Research On Clustering Algorithm Based On High Order Information

The rapid development of data mining has created a subsequent need for designing clustering strategies for multi-view data.However,both the performance of single-view and multiview clustering methods hinges on the used pairwise affinity,which is insufficient to capture the structure of data and model the affinity between samples.Thus,how to effectively capture the structure of data is an urgent problem to be solved for designing clustering algorithms.To alleviate this dilemma,a new measurement is proposed to model the high order information of the data for improving the clustering performance of the traditional clustering algorithm.This paper concentrates on utilizing the high order information to improve the clustering performance of traditional models,developing a series of research for single-view and multi-view datasets.And it proposes a single-view clustering model based on tensor similarity,a multi-dimensional clustering through a fusion of high-order similarities and a multi-view clustering based on selfweighted high-order similarity fusion,respectively.The contributions of the paper are mainly concentrated in the following aspects:Firstly,we proposed a single-view clustering algorithm based on tensor similarity.The model defines a fourth-order tensor for modeling the relationships between pairs,aiming to provide the complementary information for the pairwise similarity which is notoriously known for being vulnerable to noise contaminations and failing to capture the structure for the dataset.There are two types of tensor similarity: decomposable and indecomposable,and we connect them with the pairwise similarity.Benefiting from this,we extract the high-order similarity from the tensor similarity,which can serve as the complementary information for pairwise relationships.Finally,the extracted high-order and pairwise similarities are fused for achieving accurate clustering performance.Extensive experiments demonstrate that the combination of the pairwise and high-order similarities effectively achieves accurate and robust clustering performance.The current work serves as a proof-of-concept study,for modeling the affinities among multiple samples,and incorporates it with the pairwise one to boost the clustering performance of conventional clustering algorithms.Secondly,a multi-dimensional clustering algorithm through a fusion of high-order similarities is proposed to tackle the issue that the pairwise relationship is insufficient to explore the potential structure of multi-view data.The high-order similarity takes the information between the latent space and different spaces into consideration to characterize the intrinsic relationship among different dimensional spaces.Based on this,we perform the clustering task within the latent space by jointly learning the high-order similarity and ordinary similarity.The proposed method provides a novel strategy to multi-view clustering through optimizing the high-order and traditional pairwise similarity regularization terms simultaneously,improving the accuracy and stability of the clustering model.Finally,a multi-view clustering model based on self-weighted high-order similarity fusion is proposed,which improves the stability of multi-view clustering algorithms through robust high-order information.The high-order similarity is formulated to flexibly capture the intrinsic structure of data,characterized by combining the interactions across views.A high-order regularization based on the defined similarity is incorporated into the model and assigned with self-weighted parameters,enabling the model to focus on mutual information among views.The experimental results on four real-world datasets show the effectiveness and efficiency of the proposed multi-view clustering with self-weighted high-order similarity regularization.In conclusion,this paper provides a detailed analysis and discussion on the problem of exploring the affinity between samples by using high-order information.For single-view data,a novel clustering algorithm based on tensor similarity is proposed;For multi-view data,a multiview clustering algorithm based on high-order similarity fusion is proposed,and we extend it to the self-weighted high-order similarity multi-view clustering to further improve the robustness of the model.A large number of theoretical analyses and experimental results demonstrate that the algorithms proposed in this paper provide a basic theory for the development of clustering based on high-order information,and promote the research of the related fields,such as pattern recognition and medical image segmentation.