Low Rank Matrix Recovery And Applications In Meteorological Data

Traditional meteorological data estimation methods use interpolation strategies,and pedigree clustering and K-means clustering are common methods for climate zoning.None of these methods considers the approximate low-rank structure of the meteorological dataset,which affects the application of meteorological data estimation and climate zoning to some extent.This thesis applies the method of low rank matrix recovery to meteorological data estimation and climate partitioning.The main research content is as follows.A matrix completion method is applied to meteorological data estimation.Firstly,two meteorological elements of daily average temperature and sunshine hours of 661 meteorological stations in China from 2004 to 2013 are selected as research objects,and the approximate low rank of the dataset is validated by the cumulative contribution rate of matrix singular values.Then two groups of experiments are designed.The first group of experiments consider the data estimation of each year under different sampling probabilities.In the second group of experiments,some stations are randomly selected,and the estimation of the data of the selected stations is continuously considered.Finally,the matrix completion method is employed to estimate the missing data,and the 10-year average error is used as the evaluation index.The experimental results show that the matrix completion method can estimate the missing data and has certain robustness.A climate zoning method based on sparse subspace clustering under single view is proposed.The sparse subspace representation is adopted to construct the similaritymatrix,and then the spectral clustering method is used for zoning.In detailed experiments,five meteorological elements including daily average temperature,average relative humidity,sunshine hours,temperature difference and atmospheric pressure are selected as the research objects,and the partition results under different cluster numbers are obtained.The experimental results verify the feasibility and effectiveness of the proposed climate zoning method.The climate zoning method for sparse subspace clustering under multiple views is studied.Firstly,an optimization model for multi-view sparse subspace clustering is established.Then,the established model is solved using the alternating direction multiplier method.Finally,five kinds of meteorological elements such as daily average temperature and average relative humidity are considered,and the climate zoning results under these five views are given.Compared with the single-view method,the multi-view method considers the combined effects of multiple meteorological elements on climate partitioning.