# Inferring Long-Term Demand of Newly Established Stations for Expansion Areas in Bike Sharing System
## 3 Methodology
### Preliminary and Problem Definition  
**Definition 1**. : _Reachable Station Region. Considering how far a resident is willing to move and to get appropriate modeling of spatial factors, we define \(r\) as the radius of the farthest influencing area of a new station. In other words, when considering a location to build a new bike station, we propose to set a Euclidean distance \(r\) to extract the neighbor characteristics and features. Figure 2 gives an example. \(S_{i}\) is the target location, and we extract the density of our pre-defined POIs, which may be correlated with bike demands within the region. \begin{table}
\begin{tabular}{c c} \hline \hline
**Notations** & **Descriptions** \\ \hline \(S\) & The station set \(S=\{S_{1},S_{2},\dots\ S_{n}\}\) \\ \(C\) & The category set \(C=\{CT_{1},CT_{2},\dots\ CT_{m}\}\) \\ \(POI\) & The POI set \(POI=\{P_{1},P_{2},\dots\ P_{l}\}\) \\ \(R\) & The bike route set \(R=\{R_{1},R_{2},\dots\ R_{k}\}\) \\ \(n,m,l,k\) & Number of stations/categories/POIs/bike routes \\ \(S_{i}\) & The feature set of \(i\)th station \\ \(S_{i}\):rent & Rental demand for \(S_{i}\) six months after the establishment \\ \(S_{i}\):drop & Drop-off demand for \(S_{i}\) six months after the establishment \\ \(S_{i}\):lat & Latitude of \(S_{i}\) \\ \(S_{i}\):long & Longitude of \(S_{i}\) \\ \(S_{i}\):date & The established date (e.g., operating date) of \(S_{i}\) \\ CS (\(S_{i}\), \(S_{j}\)) & Cosine similarity between \(S_{i}\) and \(S_{j}\) \\ \(P_{I\times m}\) & Category matrix corresponding to POIs \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Notations used in this paper. Figure 1: The overview of LDA Framework. **Definition 2**. : _Nearby Stations. For the target location of a new station, we extract its top-k nearest stations whose establishment dates are earlier than the corresponding nearby stations. Three features of corresponding nearby stations are considered in our work: the difference of establishment dates, the number of cumulative demands, and the Euclidean distance between the target location and the nearby stations._  
**Definition 3**. : _Bike Route Structure. We consider the road length of bike routes and the number of intersections in road structure as features to improve the demand prediction effectiveness. The reason that we consider the road length of bike routes is because a bike station might have a great demand in the long-term if its surrounding environment contains many bike routes, which are convenient for riders to travel by taking bikes. The high number of intersections might also indicate a traffic hub with significant human mobility, leading to increased potential bike flows._  
In Figure 3, there are three kinds of bike routes, and a bike route \(R_{i}\) is composed of multiple intersections (red points) and road segments (black dotted lines). Those route segments and intersections within the reachable station region of \(S_{i}\) are needed to be included. That is, the features extracted from \(R_{1}\), \(R_{2}\), and partial of \(R_{3}\) in Figure 2 should be taken into consideration. **Definition 4**. : _Season. The period after building a station will span multiple seasons, and all of them should be considered since the commuting behavior of people will change with seasons. For each target station, we calculate how many months it will operate in each season. Spring is defined as the months from March to May, and the season changes every three months._  
**Definition 5**. : _Category Vector \(\mathbf{P_{i}}\) for Each POI. A POI \(P_{i}\) may have more than one corresponding category defined in Facebook Place API. Then, we define \(\mathbf{P_{i}}\) as:_  
\[\mathbf{P_{i}}=\{p_{i,j}\} \tag{1}\]  
_where \(p_{ij}=1\), if \(P_{i}\) belongs to \(CT_{j}\); or \(0\), otherwise._  
_Where \(CT_{j}\) is the jth element in the category set defined by Facebook._  
Figure 3: Examples of bike route intersection. Figure 2: An illustration of the reachable region of station \(S_{i}\) and the corresponding bike routes. **Problem Definition.