基于张量的方法及应用综述

Review on Tensor-based Methods and Applications

大数据时代的不断发展促使传感及移动互联设备所产生数据的规模和复杂度快速增长,呈现出多源、异构、海量的特点。因此对这些复杂数据的统一表示、降维处理以及缺失值补全等问题受到研究人员的广泛关注。张量具有对高维数据强大的表示和降维能力并能挖掘元素值之间的潜在关系,被普遍应用于这些问题的研究中。张量分解方法获取高维复杂数据的低维特征,在降低计算复杂度的同时还能够保持原有数据的内在结构,解决“维度灾难”问题。张量补全方法根据已有数据的全局结构获取低秩模型来估计缺失条目。该文从张量分解与补全的视角出发,分别总结相关经典方法的基本思想并分析各自的优缺点。从多源异构大数据分析、人脸识别、数据压缩三方面对张量分解的最新算法进行总结。针对QoS缺失数据预测、短时交通流量预测、图像恢复三个场景介绍了张量补全的最新应用。最后对未来张量研究发展中可能存在的问题与挑战进行展望。

The continuous development of the big data era has led to a dramatic increase in the scale and complexity of data generated by sensing and mobile Internet devices,showing the characteristics of multi-source,heterogeneous,and massive.Therefore,the unified representation,dimensionality reduction processing,and missing value completion of these complex data have received extensive attention from researchers.Tensors have powerful representation and dimensionality reduction capabilities for high-dimensional data,and can mine potential relationships between element values.They are widely used in the research of these problems.Tensor decomposition method obtains the low-dimensional features of high-dimensional complex data,which can reduce the computational complexity while maintaining the internal structure of original data,and can solve the"dimension disaster"problem.Tensor completion method obtains a low-rank model based on the global structure of the existing data to estimate missing items.From the perspective of tensor decomposition and completion,the basic ideas of related classic approaches as well as their advantages and disadvantages are analyzed.The latest algorithms of tensor decomposition are summarized from three aspects of multi-source heterogeneous big data analysis,face recognition,and data compression.The latest application of tensor completion is introduced from three scenarios of QoS missing data prediction,short-term traffic flow prediction,and image restoration.Finally,the problems and challenges in the future development of tensor research are prospected.