  The streaming model is an abstraction of computing over massive data streams,
which is a popular way of dealing with large-scale modern data analysis. In
this model, there is a stream of data points, one after the other. A streaming
algorithm is only allowed one pass over the data stream, and the goal is to
perform some analysis during the stream while using as small space as possible.
Clustering problems (such as $k$-means and $k$-median) are fundamental
unsupervised machine learning primitives, and streaming clustering algorithms
have been extensively studied in the past. However, since data privacy becomes
a central concern in many real-world applications, non-private clustering
algorithms are not applicable in many scenarios.
  In this work, we provide the first differentially private streaming
algorithms for $k$-means and $k$-median clustering of $d$-dimensional Euclidean
data points over a stream with length at most $T$ using $poly(k,d,\log(T))$
space to achieve a constant multiplicative error and a $poly(k,d,\log(T))$
additive error. In particular, we present a differentially private streaming
clustering framework which only requires an offline DP coreset or clustering
algorithm as a blackbox. By plugging in existing results from DP clustering
Ghazi, Kumar, Manurangsi 2020 and Kaplan, Stemmer 2018, we achieve (1) a
$(1+\gamma)$-multiplicative approximation with
$\tilde{O}_\gamma(poly(k,d,\log(T)))$ space for any $\gamma>0$, and the
additive error is $poly(k,d,\log(T))$ or (2) an $O(1)$-multiplicative
approximation with $\tilde{O}(k^{1.5} \cdot poly(d,\log(T)))$ space and
$poly(k,d,\log(T))$ additive error. In addition, our algorithmic framework is
also differentially private under the continual release setting, i.e., the
union of outputs of our algorithms at every timestamp is always differentially
private.
