Fig. 3

An example of many-to-one mapping for two different Cosine LSH-based hashcode vectors. In the example, the left hashcode vector is \(\{0,1,0, 1, 1,0,1,0,1\}\) and \(U=\{\{0,1,0\}, \{1,1,0\}, \{1,0,1\}\}\). Then the integer set \(u=\{2, 6, 5\}\) is computed through U. The modulo function is set in the format of \((a \times u_{i} + b) \mod M\), where \(a \in A\) =\(\{2,5,7\}\), \(b \in B= \{3, 1, 6\}\), \(|U_{i}| = 3\), \(n = 2\), and \(M = 3\) is the prime number closest to \(\lfloor 2^{|U_{i}|}/n \rfloor\) . The result of the modulo operation is \(v_i \in v\)= \(\{1,1,2\}\). Similarly, in the right side, we get the \(v'=\{0, 0, 2\}\). From the result, we can observe that 2 appears in both v and \(v'\) and with 1/2 probability to infer the \(u_{i}\) or \(u'_{i}\) correctly due to the modulo-based many-to-one mapping