计算机科学 ›› 2021, Vol. 48 ›› Issue (8): 66-71.doi: 10.11896/jsjkx.200900055
杨宏鑫, 宋宝燕, 刘婷婷, 杜岳峰, 李晓光
YANG Hong-xin, SONG Bao-yan, LIU Ting-ting, DU Yue-feng, LI Xiao-guang
摘要： 现代信号处理中,越来越多的领域都需要存储和分析规模大、维度高、结构复杂的数据。张量作为向量和矩阵的高阶推广,在保证原始数据内在关系的前提下,可以更为直观地表示大规模数据的结构性。张量填充作为张量分析的一个重要分支,目前已被广泛应用于协同过滤、图像恢复、数据挖掘等领域。张量填充指从被噪声污染或存在数据缺失的张量中恢复出原始张量的手段,文中着眼于当前张量填充技术中时间复杂度较高的缺点,提出了基于耦合随机投影的张量填充方法。该方法的核心包括两个部分:耦合张量分解以及随机投影矩阵。通过随机投影矩阵,文中将原始高维张量投影到低维空间内生成替代张量,同时在低维空间内实现张量填充,进而提高算法的执行效率。同时,所提算法还利用耦合张量分解将填充后的低维张量映射到高维空间,从而实现原始张量的重构。最后,通过实验分析了所提算法的有效性和高效性。
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