计算机科学 ›› 2023, Vol. 50 ›› Issue (11A): 230300073-6.doi: 10.11896/jsjkx.230300073
王杉, 刘璐
WANG Shan, LIU Lu
摘要： 土壤湿度在气象、气候等学科中起着重要作用,然而目前观测的土壤湿度数据缺少高精度、高空间分辨率,其适用性受到很大的限制。矩阵填充(Matrix Completion,MC)是压缩感知在矩阵上的应用,它针对部分缺失、污染、损毁的大规模数据,旨在将一个低秩不完整的矩阵,利用其元素间的相关性,恢复出矩阵的全部数据,适用于土壤湿度这类时空相关性高但缺失值多的数据。但其要求矩阵秩是相关或近似相关的,而土壤湿度的秩不稳定。对此,通过预设矩阵的秩,引入主成分分析方法(Principal Component Analysis,PCA),在降低矩阵维度的同时保留大部分信息,并在此基础上对具有缺失值的土壤湿度数据进行矩阵填充。实验选取了ERA-Interim 2022年部分地区的卫星土壤湿度数据,结果显示,相较于传统的MC算法,引入主成分分析的PCA-MC(Low Rank Matrix Completion)的实验结果的偏差减小了28.6%,均方根误差减小了5.78%,最大误差减小了14.8%,同时缩短了重构时间,这表明,PCA-MC方法相比MC方法可以有效地重构有缺失值的大规模矩阵。
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