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 {\it 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 algorithm as a blackbox. By plugging in existing DP coreset results via
Ghazi, Kumar, Manurangsi 2020 and Kaplan, Stemmer 2018, we achieve (1) a
(1+γ)-multiplicative approximation with
O~γ(poly(k,d,log(T))) space for any γ>0, and the
additive error is poly(k,d,log(T)) or (2) an O(1)-multiplicative
approximation with O~(k⋅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