# A Multiview Representation Learning Framework for Large-Scale Urban Road Networks
## Appendix A  
```
Input:

(a) Matrix \(\Pi=\left\{\Pi\big{[}\hat{\mathcal{G}}(1)\big{]}\,\ \Pi\big{[}\hat{\mathcal{G}}(2)\big{]}\ \dots\,\ \Pi\big{[}\hat{\mathcal{G}}(N_{s})\big{]}\right\}\)

(b) Hyperparameters \(R\) and \(L\)

(c) Subgraphs \(\big{\{}\hat{G}(1)\,\ \hat{G}(2)\dots\,\ \hat{G}(N_{s})\big{\}}\)

(d) Patches \(\big{\{}V_{patch}(1),V_{patch}(2),\dots,\ V_{patch}(N_{s})\big{\}}\)
```  
Output:  
(a) \(N\times R\) random walk sequences \([seq(i)^{(k)}],\ for\ k\in[1,R]\ and\ i\in[1,N]\) ```
**Variables:**  
\(i\): index of node in \(G\); \(k\): index of the sequence generated by the random walk process based on the same start node; \(l\): index of the node in one sequence;  
\(t\): index of random walk index; \(v(t)\): sampled node in step \(t\). ```

**Method:**

```
1.\(i=1,\ k=1,\ l=1,\ t=1,\ seq(i)^{(k)}=\varnothing//\)initialization
2.If\(i<N\)then
3. Select \(v_{i}\) as the start node
4.If\(k<R\)then
5. Set I as \(v(0)\) and append \(v_{i}\) to \(seq(i)^{(k)}\)
6.\(t\)\(\rightarrow\)\(0\), \(l\)\(\rightarrow\)\(0\)
7.For\(l\) from \(1\) to \(L\)
8.If\(v(0)\
otin\)\(\big{\{}V_{patch}(1),V_{patch}(2),\dots,V_{patch}(N_{s})\big{\}}\)then
9. Sample the next node \(v(t)\) based on \(\Pi\) utilizing the intrasubgraph index
10. Append \(v(t)\) to sequence \(seq(i)^{(k)}\)
11.Else
12. Sample the next node \(v(t)\) based on \(\Pi\) utilizing the intersubgraph index
13. Append \(v(t)\) to sequence \(seq(i)^{(k)}\)
14.Endif
15.\(t\)\(\rightarrow\)\(t+1\)
16.Endfor
17.\(k\)\(\rightarrow\)\(k+1\)
18.Endif
19.\(i\)\(\rightarrow\)\(i+1\)
20.Endif
21.Return\([seq(i)^{(k)}],k\in[1,R],i\in[1,N]\)
```

**Algorithm A1**Multiview Random Walk. ## References

* [PERSON] et al. (2020) [PERSON]; [PERSON]; [PERSON]; [PERSON] On representation learning for road networks. _ACM Trans. Intell. Syst. Technol._**2020**, _12_, 1-27. [CrossRef]
* [PERSON] et al. (2021) [PERSON]; [PERSON]; [PERSON] A temporal directed graph convolution network for traffic forecasting using taxi trajectory data. _ISPRS Int. J. Geo-Inf._**2021**, _10_, 624. [CrossRef]
* [PERSON] et al. (2020) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] HetETA: Heterogeneous information network embedding for estimating time of arrival. In Proceedings of the 26 th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Virtual, CA, USA, 6-10 July 2020; pp. 2444-2454. * [PERSON] et al. (2021) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; et al. ETA prediction with graph neural networks in Google maps. In Proceedings of the 30 th ACM International Conference on Information & Knowledge Management, Quensland, Australia, 1-5 November 2021; pp. 3767-3776. * [PERSON] et al. (2017) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Road2 Vec: Measuring traffic interactions in urban road system from massive travel routes. _ISPRS Int. J. Geo-Inf._**2017**, \(6\), 321. [CrossRef]
* [PERSON] (2016) [PERSON]; [PERSON] node2 vec: Scalable feature learning for networks. In Proceedings of the 22 nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, 13-17 August 2016; pp. 855-864. * [PERSON] and [PERSON] (2004) [PERSON] [PERSON]'s first law of geography: A big idea for a small world? _Ann. Assoc. Am. Geogr._**2004**, _94_, 269-277. [CrossRef]
* [PERSON] et al. (2021) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] The universal visitation law of human mobility. _Nature_**2021**, _593_, 522-527. [CrossRef][PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Location2 vec: A situation-aware representation for visual exploration of urban locations. _IEEE Trans. Intell. Transp. Syst._**2019**, _20_, 3981-3990. [CrossRef]
* [PERSON] et al. (2015) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] LINE: Large-scale information network embedding. In Proceedings of the 24 th International Conference on World Wide Web, Florence, Italy, 18-22 May 2015; pp.