  In recent years, data streaming has gained prominence due to advances in
technologies that enable many applications to generate continuous flows of
data. This increases the need to develop algorithms that are able to
efficiently process data streams. Additionally, real-time requirements and
evolving nature of data streams make stream mining problems, including
clustering, challenging research problems.
  In this paper, we propose a one-pass streaming soft clustering (membership of
a point in a cluster is described by a distribution) algorithm which
approximates the "soft" version of the k-means objective function. Soft
clustering has applications in various aspects of databases and machine
learning including density estimation and learning mixture models. We first
achieve a simple pseudo-approximation in terms of the "hard" k-means algorithm,
where the algorithm is allowed to output more than $k$ centers. We convert this
batch algorithm to a streaming one (using an extension of the k-means++
algorithm recently proposed) in the "cash register" model. We also extend this
algorithm when the clustering is done over a moving window in the data stream.
