Research On Fast And Effective Subspace Clustering Methods

Clustering analysis is an important unsupervised learning method,which aims to mine the potential data structure and rules in data and divide the data into multiple clusters.It is an important data analysis and processing tool in data mining,machine learning and signal processing areas,and has important research value and application prospects.With the development of computer technology and various sensor technologies,the ability of data acquisition and collection is greatly improved,and the dimension and scale of data are becoming larger and larger.Traditional clustering algorithm is no longer effective because it cannot overcome the curse of dimensionality.Subspace clustering algorithm takes advantage of the data characteristics that high-dimensional data may be distributed in multiple-subspaces structures,and divides the samples into multiple subspace clusters,which greatly improves the clustering performance on high-dimensional data.It has gradually become an important clustering analysis method for high-dimensional data,and has received extensive attention and research in the past decade.However,when it comes to the dataset with higher dimension and larger amount of data,the subspace clustering algorithm exposes the problems of low efficiency and low clustering performance.In addition,current subspace clustering algorithms can not effectively deal with time series data and data drawn from highly nonlinear manifolds.Aiming at the problems and shortcomings of existing subspace clustering algorithms in high-dimensional data processing,efficiency improvement,time series data processing and nonlinear manifold data processing,this paper proposes four fast and efficient clustering algorithms.The main work of this paper is as follows:(1)Aiming at the problem that the existing subspace clustering algorithms are lack of effective dimensionality reduction when dealing with high-dimensional data,this paper proposes a subspace clustering algorithm which simultaneously learns the dimensionality reduction projection matrix and the self-representation coefficient matrix.We design and implement a joint learning framework combining dimensionality reduction and selfrepresentation learning.Through the learning framework,the dimensionality reduction projection matrix is obtained,and the self-representation based subspace clustering is carried out in the low dimensional space after the dimensionality reduction,which greatly reduces the clustering operation time and improves the clustering accuracy of the model.(2)Aiming at the problems of high time complexity and slow running efficiency of existing subspace clustering algorithms,a fast low rank subspace clustering algorithm based on matrix decomposition is proposed.The nuclear norm optimization problem is transformed into the Frobenius norm problem of two small matrices,which greatly reduces the time complexity of the algorithm and improves the efficiency of the algorithm.(3)For the application scenario of time-series data segmentation,a time-series subspace clustering algorithm based on elastic network regularization is proposed.In this algorithm,the association between adjacent frames in time domain is fully considered.The elastic net regularization constraint and time-domain smooth regularization term with block diagonalization approximation characteristics and grouping effect characteristics are designed and applied,which greatly improves the accuracy of subspace clustering algorithm applied to time series data segmentation.(4)For the data distributed on the nonlinear manifold structure,this paper proposes an end-to-end deep clustering network,which uses the self-augmentation consistency of data and the balance of the number of categories to guide the network training.The effectiveness of the proposed method is verified by comparing with the related algorithms on several common image data sets.