# A Spatiotemporal Multi-View-Based Learning Method for Short-Term Traffic Forecasting

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Construction of Space-Time Cuboid

#### 2.2. ST-KNN Model

#### 2.3. Multi-View-Based Learning

Algorithm 1: Training of MVL-STKNN |

Input: Near spatiotemporal cuboids: $\left\{XC\_H{t}_{{L}_{j}},XC\_T{r}_{{L}_{j}}\right\}$; |

Periodic spatiotemporal cuboid: $\left\{XP\_H{t}_{{L}_{j}},XP\_T{r}_{{L}_{j}}\right\}$; |

Trend spatiotemporal cuboid: $\left\{XQ\_H{t}_{{L}_{j}},XQ\_T{r}_{{L}_{j}}\right\}$; |

Lengths of closeness, period, trend: $lc$,$lp$,$lq$; |

Number of candidate neighbors: $K$; |

Parameter of Gaussian function: $a$. |

Output: MVL-STKNN model $\mathcal{M}$. |

// construct training instances |

1 $\mathcal{D}\leftarrow \varnothing $ |

2 For all time interval $t$ in the training spatiotemporal cuboids |

3 // ${n}_{hd}+ml+1<t\le {n}_{td}+{n}_{hd}+ml+1$ |

4 $\widehat{{v}_{t+1,sc}^{{L}_{j}}}$ = ST-KNN($XC\_H{t}_{{L}_{j}},M{C}_{t}^{{L}_{j}}\left(lc,ln\right),K,a$) //$M{C}_{t}^{{L}_{j}}\left(lc,ln\right)\in \left\{XC\_T{r}_{{L}_{j}}\right\}$ |

5 $\widehat{{v}_{t+1,sp}^{{L}_{j}}}$ = ST-KNN($XP\_H{t}_{{L}_{j}},M{P}_{t}^{{L}_{j}}\left(lp,ln\right),K,a$) //$M{P}_{t}^{{L}_{j}}\left(lp,ln\right)\in \left\{XP\_T{r}_{{L}_{j}}\right\}$ |

6 $\widehat{{v}_{t+1,sq}^{{L}_{j}}}$= ST-KNN($XQ\_H{t}_{{L}_{j}},M{Q}_{t}^{{L}_{j}}\left(lq,ln\right),K,a$) //$M{Q}_{t}^{{L}_{j}}\left(lq,ln\right)\in \left\{XQ\_T{r}_{{L}_{j}}\right\}$ |

7 Put a training instance $\left(\left\{\widehat{{v}_{t+1,sc}^{{L}_{j}}},\widehat{{v}_{t+1,sp}^{{L}_{j}}},\widehat{{v}_{t+1,sq}^{{L}_{j}}}\right\},{v}_{t+1}^{{L}_{j}}\right)$ into $\mathcal{D}$ |

8 End for |

// Training the model |

9 $\mathcal{M}\leftarrow Muti\_view\_learning\left(\mathcal{D}\right)$ // Neural network training |

10 Output the learned MVL-STKNN model $\mathcal{M}$ |

Algorithm 2: Prediction of MVL-STKNN |

Input: Near spatiotemporal cuboids: $\left\{XC\_H{t}_{{L}_{j}},XC\_T{s}_{{L}_{j}}\right\}$; |

Periodic spatiotemporal cuboid: $\left\{XP\_H{t}_{{L}_{j}},XP\_T{s}_{{L}_{j}}\right\}$; |

Trend spatiotemporal cuboid: $\left\{XQ\_H{t}_{{L}_{j}},XQ\_T{s}_{{L}_{j}}\right\}$; |

Lengths of closeness, period, trend: $lc$,$lp$,$lq$; |

Number of candidate neighbors: $K$; |

Parameter of Gaussian function: $a$. |

Output: Set of test sample predictions: ${\chi}_{{L}_{j}}$. |

1 For all time interval $t$ in the test spatiotemporal cuboids |

2 // ${n}_{td}+{n}_{hd}+ml+1<t\le tc$ |

3 $\widehat{{v}_{t+1,sc}^{{L}_{j}}}$ = ST-KNN($XC\_H{t}_{{L}_{j}},M{C}_{t}^{{L}_{j}}\left(lc,ln\right),K,a$) //$M{C}_{t}^{{L}_{j}}\left(lc,ln\right)\in \left\{XC\_T{s}_{{L}_{j}}\right\}$ |

4 $\widehat{{v}_{t+1,sp}^{{L}_{j}}}$ = ST-KNN($XP\_H{t}_{{L}_{j}},M{P}_{t}^{{L}_{j}}\left(lp,ln\right),K,a$) //$M{P}_{t}^{{L}_{j}}\left(lp,ln\right)\in \left\{XP\_T{s}_{{L}_{j}}\right\}$ |

5 $\widehat{{v}_{t+1,sq}^{{L}_{j}}}$= ST-KNN($XQ\_H{t}_{{L}_{j}},M{Q}_{t}^{{L}_{j}}\left(lq,ln\right),K,a$) //$M{Q}_{t}^{{L}_{j}}\left(lq,ln\right)\in \left\{XQ\_T{s}_{{L}_{j}}\right\}$ |

6 $\widehat{{v}_{t+1}^{{L}_{j}}}\leftarrow \mathcal{M}\left(\widehat{{v}_{t+1,sc}^{{L}_{j}}},\widehat{{v}_{t+1,sp}^{{L}_{j}}},\widehat{{v}_{t+1,sq}^{{L}_{j}}}\right)$ // Obtain the predicted values |

7 Put $\widehat{{v}_{t+1}^{{L}_{j}}}$ into ${\chi}_{{L}_{j}}$ // Save the predicted values into set ${\chi}_{{L}_{j}}$ |

8 End for |

9 Return the set of predictions ${\chi}_{{L}_{j}}$ |

## 3. Performance Evaluation

#### 3.1. Data Preparation

#### 3.1.1. Data Sources

#### 3.1.2. Data Processing

#### 3.2. Evaluation Metrics

#### 3.3. Variable Estimation

#### 3.3.1. Calibrating the Parameters of ST-KNN Model

#### 3.3.2. Calibrating the Temporally Dependent Parameters

#### 3.4. Test of Spatial Heterogeneity

#### 3.5. Accuracy Comparison

#### 3.6. Impact of Space-Time Weighting Matrix

#### 3.7. Impact of Spatial and Temporal Dependencies

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Dataset | PeMS | Beijing |
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Time span | 15 August 2016–14 October 2016 | 1 March 2012–30 April 2012 |

Time interval | 5 min | 5 min |

Number of link | 59 | 30 |

Parameters | Values |
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$a$ | 0.009 |

$K$ | 5 |

$lc$ | 2 |

$lp$ | 1 |

$lq$ | 2 |

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## Share and Cite

**MDPI and ACS Style**

Cheng, S.; Lu, F.; Peng, P.; Wu, S. A Spatiotemporal Multi-View-Based Learning Method for Short-Term Traffic Forecasting. *ISPRS Int. J. Geo-Inf.* **2018**, *7*, 218.
https://doi.org/10.3390/ijgi7060218

**AMA Style**

Cheng S, Lu F, Peng P, Wu S. A Spatiotemporal Multi-View-Based Learning Method for Short-Term Traffic Forecasting. *ISPRS International Journal of Geo-Information*. 2018; 7(6):218.
https://doi.org/10.3390/ijgi7060218

**Chicago/Turabian Style**

Cheng, Shifen, Feng Lu, Peng Peng, and Sheng Wu. 2018. "A Spatiotemporal Multi-View-Based Learning Method for Short-Term Traffic Forecasting" *ISPRS International Journal of Geo-Information* 7, no. 6: 218.
https://doi.org/10.3390/ijgi7060218