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

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## Abstract

**:**

## 1. Introduction

## 2. Study Area, Data, and Methodology

#### 2.1. Study Area and Data Sources

#### 2.2. Nonnegative Tensor Factorization

## 3. Patterns Recognition Result

## 4. Result Analysis

#### 4.1. Overall Evaluation of the Pattern

#### 4.2. The Trend of Development of CAT1 Airports

#### 4.3. Pattern Analysis and Comparison

#### 4.3.1. Departure Traffic

#### 4.3.2. Arrival Traffic

#### 4.4. Inspiration for Practical Application

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Number of patterns computation result. The red dot and red circle indicates the construct ratio corresponding to the different number of patterns and the selected number of patterns.

**Figure 2.**Departure pattern 1: Decomposition results of departure tensor. the supply level pattern score bars in Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14 and Figure 15 are marked with different colors to distinguish different clusters for each supply configuration pattern.

**Figure 18.**The desired departure time (DDT) distribution for business travel over long distances (Cascetta E et al. [21]).

Indicator | Cities (Airports) | HSR Coverage Ratio |
---|---|---|

CAT1 | Beijing (PEK), Shanghai Pudong (PVG), Shanghai Hongqiao (SHA), Guangzhou (CAN) | 100% |

CAT2 | Tianjin (TSN), Dalian (DLC), Hangzhou (HGH), Xiamen (XMN), Nanjing (NKG), Qingdao (TAO), Fuzhou (FOC), Shenzhen (SZX), Wuhan (WUH), Haikou (HAK), Changsha (CSX), Sanya (SYX), Chengdu (CTU), Kunming (KMG), Chongqing (CKG), Xi’an (XIY), Urumchi (URC), Shenyang (SHE), Harbin (HRB), Zhengzhou (CGO), Jinan (TNA), Nanning (NNG), Guiyang (KWE) | 100% |

CAT3 | Nanchang (KHN), Zhuhai (ZUH), Yinchuan (INC), Taiyuan (TYN), Xining (XNN), Hohhot (HET), Changchun (CGQ), Shijiazhuang (SJW), Ningbo (NGB), Lanzhou (LHW), Hefei (HFE), Guilin (KWL), Wenzhou (WNZ) | 76.9% |

CAT4 | The remaining cities (airports) | 21.3% |

Pattern ID | Optimal Cluster Number | Silhouette Coefficient | $\overline{\mathrm{SP}}$ |
---|---|---|---|

Departure pattern 1 | 3 | 0.8512 | 1.8102 |

Departure pattern 2 | 5 | 0.8452 | 0.3108 |

Departure pattern 3 | 3 | 0.8658 | 8.5821 |

Departure pattern 4 | 3 | 0.8108 | 0.4131 |

Departure pattern 5 | 4 | 0.8482 | 1.1791 |

Departure pattern 6 | 2 | 0.9897 | 73.068 |

Departure pattern 7 | 5 | 0.8663 | 0.8069 |

Arrival pattern 1 | 5 | 0.8272 | 1.5222 |

Arrival pattern 2 | 2 | 0.8233 | 2.3483 |

Arrival pattern 3 | 2 | 0.9753 | 9.8210 |

Arrival pattern 4 | 5 | 0.8700 | 1.8622 |

Arrival pattern 5 | 3 | 0.9324 | 4.1883 |

Arrival pattern 6 | 5 | 0.8313 | 1.0773 |

Arrival pattern 7 | 4 | 0.8224 | 0.8289 |

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## Share and Cite

**MDPI and ACS Style**

Zhong, H.; Qi, G.; Guan, W.; Hua, X.
Application of Nonnegative Tensor Factorization for Intercity Rail–Air Transport Supply Configuration Pattern Recognition. *Sustainability* **2019**, *11*, 1803.
https://doi.org/10.3390/su11061803

**AMA Style**

Zhong H, Qi G, Guan W, Hua X.
Application of Nonnegative Tensor Factorization for Intercity Rail–Air Transport Supply Configuration Pattern Recognition. *Sustainability*. 2019; 11(6):1803.
https://doi.org/10.3390/su11061803

**Chicago/Turabian Style**

Zhong, Han, Geqi Qi, Wei Guan, and Xiaochen Hua.
2019. "Application of Nonnegative Tensor Factorization for Intercity Rail–Air Transport Supply Configuration Pattern Recognition" *Sustainability* 11, no. 6: 1803.
https://doi.org/10.3390/su11061803