# Tensioned Multi-View Ordered Kernel Subspace Clustering
## 1 Introduction  
With the exponential growth of online data, clustering tasks enable people to get rid of the heavy workload of grouping, and automatically labeling samples becomes possible. Sparse Subspace Clustering algorithms can effectively capture the intrinsic geometric characteristics of data [1] to carry out effective data segmentation [2, 3]. Nowadays, multi-view heterogeneous data have brought about various forms of expression online; as a result, multi-view subspace clustering has become mainstream. For example, when a visual object is caught by different cameras with different angles, the visual object can be presented with different views with diverse rotation views and distinct zoom compositions. In this way, multi-view data enriches the information of the samples. Naturally, multi-view subspace clustering mines complementary information from different perspectives, which is helpful for identifying potential low-dimensional subspace structures in high-dimensional datasets [4]. Current multi-view subspace clustering algorithms work well, relying on complete multi-view data. But in real life, the data of views are often missing seriously, so incomplete multi-view subspace clustering algorithms face great challenges, while normal multi-viewmethods have no effect [5; 6; 7] under these circumstances. For example, due to the different camera lights or angles, the obtained data often suffers from information loss in real scenarios. These reasons limit clustering tasks to acquire low-dimensional representations of data with incomplete feature descriptions. In text analysis, various language grammatical structures and expressions result in distinct semantic information. There is no doubt that data deficiency will disrupt the correlation between different views of the original data, and it can lead to different emotional orientations. In scenarios of treatment, the loss of sample data due to sensor failures is very common, and the legacy data is often accompanied by complex noise. Of course, the loss of samples may be random, regular, or even related to some variables. Therefore, in the big data era, it is extremely difficult to accurately identify these loss patterns, and multi-view subspace clustering algorithms are difficult to effectively handle these complex scenarios. So, incomplete multi-view subspace clustering has turned into a research hotspot with great challenges. Incomplete data results in the loss of the effective information they contain. [PERSON] generated the probability distribution [8] for each sample of each view, attempting to learn the unified probability distribution of the sample in distinct views with the merging method, and such an integrated embedding was generated in the low-dimensional space to effectively preserve the neighbor relationship. [PERSON] obtained the robust graph representation of each view through semi-non-negative matrix factorization and then used Laplacian regularization to perform fusion learning on the graph [9]. The discriminative Sparse Representation learning (DSRL) model measured the similarity of existing features and simultaneously integrates the sparse regularization term and the consistent regularization term to learn a discriminative dictionary [10] from the original samples. [PERSON] adopted a multi-view graph learning technique in spectral subspace incomplete clustering for the general representation and then used k-means for data partitioning [11]. The adversarial Incomplete Multi-view Subspace Clustering [12] framework combined element reconstruction and generative adversarial networks to seek common latent representations of multi-view data for inferring missing data. Another framework with Robust Matrix Completion [13] introduced low-rank constraints to estimate missing values. These shallow models above often ignore the clustering structure characteristics among multi-view data, thus failing to mine the dependencies between different views well.