Research On Robust Kernel Low-rank Representation Algorithm Of High-dimensional Data By Tensor Decomposition

With the rapid development and wide applications of information technology,the data interaction becomes more frequently while the size of the data is larger and the structure is more and more complex.Such as text data,image data,biological data and so on.Analyzing these data and getting useful information for people is of practical significance.As an effective method of data processing,Low Rank Representation can effectively deal with the data matrix and the dimension reduction of noise.Moreover,LRR algorithm has a good capability of recovering missing values on the lost or damaged data.Therefore,the algorithm has been widely used in many fields after it was proposed.There are still some shortcomings of low rank representation although it is becoming much mature.The algorithm can only handle the nonlinear data with only one type of feature by using the low rank representation algorithm based on the kernel function.When the data has multiple features,the algorithm can't be handled well.But in the real-world,the data that people need to processing often has multiple feature attributes.The traditional kernel low rank representation algorithm often transforms these data into a vector or matrix form,which will not only destroy the spatial structure of the data,but also loses some of the information of the data.In this paper,kernel low-rank representation of high-dimensional data by robust tensor decomposition is proposed to deal with multiple characteristic attribute problems of high-dimensional data which the traditional kernel low-rank representation algorithm can't do.On one hand,the integrity of the data is ensured as it is processed by constructing the high-order data and is decomposed by Tucker decomposition.On the other hand,the linear separable data is guaranteed as the kernel function is used to map the decomposed nonlinear data into the new feature space.In this paper,the theoretical analysis and detailed deduction of the RTDKLRR algorithm are carried out,and the optimal solution of the algorithm is solved based on the alternating direction method.The synthetic data sets and the real-world data sets are constructed to test the effectiveness of the algorithm,and the data noise is dopedin the data set to verify the robustness of the algorithm to the noise.We use clustering error rate as the evaluation criterion of the algorithm,which is compared with the existing research work so as to verify the rationality of the algorithm.