Individual privacy preservation has become an important issue with the development of big data technology. The definition of ρ-differential identifiability (DI) precisely matches the legal definitions of privacy, which can provide an easy parameterization approach for practitioners so that they can set privacy parameters based on the privacy concept of individual identifiability. However, differential identifiability is currently only applied to some simple queries and achieved by Laplace mechanism, which cannot satisfy complex privacy preservation issues in big data analysis. In this paper, we propose a new exponential mechanism and composition properties of differential identifiability, and then apply differential identifiability to k-means and k-prototypes algorithms on MapReduce framework. DI k-means algorithm uses the usual Laplace mechanism and composition properties for numerical databases, while DI k-prototypes algorithm uses the new exponential mechanism and composition properties for mixed databases. The experimental results show that both DI k-means and DI k-prototypes algorithms satisfy differential identifiability.

In the era of big data, next-generation sequencing produces a large amount of genomic data. With these genetic sequence data, research in biology fields will be further advanced. However, the growth of data scale often leads to privacy issues. Even if the data is not open, it is still possible for an attacker to steal private information by a member inference attack. In this paper, we proposed a private profile hidden Markov model (PHMM) with differential identifiability for gene sequence clustering. By adding random noise into the model, the probability of identifying individuals in the database is limited. The gene sequences could be unsupervised clustered without labels according to the output scores of private PHMM. The variation of the divergence distance in the experimental results shows that the addition of noise makes the profile hidden Markov model distort to a certain extent, and the maximum divergence distance can reach 15.47 when the amount of data is small. Also, the cosine similarity comparison of the clustering model before and after adding noise shows that as the privacy parameters changes, the clustering model distorts at a low or high level, which makes it defend the member inference attack.