Multi-view Clustering Via Graph Learning

With the rapid development of Internet and sensor technology,the acquired data evolved from the past single view description to the ubiquitous multiple views description.Therefore,multi-view learning become a research hotspot in artificial intelligence,machine learning and other fields.As a main research direction,multi-view clustering has developed rapidly in the past few decades.Therein,the graph learning methods have attracted increasing attention due to their simplicity and efficiency.However,affected by the heterogeneous information between different views and the possible noise,most of these methods are limited to the fact that the shared graph directly learned from multiple views or graphs can not well depict the intrinsic structure of all views.To address these problems,the paper studies robust graph learning based methods from graph input and sample input respectively.Specifically,there are four methods as follows.The existing Markov based multi-view clustering methods ignore the priori target rank information,degrade the clustering performance for noised multi-view data.To address this problem,we propose a novel multi-view clustering method via integrating global and local graphs,which efficiently embeds the prior information of target rank into the uniform graph learning model,by minimizing the partial sum of singular values(PSSV)instead of the nuclear norm.In this method,both the local and global geometric structure are considered by using both the local graph from each view and the global graph from the concatenated features as the input graphs.Extensive experimental results on one synthetic and eight benchmark datasets demonstrate that the proposed method outperforms the stateof-the-art approaches.The existing graph input clustering methods directly employ the graphs calculated from the original multi-view data as dictionaries to learn the similarity matrix shared by multiple views.This reduces the flexibility of these methods due to the fact that multi-view data usually contain noise or the variation between multi-view data points,which should belong to the same cluster,is larger than the variation between data points belonging to different clusters.To address these problems,we propose a novel method,namely graph-based latent subspace learning for multi-view clustering(GSL-MC).GSL-MC linearly projects the graphs calculated from each view into a shared subspace,and simultaneously performs manifold learning on the obtained latent subspace to adaptively learn the similarity matrix.Finally,GSL-MC integrates the latent graph subspace learning,manifold learning and spectral clustering into a unified framework.Thus,the complementarity of multiple views,the local structure and the clustering structure are all efficiently exploited.Our model is intuitive and can be optimized efficiently by using the augmented Lagrangian multiplier algorithm.Extensive experiments on benchmark datasets demonstrate the superiority of the proposed method.The similarity matrix,which is learned by the existing multi-view clustering methods via subspace learning,cannot well characterize both the intrinsic geometric structure of the latent representation and the neighbor relationship between data.To overcome this problem,we linearly transform the original data to a low-dimensional subspace which is shared by all views,and simultaneously perform manifold learning on the derived latent representation to adaptively learn a shared similarity matrix.The learned latent representation has a lowrank structure without solving the nuclear norm,which efficiently reduces the computational complexity.Finally,we integrate clustering,manifold learning,and latent representation learning into a unified framework and develop a novel multi-view clustering method via latent similarity learning.Consequently,the adaptively learned latent representation and similarity matrix can well depict the intrinsic structure and clustering structure.Extensive experiments on five benchmark datasets demonstrate the superiority of our method.Despite the promising preliminary results,the tensor nuclear norm based multi-view clustering methods are incapable of dealing with real problems such as noise and illumination changes.The major reason is that tensor nuclear norm minimization(TNNM)regularizes each singular value equally,which does not make sense in the existence of noise.In this case,the singular values represent different perspectives and should be treated differently.To this end,we embed the prior knowledge of each singular value into the tensor-Singular Value Decomposition(t-SVD)based nuclear norm,study the weighted tensor nuclear norm based on t-SVD and develop an efficient algorithm to solve the weighted TNNM(WTNNM)problem.Theoretical analysis illustrates that the existing tensor nuclear norm minimization model is a special case of the proposed model.We further apply the WTNNM algorithm to multi-view clustering by exploiting the high order correlations embedded in different views.Extensive experimental results reveal that our WTNNM method is superior to several state-of-the-art multi-view clustering methods in terms of performance.