  In today's data-driven world, the sensitivity of information has been a
significant concern. With this data and additional information on the person's
background, one can easily infer an individual's private data. Many
differentially private iterative algorithms have been proposed in interactive
settings to protect an individual's privacy from these inference attacks. The
existing approaches adapt the method to compute differentially private(DP)
centroids by iterative Llyod's algorithm and perturbing the centroid with
various DP mechanisms. These DP mechanisms do not guarantee convergence of
differentially private iterative algorithms and degrade the quality of the
cluster. Thus, in this work, we further extend the previous work on
'Differentially Private k-Means Clustering With Convergence Guarantee' by
taking it as our baseline. The novelty of our approach is to sub-cluster the
clusters and then select the centroid which has a higher probability of moving
in the direction of the future centroid. At every Lloyd's step, the centroids
are injected with the noise using the exponential DP mechanism. The results of
the experiments indicate that our approach outperforms the current
state-of-the-art method, i.e., the baseline algorithm, in terms of clustering
quality while maintaining the same differential privacy requirements. The
clustering quality significantly improved by 4.13 and 2.83 times than baseline
for the Wine and Breast_Cancer dataset, respectively.
