Application Of Kernel 2D Ridge Regression For 2D Data In Subspace Clustering

Clustering algorithm is one of the main tasks in data mining,which is mainly used to find unknown object categories in database.As the mainstream clustering algorithm,subspace clustering is widely used in computer vision,artificial intelligence,network analysis and pattern recognition.At present,there are many research achievements on subspace clustering,among which,the subspace clustering algorithm based on spectral clustering has remarkable clustering effect.In the application of clustering analysis,high-dimensional data is common,especially for two-dimensional data(that is,a sample is a matrix)algorithm research is very scarce.For 2D data,the existing subspace clustering method usually needs to transform 2D data into vector as pre-processing data.However,this method seriously damages the structure information of 2D data,neglects the important relevance between original structure and original data.In order to overcome the shortcomings of existing subspace clustering algorithms,this paper proposes a subspace clustering algorithm based on kernel and ridge regression for two-dimensional data,named KTRR.The research of clustering algorithm is as follows:(1)At the Data pre-processing stage,unlike existing methods that perform data vectorization before further processing,the proposed KTRR directly seeks low-dimensional representation on the two-dimensional data with a projection imposed on them.The projection helps retain the most representative two-dimensional features of the data and thus improves the learning capability of the model with such inherent structural information of two-dimensional data.(2)To take the nonlinear relationships of data into consideration,kernel trick for two-dimensional data is adopted such that the new model is capable of capturing nonlinear structures from the data and thus seek more accurate low-dimensional representation;(3)KTRR performs the learning tasks of two-dimensional feature extraction,representation learning,and nonlinear relationship discovery on manifold in a seameslessly integrated framework,such that the learning tasks mutually enhance each other and lead to improved learning capability;(4)The proposed optimization algorithm guarantees the decreasing property of the objective value and thus the convergence is theoretically guaranteed.Extensive experimental results show that the proposed KTRR algorithm has good clustering performance compared with the current mainstream subspace clustering algorithm.