Two-Dimensional Clustering Algorithms Based On Sparse Constraints

As an unsupervised learning method,clustering has been widely used in pattern recognition,artificial intelligence,data mining,biomedicine and other fields.Generally,clustering is to divide sample points into different clusters according to some criteria.It is expected that similar points will be in the same cluster and different points in different clusters.So far,many clustering algorithms have been proposed according to different criteria.Although these algorithms can partition data to some extent,the following problems still exist:(1)The development of information technology increases the size and complexity of data and the dimension of data is getting higher and higher.Processing high-dimensional data is an urgent problem for cluster analysis.(2)The traditional clustering method preprocesses twodimensional data into one-dimensional vector,which destroys the original spatial structure and increases the computational cost.Based on this,we focus on exploring the clustering analysis method of two-dimensional data,and presents the feature representation method which integrats dimensionality reduction and clustering.Firstly,a two-dimensional sparse fuzzy k-mean clustering(2DSFKM)algorithm is proposed.When processing high-dimensional data,the clustering algorithm needs to reduce the dimensionality of the data in advance.However,in traditional methods,dimensionality reduction process and clustering process are carried out independently,making it difficult to accurately cluster.In this paper,we integrate them into a unified algorithm framework to find a better subspace for feature representation.In addition,we directly take two-dimensional data matrix as input and retain the underlying structure information.Sparse quadratic regularization is introduced to improve the robustness of the clustering algorithm to outliers and to solve the problem that outliers will affect the clustering effect.Secondly,since the above methods can only get the local optimal solution of the algorithm,this paper further proposes a two-dimensional sparse spectrum clustering(2DSSC)algorithm.Compared with the traditional method,in which the similarity matrix is first learned and then the features are clustered,the proposed algorithm integrates similarity matrix learning and clustering into an algorithm framework,and achieves perfect expression of features in dynamic iterations.In order to achieve an ideal neighborhood distribution in spectral clustering and make each sample in the graph have only one neighbor point,we introduce a sparse regular term to regularize the structure of the data graph.Besides,we take the original structure of two-dimensional data as input to preserve the structure of the original location information.In this paper,experiments are carried out on dozens of data sets and compared with common algorithms.Quantitative experimental results show that the proposed algorithm model can find feature subspace dynamically and adaptively,and effectively retain twodimensional data structure information.The proposed algorithms show good clustering effect on the evaluation index.