Improving Demand Forecasting in Open Systems with Cartogram-Enhanced Deep Learning

TL;DR

Open systems such as public bicycle sharing exhibit open, imbalanced demand patterns that challenge forecasting. The authors integrate Voronoi-based cartograms with a multi-resolution spatio-temporal convolutional graph attention network, adding batch attention and a simplified GAT node-update to improve accuracy. The approach enables accurate predictions for new stations lacking historical data and supports long-horizon forecasts, demonstrated on Seoul bike data. The work advances demand forecasting in open systems and offers a framework transferable to other micro-mobility and moving-crowd scenarios.

Abstract

Predicting temporal patterns across various domains poses significant challenges due to their nuanced and often nonlinear trajectories. To address this challenge, prediction frameworks have been continuously refined, employing data-driven statistical methods, mathematical models, and machine learning. Recently, as one of the challenging systems, shared transport systems such as public bicycles have gained prominence due to urban constraints and environmental concerns. Predicting rental and return patterns at bicycle stations remains a formidable task due to the system's openness and imbalanced usage patterns across stations. In this study, we propose a deep learning framework to predict rental and return patterns by leveraging cartogram approaches. The cartogram approach facilitates the prediction of demand for newly installed stations with no training data as well as long-period prediction, which has not been achieved before. We apply this method to public bicycle rental-and-return data in Seoul, South Korea, employing a spatial-temporal convolutional graph attention network. Our improved architecture incorporates batch attention and modified node feature updates for better prediction accuracy across different time scales. We demonstrate the effectiveness of our framework in predicting temporal patterns and its potential applications.

Figures (7)

• Figure 1: The usage of public bicycles in Seoul. Snapshots of rentals (one of the two types of demand) (a) at 18:00, June 3rd, 2018 and (b) at 18:00, June 3rd, 2019. The sum $X$ of rentals in a cell on a grid is indicated by color on a logarithmic scale. Note that a cell marked by a red arrow solely has a newly installed station in year 2019, of which the administrative-gu is Eunpyeong-gu. (c) A time series of rentals in the year 2019. The mean value spanning a week is plotted as guidance to showcase the quasi-periodicity (we actually use the original sequence, not this mean value). As an illustrative example, we mark the $\tau_d$ points of rentals $X$ required to predict $X(t+\Delta t_h)$, when considering a day resolution $\Delta t_d$.
• Figure 2: The architecture of the training process by the ST-CGA network model. We construct the demand dataset $\mathbb{X}(t_b)$ which contains the demand for $M\times N$ cells at $B$ different pivot time $t_b$'s with various temporal resolutions in Eq. (\ref{['eq:input_x']}). The self-attention (in fact, batch attention) process (see Appendix \ref{['seca:selfattention']} for notation) offers the node feature matrix between cells (nodes). The all-to-all structure in terms of the network becomes an input of the graph attention network, and graph attention first provides attention scores $\alpha$ regarded as the link weights of the pair of nodes. The node feature $\mathbf{y}_u$ is updated by the attention scores and learnable important matrix. As an example, herein we illustrate the ego-centric connection structure. The input data with each temporal resolution are trained in parallel and then merged after the CNN. After some iterations with backpropagation, we finally obtain the prediction values at $t_b+\Delta t_h$, i.e., $\hat{\mathbf{X}}(t_b+\Delta t_h)$.
• Figure 3: The original map and cartogram with the Voronoi tessellation. The station within a Voronoi cell and the relative area distribution of the original empirical data [(a), (c)] and those of the cartogram [(b), (d)]. (a), (b) every polygon (Voronoi cell) contains only one station. (c), (d) The distribution of the polygon's relative area. The relative area is obtained by scaling the largest area in (a).
• Figure 4: The similarity of the demand patterns of stations within a cell before [(a), (c)] and after [(b), (d)] using the cartogram (representatively, the rental for the year 2019). (a), (b) Pearson's correlation coefficient $\rho$ for every cell. (c), (d) The coefficient of variation $v$. The cells with $\rho=1$ and $\nu=0$ colored in gray have only one station each.
• Figure 5: The analysis for the attention score between every cell pair in the graph attention network, for the training data (year 2018). (a) The yearly average attention score, or weighted adjacency matrix. The 255 cells correspond to a (coarse-grained) node, and the average attention score $\alpha_{ij}$ represents the weight of the link. The higher $\alpha_{ij}$ has a darker color. Clusters with low and high $\alpha$'s are surrounded by the two boxes in the upper left corner and lower right corner, respectively. The locations of the stations belonging to the nodes in the cluster with (b) the low attention scores and (c) the high attention scores are shown in the original map.