Study On Spectral Clustering For High-dimensional Data

Spectral clustering is widely applied because it can identify the internal patterns in data sets.However,data sets in practical applications are generally characterized by high dimension,complexity and diversity and so on,which leads to the problems of poor robustness of existing spectral clustering methods.Therefore,the dissertation aims at an efficient and accurate spectral clustering for high-dimensional data,especially different types of data,by combining sparse learning,dimension reduction,graph learning and so on,and deeply studies the graph representation construction and optimization.Specifically,the dissertation proposes four spectral clustering methods for high-dimensional data,and then explores the fusion problem of various high-dimensional clustering methods.The main contributions of the dissertation are as follows:1.A one-step clustering method based on spectral rotation is proposed for highdimensional data.There are mainly three problems that limit the performance of traditional clustering,including the diversity and complexity of data distribution,the highdimensional data with redundancy usually,and the multi-step learning strategy which is easy to lead to the suboptimal clustering results.To address the above problems,subspace learning and attribute selection are utilized to reduce the influence of redundant information of original data,and robust spectral representation is learned to capture the intrinsic relationship of data.Furthermore,hypergraphs during subspace learning are constructed to learn the spectral representation to preserve higher-order data relationships.In addition,one-step spectral rotation clustering is applied to obtain the final clustering result,and then an effective optimization algorithm for the proposed method is proposed to solve the objective function with faster convergence.Finally,experimental analysis on real data sets proves that the proposed clustering method is superior to the classical spectral clustering methods in terms of four common clustering evaluation indexes.2.A high-dimensional clustering method based on balanced constraints is further proposed for high-dimensional data with a proportional degree of model results.Due to the inherent characteristics of data distribution,traditional clustering methods cannot guarantee the balance of clustering results,which is inconsistent with many practical requirements.Based on the one-step spectral rotation clustering,the robust lowdimensional spectral representation,spectral rotation and clustering indicator matrix are optimized in a unified learning framework.What’s more,the Exclusive Lasso regularization term(cluster balance penalty factor)is added to constrain the clustering result generating a similar size of clusters.In addition,an iterative optimization algorithm is proposed to solve the objective function quickly.Compared with other clustering methods on real data sets,the experimental results show that the proposed clustering method can simultaneously output the more balanced clustering results,and the superior clustering performance.3.A one-step spectral rotation clustering based on balanced self-paced learning is proposed for imbalanced and high-dimensional data.In real applications,data usually have high-dimension and imbalanced distribution.However,conventional clustering methods ignore the redundancy of high-dimensional data by disordering the distribution.Moreover,the existing clustering methods generally only favor the clustering results of clusters with large samples,but they ignore the clustering performance of clusters with small samples,which are often more valuable for research.To tackle these problems,the dissertation applies balanced self-paced learning to learn the sample weight during the training process and conduct balanced sampling,and then integrates the feature selection and sample selection during model training,eventually improving the robustness of models.Experimental results on synthetic data sets and real-world imbalanced data sets demonstrate that the proposed method could quickly obtain competitive clustering performance.4.Global and local structure preservation for nonlinear high-dimensional spectral clustering is proposed.Because the traditional spectral clustering method only considers the global structure information or local structure information of data,it cannot provide comprehensive data information for the clustering task.In addition,the traditional clustering methods only consider the similarity relation of Euclidean space,which may not get the optimal clustering performance in nonlinear space.To solve these problems,the dissertation considers preserving both the global and local structure of data,exploring the nonlinear similarity relationship,and embedding dimension reduction and the low-rank constraint into the adaptive graph learning framework.These constraints are considered in the unified optimization framework to achieve one-step clustering.Experimental results on real data sets show that the proposed method has a better clustering performance than the existing methods.