  Several applications require counting the number of distinct items in the
data, which is known as the cardinality counting problem. Example applications
include health applications such as rare disease patients counting for adequate
awareness and funding, and counting the number of cases of a new disease for
outbreak detection, marketing applications such as counting the visibility
reached for a new product, and cybersecurity applications such as tracking the
number of unique views of social media posts. The data needed for the counting
is however often personal and sensitive, and need to be processed using
privacy-preserving techniques. The quality of data in different databases, for
example typos, errors and variations, poses additional challenges for accurate
cardinality estimation. While privacy-preserving cardinality counting has
gained much attention in the recent times and a few privacy-preserving
algorithms have been developed for cardinality estimation, no work has so far
been done on privacy-preserving cardinality counting using record linkage
techniques with fuzzy matching and provable privacy guarantees. We propose a
novel privacy-preserving record linkage algorithm using unsupervised clustering
techniques to link and count the cardinality of individuals in multiple
datasets without compromising their privacy or identity. In addition, existing
Elbow methods to find the optimal number of clusters as the cardinality are far
from accurate as they do not take into account the purity and completeness of
generated clusters. We propose a novel method to find the optimal number of
clusters in unsupervised learning. Our experimental results on real and
synthetic datasets are highly promising in terms of significantly smaller error
rate of less than 0.1 with a privacy budget {\epsilon} = 1.0 compared to the
state-of-the-art fuzzy matching and clustering method.
