Tensor Decomposition Models And Algorithms For Multi-way Clustering

With the explosion of data,it has become one of the main challenges to mine useful knowledge from high-order data.Tensor decomposition provides powerful means for highorder data analysis.As an important unsupervised learning tool,clustering achieves efficient data compression and feature extraction under label-free conditions.Multi-way clustering not only inherits the advantages of classical clustering,but also makes good use of the multi-linear structure of high-order data to achieve simultaneous clustering and to mine the complex relationships in multiple dimensions.Accordingly,it is significant to explore multi-way clustering methods.However,the existing methods often perform a tensor decomposition first and then employ traditional clustering algorithms(e.g.K-means)in each dimension,which makes it difficult to obtain optimal performance.Moreover,these methods lack efficient means of dealing with cross-membership,large-scale and incomplete nature of the data.This study addresses the above challenges and presents the following original works:1.A flexible multi-way clustering model based on approximately orthogonal nonnegative Tucker decomposition(AONTD)is proposed for cross-membership analysis.With the equivalence of NMF and K-means,the latent “tensor block” structure can be revealed for multiway clustering.Besides,the constraint of approximate orthogonality allows the processing of multi-degrees or single-degree of membership(“soft-or hard-clustering”),as well as resistance to noise interference.Moreover,the constraint of cross-memberships “sum to 1” further ensures the accuracy of flexible multi-way clustering.The AONTD model also employs accelerated proximal gradient(APG)and hierarchical alternating least squares(HALS)to improve efficiency,achieving a more competitive performance compared to other methods.2.A random Tucker compression method(Rand Tucker)is proposed to address large-scale issue.The distributed Rand Tucker splits a big tensor into sub-tensors for easier processing,thus a big tensor decomposition is transformed into several small tensor decomposition.This is the basis for flexible fast CP decomposition(FFCP)and efficient multi-way clustering based on AONTD,providing an important tool for large-scale data compression and data mining.3.A clustering-based data completion method is proposed for data missing issue.Traditional completion methods exploit the low-rank properties of data and achieve data completion through SVD or its variants.Since SVD destroys the physical properties of data,we consider embedding the multi-way clustering into the tensor completion.In this way,the performance of data mining and data completion is simultaneously improved.Notably,this strategy is easy to implement and preserves the physical properties of data.Overall,this study provides important tools for big tensor analysis,which further expends the application area of tensor decomposition.