s i m(q +,P id )) with the threshold δ.
The SO could then be defined as:
Similar(51)
Let us consider the first case in which the query q + is composed of k+1 queries (i.e., the initial query and k fake queries).
The query Q could be a set of range queries that asks statistical information of the dataset.
For the purposes of this exposition, let the query Q = CCGTT and the subject S = TCGT.
where c(q i,u j ) is a function that defines the cost between the query vector q i and the utterance vector u j and mathrm{M}^{mathrm i,j) = text{min}left(mathrm{M}_{i-1,j},mathrm{M}_{i-1,j-1},mathrm{M}_{i,j-1}right), (3).
where s i, i∈{1,…,m}, is the cosine similarity1 between the query vector q and v i representing tweet t w i, and m i,j is the (normalized) term frequency of term t j in tweet t w i.
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