张量分解算法研究与应用综述

Research and Application of Tensor Decomposition Algorithm

张量分解是处理大规模数据的一种方法,它能有效的对数据进行降阶,由于高阶张量具有唯一性、对噪声更鲁棒、不破坏原数据的空间结构和内部潜在信息等优点,被广泛应用于神经科学、信号处理、图像分析、计算机视觉等领域。论文首先对传统的降维方法进行了介绍,指出这些方法存在的问题和不足。其次对张量分解的三种经典算法:CP分解、Tucker分解以及非负张量分解从算法的求解、基本思想、算法框架以及算法应用等方面进行概括分析,对CP分解算法和Tucker分解算法从多角度进行对比分析。最后对张量分解的现状以及实际应用进行了归纳和总结,并对未来的研究发展趋势进行了分析和展望。

Tensor decomposition is a significant method to deal with large-scale data, which can reduce the data effectively. The high-order tensor is widely used in neuroscience, signal processing, image analysis, computer vision and other fields as it has such advantages as uniqueness, robustness to noises and zero impact on the original data of the spatial structure and internal potential information. In this paper, the traditional dimensionality reduction methods were introduced firstly, and their problems and shortcomings were also discussed. Secondly,general analysis of three classical algorithms of tensor decomposition was carried out from the aspects of algorithm, basic ideas, algorithm framework and algorithm applications of CP decomposition, Tucker decomposition and non-negative tensor decomposition. Then, The CP decomposition algorithm and the Tucker decomposition algorithm were compared and analyzed from different angles. Finally, the present situation, practical application and future research trends of tensor decomposition were summarized and analyzed.