Multi-View and Multi-Order Structured Graph Learning

Recently, graph-based multi-view clustering (GMC) has attracted extensive attention from researchers, in which multi-view clustering based on structured graph learning (SGL) can be considered as one of the most interesting branches, achieving promising performance. However, most of the existing SGL methods suffer from sparse graphs lacking useful information, which normally appears in practice. To alleviate this problem, we propose a novel multi-view and multi-order SGL (M
$^2$
SGL) model which introduces multiple different orders (multi-order) graphs into the SGL procedure reasonably. To be more specific, M
$^2$
SGL designs a two-layer weighted-learning mechanism, in which the first layer truncatedly selects part of views in different orders to retain the most useful information, and the second layer assigns smooth weights into retained multi-order graphs to fuse them attentively. Moreover, an iterative optimization algorithm is derived to solve the optimization problem involved in M
$^2$
SGL, and the corresponding theoretical analyses are provided. In experiments, extensive empirical results demonstrate that the proposed M
$^2$
SGL model achieves the state-of-the-art performance in several benchmarks.