  Tensor-based multi-view subspace clustering (MSC) can capture high-order
correlation in the self-representation tensor. Current tensor decompositions
for MSC suffer from highly unbalanced unfolding matrices or rotation
sensitivity, failing to fully explore inter/intra-view information. Using the
advanced tensor network, namely, multi-scale entanglement renormalization
ansatz (MERA), we propose a low-rank MERA based MSC (MERA-MSC) algorithm, where
MERA factorizes a tensor into contractions of one top core factor and the rest
orthogonal/semi-orthogonal factors. Benefiting from multiple interactions among
orthogonal/semi-orthogonal (low-rank) factors, the low-rank MERA has a strong
representation power to capture the complex inter/intra-view information in the
self-representation tensor. The alternating direction method of multipliers is
adopted to solve the optimization model. Experimental results on five
multi-view datasets demonstrate MERA-MSC has superiority against the compared
algorithms on six evaluation metrics. Furthermore, we extend MERA-MSC by
incorporating anchor learning to develop a scalable low-rank MERA based
multi-view clustering method (sMREA-MVC). The effectiveness and efficiency of
sMERA-MVC have been validated on three large-scale multi-view datasets. To our
knowledge, this is the first work to introduce MERA to the multi-view
clustering topic. The codes of MERA-MSC and sMERA-MVC are publicly available at
https://github.com/longzhen520/MERA-MSC.
