An Active Three-way Clustering Method Via Low-rank Representation For Multi-view Data

In recent years,multi-view clustering algorithms have shown promising performance by combining multiple sources or views of datasets.A problem that has not been addressed satisfactorily is the uncertain relationship between an object and a cluster.For highdimensional data,traditional similarity measurement methods based on distance measures become inapplicable.Thus,this thesis conducts the research on the multi-view clustering problem of high dimensional data via low-rank representation,three-way clustering and active learning methods.This thesis adopts a three-way clustering representation to describe the uncertainty between an object and a cluster.Different with the traditional hard clustering methods which use two regions to describe a cluster.The three-way clustering representation uses three regions,namely,core region,fringe region and trivial region,to reflect the three types of relationships between an object and a cluster,namely,belong-to definitely,uncertain and not belong-to definitely.Objects located at the edge of clusters can be observed intuitively through three-way clustering representation.This thesis proposes a multi-view data fusion algorithm based on low-rank representation to obtain the consistent information from multiple views.In the algorithm,multiple views are projected into one common lower dimensional subspace and the lowrank constraint is applied on each view.The solution of its global optimization problem is used for constructing similarity graph.Consider the diversity among different views,a consistent low-rank matrix is introduced which represents the latent clustering structure shared by all views.The weight of each view also can be adjusted adaptively by measuring the inconsistency between the consistent low-rank matrix with low-rank matrix of each view.The optimization problem of objective function is solved by the improved augmented Lagrangian multiplier algorithm.Several experiments are conducted on real-world datasets such as SensIT,3-Sources and Digits.With the aid of the three-way clustering representation,this thesis devises an active learning strategy based on uncertainty sampling.It measures the uncertainty of objects in fringe regions based on the entropy concept,and the object with the highest uncertainty is selected to be queried.Obviously,it is reasonable that to restrict the searching space to fringe regions according to the meaning of the three-way clustering.Thus,the cost of searching is much less than that of in the universe.Several experiments are conducted on real-world datasets,which validate the effectiveness of the proposed method.