  The emergence and rapid development of the Internet of Medical Things (IoMT),
an application of the Internet of Things into the medical and healthcare
systems, have brought many changes and challenges to modern medical and
healthcare systems. Particularly, machine learning technology can be used to
process the data involved in IoMT for medical analysis and disease diagnosis.
However, in this process, the disclosure of personal privacy information must
receive considerable attentions especially for sensitive medical data. Cluster
analysis is an important technique for medical analysis and disease diagnosis.
To enable privacy-preserving cluster analysis in IoMT, this paper proposed an
Efficient Differentially Private Data Clustering scheme (EDPDCS) based on
MapReduce framework. In EDPDCS, we optimize the allocation of privacy budgets
and the selection of initial centroids to improve the accuracy of
differentially private K-means clustering algorithm. Specifically, the number
of iterations of the K-means algorithm is set to a fixed value according to the
total privacy budget and the minimal privacy budget of each iteration. In
addition, an improved initial centroids selection method is proposed to
increase the accuracy and efficiency of the clustering algorithm. Finally, we
prove that the proposed EDPDCS can improve the accuracy of the differentially
private k-means algorithm by comparing the Normalized Intra-Cluster Variance
(NICV) produced by our algorithm on two datasets with two other algorithms.
