Demand-driven Urban Facility Visit Prediction

As defined, regions are living places or workplaces for citizens, making them a complex composition of a population with various demographic backgrounds and different kinds of urban venues. For each urban region, we denote the attributes of people living in it, people working there, and distribution of local venues as its demographic attribute \(\mathbf {r}\).

Facilities often possess more properties, including level or function. For instance, hospitals are ranked according to their scale, number of beds, and function. Due to their educational content, public schools are divided into elementary, secondary, and tertiary schools. We denote the facility attributes as \(\mathbf {f}\).

Urban facilities are designed to provide service for citizens. Citizens visit facilities to fulfill their typical needs, e.g., medical, entertainment, transport, and education. Mobility data are widely used in urban computing tasks to depict citizens’ behaviors in the urban space. Each mobility record that visits an urban facility can be traced back to its origin region. We aggregate visit records at the region level and define them as facility visits.

In most cases, both facilities and regional populations are not evenly distributed within the urban area. Their spatial distribution and corresponding distances also play a critical role in predicting the region’s visits to facilities. We define the geographic distances between each urban region’s centroid and each urban facility as a matrix \(D\in \mathbb {R}^{N\times M}\).

Based on the above-introduced concepts and notations of urban factors defined, we define the urban facility visit prediction problem as follows:

We collect the facility visit record data from Tencent Map, one of the largest online map application services in China. Datasets are gathered in three large Chinese cities, i.e., Changsha, Zhengzhou, and Chongqing, covering the period from April to July 2021. Basic statistics of three cities’ datasets are listed in Table 2. Changsha and Zhengzhou are located in Middle China. They are the capital cities as well as the political and cultural centers of Hunan Province and Henan Province, respectively. Chongqing is one of the four province-level municipalities in Southwestern China. According to the 7th national census of China conducted in 2020, the three cities ranked 17th, 11th, and 1st in household-registered population among all mainland Chinese cities, making them representative of large cities in China.

Tencent Map divides each city into thousands of urban regions. Their boundaries are drawn in Figure 1. The boundaries are determined by urban road networks and natural barriers, like the Xiangjiang River that flows through Changsha city, as shown in Figure 1(a). Regions in city centers have smaller sizes than regions in the peripherals because of the higher population density in city centers.

For ethical considerations, the demographic information of citizens is processed and aggregated at the urban region level. The residential and working population with their corresponding gender and age compositions are collected. Ages are binned into eight levels, i.e., 0 to 17 years, 18 to 24 years, 25 to 30 years, 31 to 35 years, 36 to 40 years, 41 to 45 years, 46 to 60 years, and over 60 years. The fractions of sub-populations are illustrated in Figure 2. Male citizens are slightly more common than female citizens in all cities. Citizens aged between 18 and 24 years are the largest age group among Tencent Map users. Children, adolescents, and seniors only make up approximately 15% of the user population. Based on the demographic attributes of urban regions, we filter out regions with a summation of residential and working populations lower than 100. After this preprocessing, Changsha, Zhengzhou, and Chongqing have 1,553, 1,418, and 2,780 urban regions, respectively. The total residential populations covered by our dataset in three cities are 7.86, 9.46, and 16.64 million, covering 78.12%, 74.93%, and 51.84% of their population according to the latest national census. This high proportion of population coverage ensures the effectiveness of our facility visit dataset.

Our work focuses on three important categories of urban facilities, i.e., general hospitals, public schools, and shopping malls. The numbers of these facilities are listed in Table 2, and their spatial distributions are illustrated in Figure 1. Three categories of facilities serve to meet residents’ medical, education, and entertainment needs. Their functional disparity brought a large discrepancy in the amount and spatial distribution. Schools denoted as white dots are distributed widely and more evenly across the whole urban space. In comparison, hospitals (red dots) and shopping malls (blue dots) are mostly located in the city center, leaving the peripheral districts with low accessibility to medical and shopping resources.

Among three facility categories, we identify the facility level of hospitals and schools as their attributes. General hospitals are classified into six levels according to China’s medical system, which are 3A, 3B, 3C, 2A, 2B, and 2C, decreasing in their scale order. Third-class hospitals have higher medical supply capabilities than second-class hospitals. Public schools are classified into elementary and secondary schools. The distributions of facility levels are listed in Table 2.

We aggregate visits to facilities at the urban region level in each month from April to July 2021, according to the user’s workplace and resident place. We calculate the average of the total number of visits to each facility category in three cities during the four months, shown in Table 2. There are significant differences in visit patterns among the three cities. For instance, the number of visits to malls per capita in Changsha and Chongqing, which are famous tourist cities, is twice the amount in Zhengzhou, while Chongqing and Zhengzhou citizens visit schools more often than people living in Changsha. This discrepancy in visit patterns exerts the challenge of achieving good prediction performance across all cities and facility categories. For each region, we calculate the average value of the monthly total visits \(v_i\) and pairwise facility visits \(V_{i,j}\)’s from April to July 2021. To summarize, the research datasets in three large cities possess different facility visit patterns while covering a large proportion of the urban population, making them representative and appropriate for the research on facility visit prediction.

It is worth noticing the ethical considerations that have been taken into the current research. The visit records are collected with the knowledge and consent of users. Random Gaussian perturbations are added to the coordinates of visit records. Individual identifications are masked before further processing. Then, the individual-level records are aggregated into urban region-level records before being provided to researchers. Under these protocols, researchers do not have access to any individual-level metadata and are regulated by strict non-disclosure agreements. The facility visit datasets are stored on a secure offline server, which is only accessible to permitted researchers. These measures ensure that there are no privacy and security issues in the research.

To validate the mechanism that both demand and accessibility affect facility visits, We perform preliminary analyses of the correlations between facility visits and regional attributes. Specifically, we investigate the influence of the age distribution, region’s population, and travel cost on facilities, which represent demographics and the accessibility to the facility. Without loss of generality, we take Changsha city as an example, and the results are discussed as follows.

First, we compare the coarse-grained hospital visitations of different age groups divided by the percentage of the senior population (over 60 years) and the junior population (under 25 years), which are shown in Figure 3(a) and Figure 3(b), respectively. Red dotted lines represent the linear fits of the population percentage and hospital visits for all 1,553 Changsha regions. The color of a dot represents its kernel density, whereas dense dots have brighter colors. As we can observe in Figure 3(a), the visit frequency to hospitals is positively correlated with the percentage of the senior population, while in Figure 3(b), such frequency is negatively correlated with the percentage of the junior population. The heterogeneous visits among different groups demonstrate that the demand for urban facilities is highly correlated with demographic distributions. Besides, Figure 3(c) shows the negative correlation between senior population percentage and the region’s per capita school visits, indicating distinct visit patterns of different facility categories.

Second, we investigate how the cost of travel affects hospital visits, where we leverage the geodesic distance from the region centroid to the hospital as the regional travel cost. An apparent observation in Figure 3(d) is that the visit frequency decays superlinearly with the travel cost. In addition, we take the hospital class into consideration, including second-class hospitals, denoted as orange dots, and third-class hospitals, blue dots. It shows that blue dots are located above orange dots under some travel costs, indicating that third-class hospitals have more visits than second-class hospitals. The red dotted curve acts as a threshold of facility visits for the given spatial distance, because the majority of dots are located below it.

Finally, we examine the correlation between a region’s total population and total hospital visits and visualize the results in Figure 3(e). In general, it reveals a positive correlation between the population and visits. However, regions with similar populations do not exhibit similar visit amounts, as the red box illustrates. The high variance suggests potential factors that contribute to hospital visits other than population.

The above analysis suggests the influence of demographics and distance on visits to urban facilities. These observations further motivate us to explicitly characterize demographic-based demand and distance-based accessibility in the demand-driven facility visit prediction model.

The logical structure of our proposed framework of urban facility visits is shown in Figure 4. The fundamental idea is to define an urban region i’s visits to facilities as the process of fulfilling its population’s demands for that category of the facility. Represented as the top branch in the figure, a region’s total number of facility visit \(v_i\) is determined by its facility demand \(d_i\) and its capability of facility demand fulfillment \(\alpha _i\). We assumewhich denotes that the visit is the product of demand and the capability to be fulfilled. Notice that only the region’s number of visits to facilities is observable. Demand \(d_i\) and demand fulfillment capability \(alpha_i\) are both undetectable.

Our first observation in Section 3.3 postulates that the preference for facilities is strongly related to regional demographics. Here we define this “preference” as the region’s facility demand \(d_i\) determined by its demographic attributes \(\mathbf {r}_i\),which maps \(\mathbf {r}_i\)’s to \(d_i\)’s, revealing the emergence of underlying facility demands.

Due to the high variation we observed in Figure 3(e), the facility visits are not determined only by demographic attributes. According to our proposed visit framework, such variation can be attributed to the capability of facility demand fulfillment, which is determined by the region’s accessibility to each facility \(A_{i,j}\)’s,

In addition to original demand derived from demographic attributes, accessibility also affects the distribution of the region’s visits to each facility. The total number of visits \(v_i\) is distributed proportionally to the region’s accessibility \(A_{i,j}\) to each facility in the right part of Figure 4,where \(V_{i,j}\) is the number of pairwise visits from region i to facility j.

Based on former definitions, the accessibility of a facility represents the citizen’s preference when choosing a facility to visit. This preference is modeled as a function of spatial distance in the classic gravity model [64], deep gravity model [42], and the Huff model [19]. These measures inspire us to construe the accessibility as a function of the region’s distance to the facility \(D_{i,j}\) and the facility’s properties \(\mathbf {f}_i\),where we split the influence of distance and the influence of facility properties to form a simplified hypothesis that facilities in the same category have the same accessibility decaying pattern.

Our proposed framework of facility visits connects regional demographic attributes, which generate potential demand, distances between regions and facilities that affect pairwise accessibilities, and the spatial distribution of all available facilities that generate a capability of demand fulfillment. It disassembles facility visits into two explainable components: facility demand and capability of demand fulfillment. In this way, the underlying demand and the capability to fulfill it provide deep insight into the pattern of urban facility use as well as a great opportunity to provide better facility service to citizens, making the proposed framework a good leap from the simple characterization of visits as a function of various data sources to a model that embeds meaningful information and knowledge of citizens and facilities.

To realize the proposed framework, we design a neural network model for facility visit prediction, which is shown in Figure 5. We directly conduct the facility visit prediction task based on the framework by fitting the functions f, g, and h’s with Multi-layer Perceptrons (MLPs), a kind of fully connected network, that collectively construct a neural network. Neural networks have been shown to perform well in predicting complex functions in a variety of urban computing tasks [13, 47, 51], and current deep learning technologies have been well developed to efficiently optimize the goal of prediction tasks. The details of our facility visit prediction model are shown in Figure 5.

We first use MLP\(_f\) to generate demands from a region’s demographic attributes, fitting the function f in Equation (2). Multi-layer Perceptrons are a sequence of feed-forward fully connected network layers, where the input of a layer is the activation of the output of the previous layer. The activation function can be nonlinear, which can make the MLP a complicated nonlinear function. For a given region i, the model calculates its demand \(d_i\) by feeding its demographic attributes \(\mathbf {r}_i\) and its neighboring regions’ attributes \(\mathbf {r}_{n_{i1}}, \mathbf {r}_{n_{i2}}, \dots , \mathbf {r}_{n_{iK}}\) to MLP\(_f\) and aggregate the outcomes with a learnable parameter w as follows:where \(n_{ij}\) is the jth nearest region to i and K is the number of selected neighboring regions. This spatial smoothing can reduce the errors brought by data collection, which is that visits paid by a citizen living in the region \(n_{i1}\) might be counted on region i. The parameter w is confined to the range between 0 and 1, weighting the local facility demand and the average of neighboring demands.

MLP\(_{h_1}\) and MLP\(_{h_2}\) are introduced to model region i’s accessibilities to M facilities. For each facility j, MLP\(_{h_1}\) takes the distance from it to region i as its input and generate a scalar value as the region’s spatial accessibility to j. MLP\(_{h_2}\) is fed by the properties of each facility \(\mathbf {f}_j\), generating another scalar value for each facility that represents its empowered accessibility. The accessibility from region i to each facility j is then calculated as the product of two MLP’s outputs:

Given the region’s accessibilities to all facilities, we then use another MLP to fit the function g in Equation (3), which generates the region’s capability to fulfill its facility demand \(\alpha _i\) from all accessibilities \(A_{i,1},\dots , A_{i,M}\) as follows:Because the demand fulfillment capability \(alpha_i\) represents the fraction of demand realized, the activation of the MLP’s last layer \(_g\) is set to the sigmoid function \(\sigma (x)=\frac{1}{1+\text{e}^{-x}}\), which is an activation function with a value domain ranging from 0 to 1.

Finally, the model generates a predicted value of region i’s total facility visit \(\hat{v}_i\) by multiplying the predicted demand \(\hat{d}_i\) and capability of demand fulfillment \(\alpha _i\). Then it distributes the total number of facility visits in proportion to the region’s accessibility to each facility \(A_{i,j}\),

The objective function of the model is to minimize the squared error of the prediction value and true value of visits,where \(\lambda\) is a hyper-parameter that tunes the weight of the loss of pairwise visit predictions in the objective function. Since the pairwise visits and the region’s total visits are coupled, selecting the proper \(\lambda\) is necessary to improve the prediction performance.

Following the proposed framework, our proposed prediction model learns disentangled representations for two essential considerations: demand and fulfillment. In this way, we are able to model these underlying factors to facilitate the prediction task explicitly. Furthermore, our model supports regional demand recovery, which enables us to sense and infer deeper urban knowledge.

To characterize deterministic functions \(f, g, h_1, h_2\), we employ four feed-forward networks. Each MLP has two 16-dimensional hidden layers with the ELU [6] activation function. A ReLU nonlinearity is applied to the outputs of MLP\(_f\), MLP\(_{h_1}\), and MLP\(_{h_2}\), to ensure non-negative values of demands and accessibilities. A sigmoid function is applied to the output of MLP\(_g\) to bound the value of \(\alpha\) between 0 and 1. The number of selected neighboring regions for spatial smoothing K is set to 5. The weight of pairwise objective function \(\lambda\) in Equation (10) is set to 1,000, which is in the same order of magnitude as the number of urban regions. The model is optimized with an Adam optimizer with an initial learning rate of 0.001 [24].

We compare our model with several baseline models, which are as follows:

For the visit dataset of each city, and each facility category, i.e., hospital, school, and mall, we randomly split the urban regions and take 80% of them for training, 10% for validation, and 10% regions for testing. For each training region, the numbers of its pairwise visits to each facility are utilized as ground-truth values to fit the model. We train our model and each of the baseline models on the training set. We adopt the grid search strategy to tune hyper-parameters to achieve the minimum root mean square error of region visits on the validation set. Specifically, we tune the dimension of hidden layers, the activation function, and batch size for our methods, MLP, and DG. We tune the dimension of convolution layers and the method for aggregating node features for GCN.

In Figure 6, we demonstrate the training score (square root of Equation (10)) and validation score of our method and two baseline methods—MLP and DG. The convergence of an algorithm is determined when the best validation score is stagnant for over 200 batches. As shown in Figure 6(a), our proposed method has faster convergence than baseline models with slightly lower training loss. Validation score curves in Figure 6(b) validate that our method achieves the best validation score.

We then calculate the performance metrics on the same test set for each model. We use three metrics to evaluate the prediction performance, including Normalized Root Mean Square Error (NRMSE), Symmetric Mean Absolute Percentage Error (SMAPE), and Common Part of Commuters (CPC), which are widely used in mobility flow prediction [39, 42]. Considering the large standard deviation due to outliers, we take the logarithm of the visit number for optimization and evaluation. The mathematical expressions of the three metrics are listed as follows:where \(v_i\) and \(\hat{v}_i\) represent the real and estimated number of visits (region total visit or pairwise visit).

Table 3 illustrates the performance of our model and baselines on nine testing sets (three cities and three categories). Based on the results listed in Table 3, we have the following observations:

In summary, our proposed prediction model achieves better overall performance than baselines without deconstructing facility visits into demand and capability of fulfillment in facility visit prediction tasks, which demonstrates its ability to predict urban visit patterns precisely while preserving the latent mechanism of the patterns.

The framework that decomposes facility visits into facility demands and the capability to fulfill these demands can help predict urban facility visits more accurately. Given the improvement in prediction metrics, one important question is to evaluate the rationality of estimated facility demands and \(\alpha\)’s in the prediction model. In this part, we take Changsha as an example and examine its recovered demands.

We observe that the total number of regional visits to facilities \(v_i\) is positively correlated with the region’s population but is highly deviated, as illustrated in Figure 3(e). The large range of deviation is attributed to the spatial heterogeneity in accessibility to facilities. Now that we model demand and accessibility separately, the region’s demand should have a smaller deviation than the observed visits. This is corroborated by facility demands recovered from our prediction model. We draw the relation between estimated regional hospital demands and the regional population in Figure 7(a). We also illustrate the spatial distribution of normalized logarithm facility demands and normalized logarithm population in Figure 8. The Pearson correlation coefficient is 0.9316 with a relatively lower deviation compared with 0.5726, the correlation coefficient between hospital visits and the population. The correlation coefficients for school and mall demands are 0.8925 and 0.8759, respectively. The spatial distributions in Figure 8 show the high similarity between normalized demands and normalized populations. This smaller deviation is in line with the mechanism that demand is an intrinsic factor of the population.

The deviation in demands and the difference in the spatial distributions of demands for three facility categories are attributed to regional demographics. To study how demographic composition determines a region’s demand for facilities, we calculate the correlation between a region’s per capita estimated demand and the percentages of each demographic group. From the results shown in Figure 7(b), we observe several insightful patterns. First, male and female citizens possess different levels of demands on three facility categories. Male citizens have higher demands for schools and malls, while female citizens have higher demands for hospitals. This observation can explain some gender inequalities in urban spaces where women need to carry more medical and healthcare burdens while lacking education opportunities [2, 16]. Second, the percentage of the age group from 0 to 17 years is negatively correlated with demands for all categories. This may be attributed to the fact that students should not carry mobile phones to school. Therefore, these visits are not sensed in the datasets, which causes the model to learn a negative correlation between the percentage of non-adult citizens and school demands. In contrast, the age group with a positive correlation with school demands (25 to 30, 31 to 35, and 41 to 45) could be parents picking their children up from school. Third, senior citizens over 60 have high demands for hospitals and low demands for schools and malls. This is consistent with the preliminary analysis in Section 3.3. The elderly population’s demand for education and entertainment falls sharply, while their age brings increased medical demands. The well-explained heterogeneity in facility demands across demographic groups reinforces the rationality of estimated demands in our model, providing deeper insights into urban facility planning with demographic and demand factors taken into account.

To summarize, compared with number of visits, facility demands estimated by the model are highly correlated with region population, restoring citizens’ intrinsic attributes. Correlation analyses on facility demands and population composition demonstrate the heterogeneity in facility demands among different demographic groups. These observations consolidate the rationality of the facility demands recovered by our model.

Urban facilities are key infrastructure for the survival and life of citizens living in the city. An unbalanced facility distribution will deprive some citizens of the opportunity to fulfill their specific demands by depositing spatial barriers. Numerous works in the field of transportation and urban planning have studied the accessibility to urban places and its relation to spatial distance [37, 57]. In our proposed framework of facility visits, we model the capability of an urban region’s citizens to fulfill their facility demands as a function of the region’s accessibility to all urban facilities, while accessibility is measured by geodesic distances from the region to facilities. The capability of fulfilling demand \(\alpha\) and accessibilities to facilities can be explicitly retrieved from learned prediction models. To answer RQ3, we examine the spatial distribution of \(\alpha\)’s and the function to calculate accessibility from distance.

Due to the pervasiveness of mobile phones, researchers can efficiently sense large-scale human mobility data in urban spaces. A growing area of research is concerned with the predictions of citizens’ mobility, ranging from collective mobility flow to individual mobility behavior, by leveraging diverse sources of sensed signals in the urban environment. One topic is to predict the mobility flows between a given origin and a given destination (OD flow prediction). The gravity model [27, 64] is a fundamental physical mechanism that assumes the flows are proportional to the population of source and destination regions and the negative quadratic of the distance between them. The radiation model [43] assumes that an origin region distributes its outward mobility flow based on the attractiveness of other regions to it. Modern methods that embed deep learning technology for OD prediction have been developed based on these theories, such as Deep Gravity [42] and Gravity Neural Network [35]. Compared with classic theories, they also collect abundant urban data sources, including user demographics and urban venues, to generate more accurate predictions [21, 38, 58, 59]. Other mobility prediction problems that consider this urban semantic information include predicting a user’s next destination based on individual behavior [20, 23, 48], the spread of epidemic [26], and traffic flows [5, 28, 29, 40, 50, 60, 61]. Recent state-of-the-art methods predict urban mobility such as traffic flows based on graph neural networks that can adequately model spatial relationships in cities by edges in the graph structure based on historical data [5, 28, 40, 60, 61]. These studies enlighten the current work on predicting mobility patterns with various urban data by methods conserving the spatial structure of urban regions. Compared with the literature on urban mobility prediction, this article mainly focuses on the semantics of citizens’ pairwise visit patterns to urban facility venues without historical mobility information, which differs from pointwise traffic prediction tasks.

Among the studies probing the mobility prediction, many efforts have been made to predict visits or use of urban facilities and resources for its critical implication on urban design and planning [8, 9, 32, 41, 53, 56, 63]. In Reference [8], researchers extract temporal signatures of visit patterns to venues and use the similarities between places to predict the popularity of new cultural venues. Ruan et al. [41] predict the crowd’s dynamic use of mobile public agents to allocate them efficiently with lower energy costs in a theme park. Yu et al. [53] leverage cellular data, Point of Interest data, satellite images, and geographic data to predict regional demands for different categories of facilities. Liu et al. [32] use a latent factor model based on region-specific demographics and facility properties to estimate facility visits from sparse taxi trip data. Visit patterns to cultural facilities are studied in Reference [63] by a Dirichlet allocation model based on social media check-in data. These studies achieve good performance in predicting visits to urban facilities by miscellaneous approaches.

Our prediction model mainly differs from previous work in three aspects. First, our method can be applied to all facility categories, instead of one specific category like cultural or sports venues [8, 63]. Second, we not only focus on the number of visits originating from one region and the number of visits to one facility but simultaneously predict pairwise visits. Finally, previous works do not consider or model citizens’ heterogeneous demands for facilities. By contrast, we explicitly model demands facilities and accessibility to them in our method to enhance the prediction accuracy and model interpretability. Despite the fact that some studies define ”demand” in their methods [32, 53], it is either visited rather than hidden demand or is not supported by rigorous analysis.

Citizens’ demands for urban facilities are intrinsic attributes that cannot be directly sensed. The urban planning literature usually uses pre-defined functions of the composition of a region’s local residents as its demand for urban facilities, e.g., transportation, public parks, or entertainment [18, 37]. In Reference [37], the authors select population groups with low mobility levels, such as the unemployed and people under the poverty line, and use a linear combination of each group’s percentage in a region to form an index of demand for transportation. The National Recreation and Park Association [3] conducts a survey on American households’ demand for different outdoor facilities and activities across various demographic groups. Hong et al. [18] adopt consumer expenditure survey data to evaluate the demand for entertainment facilities and analyze their temporal changes. Compared with classic modeling of facility demands, we use a neural network model to fit a nonlinear deterministic function of population composition to their demands, requiring little prior knowledge of potential demands.

Given citizens’ demands for facilities, the number of fulfilled visits to each facility is determined by their accessibility to it. Huff [19] models choosing places to visit as a probability distribution determined by corresponding distances and attractiveness between regions. This model is widely used in planning the sites of new facility [14, 45]. We adopt the idea of modeling accessibility as a function of distance and facility properties. Moreover, we further propose a facility demand fulfillment ratio that aggregates the accessibility to all facilities to determine total facility visits. In contrast, previous works usually use accessibility to distribute a given number of total mobility flows or visits [42].

To enhance the efficiency and interpretability of urban facility visit prediction problems, we embed the framework of treating citizens’ visits to urban facilities as the process of realizing their demands for them in a prediction model. Extensive experiments demonstrate that the proposed model can perform better than baseline models that do not dissect facility visits. Meanwhile, the prediction model can recover reasonable regional facility demands and identify places where demands are insufficiently fulfilled by current facility allocation. Implications for various aspects and disciplines can be drawn from the findings in the article.

The recovered regional facility demands can provide important guidance for urban facility planning. Take the problem of optimizing facility distribution as an example. Classic methods usually attempt to minimize the average distance to the nearest facility for the whole urban population [52]. This objective simply assumes a homogeneous facility demand across demographic groups. Our analysis has shown that citizens of different age or gender groups have heterogeneous facility demands. Substituting regional population by regional facility demand in the objective of facility optimization problems can better cater to groups with higher demands. For instance, regions with a more senior population will be allocated closer to hospitals if their high medical demands are valued.

Our method also sheds light on the assessment of current facility placement. Traditional supply–demand analysis methods are often based on pre-assumed functions of facility accessibility to evaluate the deprivation of facilities in cities [7, 22, 36]. By contrast, our method explicitly models each region’s capability to fulfill its facility demand and its accessibility to all facilities. The estimated fulfillment capability can act as a proxy of the supply–demand ratio in larger urban districts. Moreover, various forms of accessibility functions can be learned automatically by neural network models, which is a huge leap from the classical second-order decaying function.

The idea of tracing back the generation of observable variables like facility visits and deconstructing them into underlying factors like demand and capability of fulfillment in the current work has important design implications for extensive ubiquitous computing tasks. Current technologies in the ubiquitous computing community can sense signals from various sources like wearable devices and mobile networks [17, 20]. However, abstract signals like the human mind and preferences are not perceivable by sensors. Instead, they can only be measured by proxy factors like human mobility. Modeling these abstract signals in a completely logical path may lead to more robust and understandable results.

There are some limitations in the range and settings of the current work. First, we only consider three representative urban facility categories that serve citizens’ medical, educational, and entertainment demands, not covering all kinds of demands like transportation, networking access, and exercise. Second, the demographic characteristics of users are limited to gender and age; other characteristics such as education level, employment, marital status, and disability may provide more insights into understanding facility demand. Third, the datasets are limited to one provider in China. The high coverage of collected mobility records on the whole urban population guarantees the datasets’ representativeness. We leave further analysis of more categories with more demographic attributes to future work. Finally, there is no true value of facility demand to evaluate the accuracy of recovered demands. Even if we compare them with population and demographic patterns to prove their credibility, they can only be regarded as an approximation of true demands.