A Study Of Multi-view Subspace Clustering Algorithms Based On Projection And Unified Anchors

Subspace clustering,as an effective way to accomplish clustering of high-dimensional data,has shown the potential of its self-expression framework that has attracted a lot of attention from researchers.As an extension of subspace clustering,multi-view subspace clustering can effectively fuse multi-view information in multimedia applications.However,there are still some performance bottlenecks: 1)Multiple kernel subspace clustering outputs low-quality graph matrix degrading clustering performance? 2)Anchor-based Subspace Clustering selects weak discriminate anchor points.To solve these problems,we proposes corresponding solutions:1)We propose an algorithm named as Projective Multiple Kernel Subspace Clustering(PMKSC).To be specific,The key issue for Multiple kernel subspace clustering is to build flexible and appropriate graph for clustering from kernel space.However,existing MKSC methods apply the mechanism that they utilize the kernel trick on the traditional self-expressive principle where the similarity graphs are built on the respective high-dimensional(or even infinite)Reproducing Kernel Hilbert Space.We argue for this strategy that the original high-dimensional spaces usually include noise,unreliable similarity measures and therefore output low-quality graph matrix degrading clustering performance.In this paper,inspired by projective clustering,we propose to utilize the complementary similarity graph by fusing multiple kernel graphs constructed in the lowdimensional partition space.By incorporating the intrinsic structures with multi-view data,PMKSC alleviates the noise and redundancy in original kernel space and obtains high-quality similarity to uncover the underlying clustering structures.Furthermore,we design a three-step alternate algorithm with proved convergence to solve the proposed optimization problem.Compared with state-of-the-art multiple kernel and kernel subspace clustering methods,Extensive experiments prove that our proposed algorithm is effective and advanced.2)We propose an algorithm named as Scalable Multi-view Subspace Clustering with Unified Anchors(SMVSC).To be specific,Considering that most existing Multiview subspace clustering approaches’ cubic time complexity makes it challenging to apply to realistic large-scale scenarios,some researchers have addressed this challenge by sampling anchor points to capture distributions in different views.However,the separation of the heuristic sampling and clustering process leads to weak discriminate anchor points.Moreover,the complementary multi-view information has not been well utilized since the graphs are constructed independently by the anchors from the corresponding views.To address these issues,we combine anchor learning and graph construction into a unified optimization framework.Therefore,the learned anchors can represent the actual latent data distribution more accurately,leading to a more discriminative clustering structure.Most importantly,the linear time complexity of our proposed algorithm allows the multiview subspace clustering approach to be applied to large-scale data.Then,we design a four-step alternative optimization algorithm with proven convergence.Compared with state-of-the-art multi-view subspace clustering methods and large-scale methods,Extensive experiments demonstrate that our method is efficient and effective.