  Massive volumes of data continuously generated on social platforms have
become an important information source for users. A primary method to obtain
fresh and valuable information from social streams is \emph{social search}.
Although there have been extensive studies on social search, existing methods
only focus on the \emph{relevance} of query results but ignore the
\emph{representativeness}. In this paper, we propose a novel Semantic and
Influence aware $k$-Representative ($k$-SIR) query for social streams based on
topic modeling. Specifically, we consider that both user queries and elements
are represented as vectors in the topic space. A $k$-SIR query retrieves a set
of $k$ elements with the maximum \emph{representativeness} over the sliding
window at query time w.r.t. the query vector. The representativeness of an
element set comprises both semantic and influence scores computed by the topic
model. Subsequently, we design two approximation algorithms, namely
\textsc{Multi-Topic ThresholdStream} (MTTS) and \textsc{Multi-Topic
ThresholdDescend} (MTTD), to process $k$-SIR queries in real-time. Both
algorithms leverage the ranked lists maintained on each topic for $k$-SIR
processing with theoretical guarantees. Extensive experiments on real-world
datasets demonstrate the effectiveness of $k$-SIR query compared with existing
methods as well as the efficiency and scalability of our proposed algorithms
for $k$-SIR processing.
