  Graph-based clustering methods have demonstrated the effectiveness in various
applications. Generally, existing graph-based clustering methods first
construct a graph to represent the input data and then partition it to generate
the clustering result. However, such a stepwise manner may make the constructed
graph not fit the requirements for the subsequent decomposition, leading to
compromised clustering accuracy. To this end, we propose a joint learning
framework, which is able to learn the graph and the clustering result
simultaneously, such that the resulting graph is tailored to the clustering
task. The proposed model is formulated as a well-defined nonnegative and
off-diagonal constrained optimization problem, which is further efficiently
solved with convergence theoretically guaranteed. The advantage of the proposed
model is demonstrated by comparing with 19 state-of-the-art clustering methods
on 10 datasets with 4 clustering metrics.
