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.

翻译：基于张量的多视角子空间聚类（MSC）能够捕捉自表示张量的高阶相关性。当前用于MSC的张量分解方法存在展开矩阵高度不平衡或旋转敏感性问题，无法充分探索视角间/视角内的信息。利用先进的张量网络——多尺度纠缠重整化拟设（MERA），我们提出一种基于低秩MERA的MSC算法（MERA-MSC），其中MERA将张量分解为一个顶部核心因子与其余正交/半正交因子的缩并。得益于正交/半正交（低秩）因子间的多重交互，低秩MERA具有强大的表征能力，能够捕捉自表示张量中复杂的视角间/视角内信息。采用交替方向乘子法求解该优化模型。在五个多视角数据集上的实验结果表明，MERA-MSC在六项评估指标上均优于对比算法。此外，我们通过引入锚点学习扩展MERA-MSC，提出一种可扩展的基于低秩MERA的多视角聚类方法（sMERA-MVC）。在三个大型多视角数据集上验证了sMERA-MVC的有效性与效率。据我们所知，这是首次将MERA引入多视角聚类领域的工作。MERA-MSC与sMERA-MVC的代码已公开于 https://github.com/longzhen520/MERA-MSC。