During the past years, multi-view clustering algorithms have demonstrated satisfactory clustering results by fusing the multiple views of the dataset. Nowadays, the researches of dimensionality reduction and learning discriminative features from multi-view data have soared in the literatures. As for clustering, generating the suitable subspace of the high dimensional multi-view data is crucial to boost the clustering performance. In addition, the relationship between the original data and the clusters still remains uncovered. In this article, we design a new multi-view low rank sparse representation method based on three-way clustering to tackle these challenges, which derive the common consensus low dimensional representation from the multi-view data and further proceed to get the relationship between the data items and clusters. Specifically, we accomplish this goal by taking advantage of the low-rank and the sparse factor on the data representation matrix. The \(L_{2,1}\) norm is imposed on error matrix to reduce the impact of noise contained in the data. Finally, a new objective function is constructed to preserve the consistency between the views by using the low-rank sparse representation technique. The weighted low-rank matrix is utilized to build the consensus low rank matrix. Then, the whole objective function is optimized by using the Augmented Lagrange’s Multiplier algorithm. Further, to find the uncertain relationship between the data items and the clusters, we pursue the neighborhood based three-way clustering technique to reflect the data items into core and fringe regions. Experiments conducted on the real-world datasets show the superior performance of the proposed method compared with the state-of-the-art algorithms.

在过去的几年中，多视图聚类算法通过融合数据集的多个视图显示了令人满意的聚类结果。如今，从多视图数据中降维和学习判别特征的研究在文献中猛增。对于聚类，生成高维多视图数据的合适子空间对于提高聚类性能至关重要。此外，原始数据和集群之间的关系仍然没有被发现。在本文中，我们设计了一种新的基于三向聚类的多视图低秩稀疏表示方法来应对这些挑战，从多视图数据中得出共同的共识低维表示，并进一步得到数据项和集群。具体来说，我们通过利用数据表示矩阵上的低秩和稀疏因子来实现这一目标。这\(L_{2,1}\)范数被施加在误差矩阵上，以减少数据中包含的噪声的影响。最后，通过使用低秩稀疏表示技术构造了一个新的目标函数来保持视图之间的一致性。加权低秩矩阵用于构建共识低秩矩阵。然后，使用Augmented Lagrange's Multiplier算法优化整个目标函数。此外，为了发现数据项和聚类之间的不确定关系，我们采用基于邻域的三向聚类技术将数据项反映到核心和边缘区域。在真实世界数据集上进行的实验表明，与最先进的算法相比，所提出的方法具有优越的性能。