Low-rank Matrix Recovery Algorithm And Its Application In Logging Data Mining

In recent years,the Low-Rank Matrix Recovery(LRMR)theory has been widely used in the field of image de-noising,video repair and other fields,it has gradually become a research hotspot in the field of intelligent information processing.In logging data mining field,the sparseness of the noise matrix cannot be well guaranteed due to the complexity data noise sources,but the classic LRMR algorithms require that the noise matrix must be sparse,which make the algorithms show some limitations in the process of logging data de-nosing,and the de-noising effect is unstable.To solve this problem,an improved weighted LRMR algorithm is proposed based on the analysis of classic LRMR algorithms,and the improved algorithm can be applied to the logging data mining field.The main work or innovations are as follows:(1)The analysis of LRMR theoretical basis and classic algorithms.The theoretical basis and classic algorithms of LRMR,including accelerated proximal gradient(APG)algorithm,exact augmented Lagrange multiplier method(EALM)algorithm and inexact augmented Lagrange multiplier method(IALM)algorithm are analyzed and the simulation comparison was carried out.The simulation results show that compared with APG algorithm and EALM algorithm,the IALM algorithm has a significant advantage of superior calculation accuracy and faster convergence speed in data de-noising.However,there are some shortcomings need to be improved,such as the strict requirement on the sparsity of noise matrix.(2)Research on improved LRMR algorithm.In order to achieve good de-noising effect,the classic low rank matrix recovery algorithm requires the sparse matrix must be strictly sparse,and it makes some limitations in the process of data de-noising.To solve this problem,the idea of weighted norm is applied to the classic low rank matrix recovery algorithm,so an improved weighted LRMR algorithm is proposed.The algorithm can improve the ability of sparse decomposition,and reduce the influence of the singular value numerical size in the process of kernel norm approximation matrix rank at the same time.The simulation results show that improved algorithm can detect the low rank property of low rank matrix and enhance the sparsity of sparse matrix better and the stability of the solution can be guaranteed at the same time.(3)Application research on logging data mining.In order to improve the effect of logging data mining,a logging data mining model based on improved weighted LRMR algorithm model is built to identify gas layer of a gas well in Xinjiang Province.The simulation results show that the logging data after the de-nosing process of improved algorithm is slightly higher than classic algorithm in the operation time,but the recognition accuracy is significantly improved,and the data mining results are remarkable in the gas layer recognition,which satisfies the actual logging requirements completely.