基于主成分追踪的航空货运量预测研究

Prediction of Air Cargo Volume Based on Principal Component Pursuit

介绍矩阵低秩稀疏分解理论,推导矩阵低秩稀疏分解的交替方向主成分追踪算法(Principal Component Pursuit by Alternating Directions Methods PCP_ADM),并研究此理论在我国航空货运量预测中的应用。以2002—2009年我国航空货运量的按月统计数据为基础,交替主成分追踪算法不但可以得到航空货运量的逐年变化规律、季节变化规律,而且可以分析突发经济事件特别是经济危机对我国航空业的冲击。依据矩阵分解的低秩项(我国航空货运量的内在变化规律)可预测2010年每个月航空货运量,预测结果显示最大预测误差不超过8.27%,绝大部分相对误差在3%以下,为航空运力市场的调控以及民航运输业健康发展提供理论支持。

In this article,we provide the theory that the matrix can be modeled as a low-rank plus a sparse component and a noisy component.We give Principal Component Pursuit by Alternating Directions Methods（PCP_ADM） and study its application in the field of Prediction of Air Cargo Volume.According to air cargo volume statistical data in China from the year 2002 to 2009,the low matrix and sparse component of air cargo volume can be obtained by PCP_ADM.This method can also recover sparse influence of economic emergency.The maximum relative error of predicted value of Air Cargo Volume is 8.27%,almost relative error is less than 3%,this result tells us matrix decomposition of low-rank matrix and sparse matrix can be used to forecast short-term aeronautic cargo capacity,and can also provide some effective theory evidence to supervise the native aeronautic cargo market.