  Nowadays, the message diffusion links among users or websites drive the
development of countless innovative applications. However, in reality, it is
easier for us to observe the timestamps when different nodes in the network
react on a message, while the connections empowering the diffusion of the
message remain hidden. This motivates recent extensive studies on the network
inference problem: unveiling the edges from the records of messages
disseminated through them. Existing solutions are computationally expensive,
which motivates us to develop an efficient two-step general framework,
Clustering Embedded Network Inference (CENI). CENI integrates clustering
strategies to improve the efficiency of network inference. By clustering nodes
directly on the timelines of messages, we propose two naive implementations of
CENI: Infection-centric CENI and Cascade-centric CENI. Additionally, we point
out the critical dimension problem of CENI: instead of one-dimensional
timelines, we need to first project the nodes to an Euclidean space of certain
dimension before clustering. A CENI adopting clustering method on the projected
space can better preserve the structure hidden in the cascades, and generate
more accurately inferred links. This insight sheds light on other related work
attempting to discover or utilize the latent cluster structure in the
disseminated messages. By addressing the critical dimension problem, we propose
the third implementation of the CENI framework: Projection-based CENI. Through
extensive experiments on two real datasets, we show that the three CENI models
only need around 20% $\sim$ 50% of the running time of state-of-the-art
methods. Moreover, the inferred edges of Projection-based CENI preserves or
even outperforms the effectiveness of state-of-the-art methods.
