MugRep: A Multi-Task Hierarchical Graph Representation Learning Framework for Real Estate Appraisal

In this paper, the real estate marketing datasets of Beijing and Chengdu are collected from a major commercial real estate agency¹¹1https://bj.lianjia.com. The scope of Beijing ranges from January 2018 to December 2019, and that of Chengdu ranges from January 2018 to December 2020. Each dataset consists of two kinds of data, i.e., real estate transaction data and residential community data.

We take Beijing as an example. Beijing totally contains 185,151 real estate transaction records and 6,267 residential communities. Each transaction record contains the attributes of the transaction estate, e.g., transaction date, transaction price, location, room number, area, transaction ownership, whether it is free of sales tax, the residential community real estate belongs to. Figure 1(a) shows the distribution of real estate unit price in Beijing. Figure 1(b) and Figure 1(c) show the fluctuation of unit price and transaction volume over time. Figure 1(d) and Figure 1(e) show the spatial distributions of unit price and transaction volume. Overall, the variation of real estate unit price in spatial domain is greater than that in temporal domain, whereas the transaction volume is distributed more evenly across the city with a notable periodical pattern. For each residential community, our datasets contain its developer, completion year, number of estates, property fee, etc. Figure 1(f) shows the spatial distribution of residential communities in Beijing, which is positively correlated with spatial distribution of transaction volume.

Then we construct large-scale geographical datasets, including point of interest (POI) data (Li et al., 2020) and transport station data (Liu et al., 2020b). There are 1,315,353 POIs and 44,513 transport stations in Beijing, 1,116,989 POIs and 30,564 transport stations in Chengdu.

Each check-in record corresponds to a GPS request from a mobile user, which is collected through Baidu location SDK (Zhang et al., 2020; Zhu et al., 2020). There are 4,078,723,999 and 5,130,847,589 users’ check-ins in Beijing and Chengdu respectively, to support the real estate appraisal task.

The User Trip Data are collected from Baidu Maps, which records the mobility pattern of a city. The user trip data includes the origin (geographical location) and destination of a trip, user’s travel mode (e.g., drive, taxi, bus, cycle, walk), and the type (e.g., enterprise, shopping places) of trip destination. Overall, there are 73,307,426 and 66,960,348 trip records in Beijing and Chengdu, respectively.

The User Profile Data contain user profile attributes (e.g., gender, age, income level, education level), which is collected from multiple Baidu applications including Baidu Search, Baidu App and Baidu Maps. There are 2,042,718 and 1,426,860 distinct user records in Beijing and Chengdu, respectively. Each record contains a user’s demographic attributes including hometown, gender, age, and social attributes such as the industry, income level, educational level, consumption level, and whether the user is a car owner. All user profile records are anonymous and cannot be associated with sensitive personal information such as names and phone numbers.

Figure 2 shows the framework overview of MugRep, which consists of five major components: Data Warehouse, Feature Construction, Graph Construction, Representation Learning, and Multi-Task Learning. The Data Warehouse stores Real Estate Marketing Data and four additional multi-source urban data. The Feature Construction module generates seven groups of features based on the corresponding datasets in Data Warehouse. Besides, the Graph Construction module builds evolving transaction event graph based on the place and period proximity of transaction events, and constructs hierarchical heterogeneous community graph based on intra-community real estate transactions and inter-community similarities. In particular, the community similarities are quantified by additional diversified urban feature groups. After that, the Representation Learning module is introduced to derive the event-level and community-level representation of subject property, of which the integration is processed in a Multi-Task Learning module, where each task corresponds to an urban district. The corresponding task block produces the final result of Real Estate Appraisal.

In this subsection, we present the process of constructing various features based on the aforementioned multi-source urban datasets. The details of used features are listed in Table 3 of Appendix A.

The price of real estate transactions in proximal places and periods have strong dependencies. For example, for a place with a planned subway station, the real estate prices of surrounding areas usually increase synchronously. The transaction price dependencies can also be validated by Figure 1(d), i.e., the nearby real estate prices tend to be similar. However, these transactions are dispersedly distributed in spatial and temporal domains, which induces spatiotemporal asynchronism. Such asynchronously spatiotemporal dependencies among real estate transactions also distinguish our task from existing works on predicting regional future house prices (Tan et al., 2017; Ge et al., 2019), where the input are more regular time series data. It also prevents us to adopt existing spatiotemporal prediction approaches (Li et al., 2018) for our task.

To tackle above problem, we first formulate each real estate transaction as a transaction event, which is defined in Section 3. Then, we model the continuously emerging transaction events as an evolving graph $G_{e}=(V_{e},E_{e},A_{e})$, where $V_{e}=S$ is a set of real estate transaction events, $E_{e}$ is a set of edges indicating connectivity among transaction events, and $A_{e}$ denotes the proximity matrix of $G_{e}$. Specifically, we define connectivity constraint $e_{(t+1)t^{\prime}}\in E_{e}$ as

where $dist(\cdot)$ is the geographical distance between the locations of events, $\epsilon_{d}$ and $\epsilon_{\tau}$ are physical distance threshold and time interval threshold, respectively. To balance the connected events from different communities, we restrict a node at most to connect last $N_{e}$ events from each community. With real estate transaction events occurring over time, the graph $G_{e}$ evolves accordingly.

Inspired by recent success of GNN (Kipf and Welling, 2017; Velickovic et al., 2018) on processing non-Euclidean graph structures and its inductive ability to effectively generate representation for previous unseen node (Hamilton et al., 2017), we adopt graph attention networks (Velickovic et al., 2018), an effective variant of GNN, to capture event-level dependencies among real estate transactions on the evolving graph.

Specifically, to quantify the sophisticated influence of historical transaction events $s_{t^{\prime}}$ to subject property $s_{t+1}$, we introduce the attention mechanism (Zhang et al., 2021) to automatically learn the coefficient between transaction events,

where $\mathbf{v}_{e}$ and $\mathbf{W}_{e}$ are learnable parameters, $\oplus$ denotes the concatenation operation. The proximity weight between event $s_{t+1}$ and $s_{t^{\prime}}$ is further defined as

where $\mathcal{N}_{t+1}$ is a set of adjacent events of $s_{t+1}$ in $G_{e}$.

Once $\alpha_{(t+1)t^{\prime}}\in A_{e}$ is obtained, we derive the representation that integrates nearby previous transaction events by aggregating and transforming the adjacent events of subject property, defined as

where $l$ indicates the $l$-th graph convolution layer in evolving graph, $\mathbf{W}_{he}^{l}$ are learnable parameters for $l$-th graph convolution, $h_{e,t+1}^{0}=x_{t+1}$, and $I(l>1)$ is an indicator function that equals one if $l>1$ and zero otherwise. By stacking $L_{e}$ convolution layers, we can aggregate $L_{e}$-hop adjacent events to mine spatio-temporally extensive knowledge from historical real estate transaction data for more accurate subject property valuation.

As aforementioned, the real estate value is also highly correlated with the residential community it belongs to (Fu et al., 2015). Therefore, an expressive representation of community can be useful in real estate appraisal. In this work, we devise a hierarchical heterogeneous community graph convolution module, including the dynamic intra-community graph convolution block and the heterogeneous inter-community graph convolution block.

In general, a city is partitioned into several urban districts for administration. Each urban district can have distinctive urban functionalities and leads to diversified real estate price distributions, as illustrated in Figure 4. Inspire by (Zhu et al., 2016), we partition the tasks via urban districts, and each urban district corresponds to a learning task. These tasks share most of parameters of the model except have a unique fully-connected output layer to generate appraisal of distinctive distribution. Therefore, the real estate located in each urban district is valuated by

where $FC_{m}$ denotes the unique fully-connected layer of $m$-th task associated with $m$-th urban district.

Overall, our model aims to minimize the Mean Square Error (MSE) loss between the estimated unit price and the ground truth transaction unit price of real estate,

where $S_{m}$ denotes the real estate transactions set happening in $m$-th urban district, $|S|$ denotes the cardinality of $S$.

We evaluate the performance of MugRep on both Beijing and Chengdu datasets. We chronologically order each dataset based on the transaction date. For Beijing, we take the data of which the transaction date ranges from January 2018 to June 2019, as the training set, the following one month as validation set, and the rest of data for testing. For Chengdu, the training set is set from January 2018 to June 2020, the other setting are the same as Beijing. Our experiments mainly focus on (1) the overall performance comparison, (2) the ablation studies of model and features, (3) the feature importance analysis, (4) and the effectiveness check for spatially different communities. Furthermore, please refer to Appendix C for the prototype system of real estate appraisal.

Table 2 reports overall results of our methods and all compared baselines on two datasets with respect to three metrics. Overall, our model achieves the best performance among all the baselines. Moreover, we observe all ANN based algorithms (DNN, PDVM, MugRep) outperform the statistical algorithm (HA) and machine learning based algorithms (LR, SVR, GBRT), which consistently verifies the advantages of applying ANN to real estate appraisal for its extraordinary non-linear processing ability. Particularly, MugRep achieves $(6.5\%,6.6\%,5.1\%)$ and $(12.8\%,10.8\%,11.3\%)$ improvements beyond the state-of-the-art baseline PDVM for (MAE, MAPE, RMSE) on Beijing and Chengdu, respectively. The results demonstrate the effectiveness of MugRep.

In this section, we conduct ablation studies on MugRep, including model ablation and feature ablation, to further verify the effectiveness of each component and feature group. The experiments are finished for three metrics on both Beijing and Chengdu datasets.

To further evaluate the effect of our constructed features, we illustrate the top-30 most important features in Figure 7. The features are ranked by logarithmic information gain (Ke et al., 2017). As can be seen, the distribution of historical price are the most important features. The subsequent one is the district of residential community, which indicates the large difference between districts. Furthermore, we observe half of the top-30 features are from the four multi-source urban datasets, which demonstrates the effectiveness of these urban features. Among these urban features, the geographical features (Living, Entertainment, Shopping), mobility features (Travel destination) and resident population profile features (Income level, Consumption level, Industry) are ranked very high (in top-15). For the reasons that these geographical features are closely related to living quality, these mobility features are greatly relevant to travel preferences of community residents, and these resident population profile features are strongly associated with the wealth of community residents. The living quality, travel preferences, and wealth are three very important factors to reflect the real estate prices.

To evaluate the performance of MugRep on spatially diverse communities, we compute the separate MAPE for each residential community. Figure 8(a) and Figure 8(b) show the spatial distribution of MAPE and inverse transaction volume on Beijing. As can be seen, some communities with high MAPE (bright color) always have high inverse transaction volume (i.e., less transaction volume) nearby. This makes sense for two reasons: first, the historical price features of same community are important for subject property valuation, less transaction volume in the community means inaccurate or missing historical price features; second, the evolving transaction event graph convolution module of MugRep is highly correlated with nearby previous transactions, the absence of nearby transactions decreases the effectiveness of event-level representation. This result indicates further optimization can be applied to these residential communities with scarce transactions to improve the overall performance.