# Tensioned Multi-View Ordered Kernel Subspace Clustering
## 2 Incomplete Multi-View Subspace Clustering  
In most cases, each view of data is updated independently. So, the missing effective information contained in each view will lead to clustering errors in the case of incomplete multi-view situations. Early multi-view learning models (as it is shown in Table 1) such as Weighted Multi-view spectral clustering based on spectral perturbation (WMSC), Affinity aggregation for spectral clustering (AASC) and Multi-view Clustering via Adaptively Weighted Procrustes (AWP) directly ignore non-existing information [5; 6; 7] and do not fill in the missing data. These model learning methods only use complete multi-view information. Naturally, they cannot handle incomplete multi-view data. These models are to continue to be used at the expense of sacrificing certain valuable information. For incomplete clustering, a naive idea is to try to adopt the data completion method. [PERSON] [15] selected the overlapping parts of views for alignment. Furthermore, he made full use of the feature transformation of the cross-views to complete the unobserved samples and carried out modeling. [PERSON] [16] proposed an algorithm to achieve incomplete kernel completion based on low-redundancy multi-kernel and then captured the approximate subspace representation. However, such data-filling methods are prone to producing noise, which gives rise to similar instances in the same view not being well grouped. Multi-kernel learning (MKL) relies on experience to integrate different kernel functions [17; 18]. However, on this multi-view dataset with a missing sample, incomplete kernel inputs lead to difficulty in aligning multiple kernels, resulting in poor performance of kernel-based methods. DKLM utilizes a data-driven technique to retain the local manifold structure within each nonlinear subspace, thereby obtaining high-quality spectral clustering. Meanwhile, Deep Subspace Clustering Networks (DSCN) are also carried out through deep semantic mapping and are a popular modern approach [19]. Average value completion or the third subspace completion always adopts a shallow clustering structure, which cannot well handle the dependencies and differences among views. In fact, there are higher-order connections among views to construct the consensus matrix. Tensors are experts in expressing the senior-order correlation among multi-view samples in space clustering [20]. The secret lies in fully considering the clustering structure to improve the final performance. This structural characteristic of the tensor pays more attention to the clustering structure of the multi-view data to uncover the latent information from the missing data. The Low-rAnk Tensor regularization viEws Recovery (LATER) [21] jointly reconstructed and utilized the missing views in a unified model. Moreover, it learned multi-layer graphs for comprehensive similarity discovery. The low-rank tensor Learning (LRTL) method [22] fused multi-view embedding matrices to form a three-norm tensor, which aimed to obtain consistent low-dimensional embedding characteristics. While in the tensor low-rank constrained learning model [23], the tensor Schatchen p norm served as a closer approximation for tensor rank in clustering, maintaining consistency and uniqueness. The above-mentioned methods performed particularly well when dealing with missing multi-view \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Characteristics**} & \multirow{2}{*}{**Methods**} & **All Kinds of** & \multirow{2}{*}{**Kernel Functions**} & **Existence of Tensor** \\  & & **Incomplete Case** & & **Structures** \\ \hline DSCN & Deep Networks & \multirow{2}{*}{Partily} & convolutional & \multirow{2}{*}{Yes} \\ WMSC & Spectral Perturbation & No & No & No \\ AASC & Affinity Aggregation & No & No & No \\ AWP & Adaptively Weighted & No & No & No \\  & Procrustes & & & No \\  & Tensioned & & & \\  & Incomplete & & & \\ TIMKSC & Multi-View Kernel & Yes & Multi-kernels & Yes \\  & Space Clustering & & & \\ \hline \hline \end{tabular}
\end{table}