Application of Nonnegative Tensor Factorization for Intercity Rail–Air Transport Supply Configuration Pattern Recognition

With the rapid expansion of the railway represented by high-speed rail (HSR) in China, competition between railway and aviation will become increasingly common on a large scale. Beijing, Shanghai, and Guangzhou are the busiest cities and the hubs of railway and aviation transportation in China. Obtaining their supply configuration patterns can help identify defects in planning. To achieve that, supply level is proposed, which is a weighted supply traffic volume that takes population and distance factors into account. Then supply configuration can be expressed as the distribution of supply level over time periods with different railway stations, airports, and city categories. Furthermore, nonnegative tensor factorization (NTF) is applied to pattern recognition by introducing CP (CANDECOMP/PARAFAC) decomposition and the block coordinate descent (BCD) algorithm for the selected data set. Numerical experiments show that the designed method has good performance in terms of computation speed and solution quality. Recognition results indicate the significant pattern characteristics of rail–air transport for Beijing, Shanghai, and Guangzhou are extracted, which can provide some theoretical references for practical policymakers.