  Multi-view subspace clustering methods have employed learned
self-representation tensors from different tensor decompositions to exploit low
rank information. However, the data structures embedded with
self-representation tensors may vary in different multi-view datasets.
Therefore, a pre-defined tensor decomposition may not fully exploit low rank
information for a certain dataset, resulting in sub-optimal multi-view
clustering performance. To alleviate the aforementioned limitations, we propose
the adaptively topological tensor network (ATTN) by determining the edge ranks
from the structural information of the self-representation tensor, and it can
give a better tensor representation with the data-driven strategy.
Specifically, in multi-view tensor clustering, we analyze the higher-order
correlations among different modes of a self-representation tensor, and prune
the links of the weakly correlated ones from a fully connected tensor network.
Therefore, the newly obtained tensor networks can efficiently explore the
essential clustering information with self-representation with different tensor
structures for various datasets. A greedy adaptive rank-increasing strategy is
further applied to improve the capture capacity of low rank structure. We apply
ATTN on multi-view subspace clustering and utilize the alternating direction
method of multipliers to solve it. Experimental results show that multi-view
subspace clustering based on ATTN outperforms the counterparts on six
multi-view datasets.
