Extracting real estate values of rental apartment floor plans using graph convolutional networks

Abstract

Access graphs that indicate adjacency relationships from the perspective of flow lines of rooms are extracted automatically from a large number of floor plan images of a family-oriented rental apartment complex in Osaka Prefecture, Japan, based on a recently proposed access graph extraction method with slight modifications. We define and implement a graph convolutional network (GCN) for access graphs and propose a model to estimate the real estate value of access graphs as the floor plan value. The model, which includes the floor plan value and hedonic method using other general explanatory variables, is used to estimate rents, and their estimation accuracies are compared. In addition, the features of the floor plan that explain the rent are analyzed from the learned convolution network. The results show that the proposed method significantly improves the accuracy of rent estimation compared to that of conventional models, and it is possible to understand the specific spatial configuration rules that influence the value of a floor plan by analyzing the learned GCN.

Keywords

Rental apartment hedonic model floor plan access graph graph convolutional networks

Introduction

This study represents the floor plans of rental apartment buildings in Osaka, Japan, in a graph structure and demonstrates their influence on rents using a deep learning approach. Several studies reported that residential floor plan information significantly affects on real estate choices (National Association of REALTORS®, 2021; Berchick, 2021). In Japan, floor plan images are always provided with the real estate information of a house, and they are indispensable for real estate selection. Further, the floor plans for general housing complexes are classified using designations such as “3LDK,” where 3, L, D, and K represent the number of private rooms (bedrooms), living room, dining room, and kitchen, respectively. The housing market is segmented based on differences in floor plans, such as 1K for singles, 2DK for married couples, and 3LDK and above for households with children. These classifications are used as a key for rent quotes (e.g., SUUMO, 2023) and property searches. However, the actual floor plans are different even if they are expressed using the symbols of the same floor plan. In recent years, an open-floor plan with a large living room has gained popularity, increasing the value of houses by ∼7.4% (Pan, 2017) as reported in the study from the United States. Further, open plans have become popular in Japan as modern floor plans (Mizunuma, 2017); however, after the COVID-19 pandemic, privacy has become more important even in housing, and thus, the popularity of open plans has decreased (Zillow, 2020). The aforementioned real estate values and Internet property search systems do not consider such detailed differences in floor plans, and therefore, there is currently no other method to determine the differences with the naked eye.

Quantifying floor plans requires complex analytical procedures, which have been addressed in the field of Space Syntax (Hillier and Hanson, 1984). Several analysis methods are used in Space Syntax, but for floor plan analysis, the space is divided into appropriate units (i.e., nodes) and access graphs are constructed by connecting rooms and spaces connected in terms of flow lines by edges for extracting the indicators of graph depth and centrality. For example, Brown and Steadman (1991) created and analyzed graph data for 300 residential floor plans in the United Kingdom. A study by Takizawa et al. (2008) can be cited as a study that extracts structural features of residential floor plans from access graphs and incorporates them into a hedonic model, in a manner different from Space Syntax approach. In the study, access graphs were manually created from floor plan images of approximately 1,000 family-sized rental housing information in Japan, and subgraphs were enumerated using a method called graph mining (Chakrabarti, 2011). By using subgraphs that are meaningful for rent estimation, they were able to improve the accuracy of the rent estimation model compared to a rent estimation model using general explanatory variables. Limitations of the study include the fact that the access graph data was manually created from floor plan images, making large-scale analysis difficult, and the feature extraction from the access graphs was fragmentary, making it difficult to estimate how much real estate value any given floor plan has.

Thus far, several technologies were developed to overcome the abovementioned problems. The LIFULL HOME’S dataset (LIFULL Co., Ltd, 2015) is a large dataset of Japanese real estate, and after it was released, several methods were developed to extract access graphs from images automatically using deep learning (Yamada et al., 2021; Yamasaki et al., 2018) and other similar techniques.

Given this background, this study uses the LIFULL HOME’S dataset to extract access graphs automatically from a large number of floor plan images of family-oriented rental housing in Osaka Prefecture using a slightly modified version of the method described by Yamada et al. (2021). Then, we define and implement a graph convolutional network (GCN) for the access graph and propose a model that estimates the real estate value of a homomorphic access graph as the floor plan value (FPV) after learning rent estimation. The model with FPV and the hedonic method that uses other general explanatory variables are used for estimating rents, and their estimation accuracies are compared. We also analyze the features of the floor plans that explain the rents from the learned convolution network. Therefore, we propose and validate a new model for comprehensively estimating the value of real estate floor plans.

Literature review

Previous studies that quantitatively evaluated housing values and preferences frequently used indices such as neighborhood, location, size, and housing type have been used frequently (Adir et al., 1996; Lovejoy et al., 2010; Michelson, 1977; Valente et al., 2005). Some studies evaluated houses based on more detailed attributes such as the number of rooms, size, shape, room size, and facilities (Hofman et al., 2006; Goodman and Thibodeau, 2007). The latter study hypothesized that housing preferences are influenced by a combination of many detailed factors such as design, usability, and spatial configuration. However, quantifying these factors is difficult when they are considered in detail. Hofman et al. (2006) and Goodman and Thibodeau (2007) evaluated the number of rooms, area, and defined shape, which are relatively easy to quantify, as independent variables.

The Space Syntax analyses of residential floor plans were conducted for a variety of housing types, including traditional houses (Hanson, 1999), high-rise apartment buildings (Hanazato et al., 2005), and detached houses of famous architects (Ostwald and Dawes, 2018). These studies focused on relatively large and complex spaces, such as a single or small number of cities or building complexes. Brown and Steadman (1991) reported a study that dealt with only relatively simple or small but numerous floor plans, which are the subject of this study.

The evaluation of housing preferences and ease of use is not only estimated from hedonic methods but also via the subjective evaluation of floor plan images. Gao et al. (2013) and Tamura and Fang (2022) used Space Syntax to explain the evaluation results, and they revealed that the degree of privacy affects the evaluation of certain resident groups. Kato et al. (2020) and Narahara and Yamasaki (2022) conducted subjective evaluations based on the aforementioned floor plan images of the LIFULL HOME’S dataset and they combined multiple deep learning methods in their evaluation prediction models. Narahara and Yamasaki used a large sample of over 3000 subjects and inferred that the prediction model has a certain degree of reliability. The number of presented floor plans was limited because of the nature of the questionnaire, and the relationship with the rent was not evaluated.

There have been many studies on estimating the value of real estate using hedonic methods. With the development of deep learning in the late 2010s, the interior and exterior of buildings have been used as image data (Ahmed and Moustafa, 2016; You et al., 2017; Glaeser et al., 2018; Poursaeed et al., 2018) and floor plans (Solovev and Pröllochs, 2021; Hattori et al., 2021) in hedonic models. Such studies are the common motivation for this study. The approach that uses floor plan images directly does not suffer from the risk of access graph misclassification. For models trained using floor plan images, decision-making in the learned model is represented by image feature points, which are not interpretable from an architectural or real estate perspective, that is, this type of model is a black box that improves prediction accuracy.

Compared with these previous studies, our study is unique because it counts the number of unique floor plans based on access graphs estimated automatically from a large number of floor plan images, constructs a rent estimation model using a GCN, indexes it as a single-floor plan value, and explores the basis for determining the value from the graph structure.

The framework of this study is illustrated in Figure 1.

Figure 1.

Framework of this study.

Dataset preparation

This section describes the procedure and results of extracting the floor plan access graphs.

Step 1: Define an access graph

In this study, the floor plan of a house is represented as an access graph that indicates adjacency relationships from the perspective of room flow lines. A GCN is used to learn FPVs in accordance with the access graph extraction method developed by Yamada et al. (2021). Figure 2 shows an example of a floor plan and its access graph. The access graph is represented as a graph with the node labels of room types; 10 labels are used in this study. The notation “_0,_1,…” after the label indicates a sequential number that distinguishes the nodes with the same label. There are two types of room connections: (1) the rooms are separated by a door or window as a boundary, and (2) the rooms are recognized as different spaces without a physical partition, such as an entrance and a hallway; however, they are not distinguished in the access graph. Openings are treated as walls because they are not connected to other spaces by edges even if they are recognized, except for the part that serves as a border with a balcony. A Japanese room is a room with tatami mats, which is unique to traditional Japanese houses. Traditional Japanese rooms have distinctive wall and ceiling styles in addition to tatami mats, but in a typical Japanese room in apartments, the wall and ceiling are simply be wallpapered (see Figure S1 in the supplementary material).

Figure 2.

Examples of a floor plan and its access graphs.

Step 2: Filtering data and extracting access graphs

This study used the LIFULL HOME’S dataset described above, and this dataset includes three types of data. Among them, this study uses the snapshot data of rentals that include various pieces of information on approximately 5.33 million rental properties nationwide as of September 2015 and the high-resolution floor plan image data of those properties.

Table S1 in the supplementary material lists the procedure for extracting the data, which includes the access graphs necessary for this study. In Procedure 2, we use the adjacency graph extraction method developed in the literature (Yamada et al., 2021) with some modifications. The improvements and accuracy evaluations are presented in Appendix S1 in the supplementary material in the supplementary material. The graph isomorphism test in Procedure 3 determines whether the two graphs have the same topology and selects only unique access graphs. In this study, the isomorphism test considers the type of node (usage). The isomorphic function of NetworkX (NetworkX Developers, 2014) is used by setting its node-matching option. Consequently, 7970 different access graphs are extracted. A total of 19,998 access graphs are aggregated using these isomorphic graphs. A histogram that shows the number of corresponding properties in the descending order is shown in Figure S2 in the supplementary material. The access graphs are concentrated in certain types. More than half of the access graphs have one property and they tend to have a small number of properties. Access graphs that are easily misjudged tend to have a small number of properties, and the actual number of unique access graph types is likely to be less than 7970. However, the overall accuracy is approximately 80% (see Appendix S1), and the analysis is conducted by including the case where the number of properties is one. Step 3 explains the eight variables considered in Procedure 4.

Figure S3 in the supplementary material shows floor plans with the top three most frequently unique access graphs. Many recent floor plans in Japan do not have a Japanese room; however, top access graphs are those with a Japanese room.

Step 3: Prepare tabular data

We organized the common tabular data for using them to train the access graphs and in the final hedonic model. The dataset used contained 71 variables. Among these, the monthly rent without common expenses was used as the objective variable. As explanatory variables, we used the following items with high coverage: average land price, year of construction, number of passengers per day at the nearest station in 2016 (MLIT, 2016), distance to the nearest station/bus stop, building structure, housing unit area, number of building floors, and number of housing unit floors.

The average land prices were obtained using the following procedure: Public land price data (MLIT, 2015a) and prefectural land price survey data (MLIT, 2015b) for Osaka and the adjacent prefectures in 2015 were plotted using ArcGIS Pro 2.8. Kriging was performed on these points to fine tune the discontinuous values, and a continuous map of land prices was constructed (Figure S4 in the supplementary material). We used the zip code boundary polygon data of Osaka Prefecture (Kokusai Kogyo, 2020) to obtain the average land value of the raster data in each polygon because the spatial resolution of each property was limited to the zip code level. Then, this was used as the land value of the corresponding property. Figure S5 in the supplementary material shows a map of the 15,323 properties obtained in Step 2 aggregated by each zip code area. Tables 1 and S2 (in the supplementary material) summarize the tabular data used for GCN learning and rent estimation after adding the variables as indicated.

Table 1.

Basic statistics of quantitative variables (N = 15,323).

Variable	Description	Min	Mean	Median	Max	SD
Area	Area of housing unit (m²)	37	65.2	65	159	7.3
Distance	Distance to nearest station/bus stop (m)	10	865	800	37,600	629
F_Building	Number of building floors	0	5.9	5	50	4.0
F_Room	Number of floors of housing unit	1	3.6	3	77	2.8
Land price	Average land price in zip code area (Yen/m²)	0	187,824	184,500	557,725	75,396
Passenger	Number of passengers at nearest station	0	28,447	21,604	431,007	26,638
Year	Year of building completion	1933	1994	1994	2015	6.8
Rent	Rent without common expenses (Yen/month)	38,000	82,973	77,000	450,000	24,659

SD represents standard deviation.

Step 4: Extract explicit features of the access graph

We build a rent estimation model from the access graphs obtained using the GCN; however, for comparison, we also build a rent estimation model with the explicitly given graph features. We call a model with graph features a GF model. The GF model uses the total number of nodes and edges that constitute each access graph, number of nodes for each room type, maximum depth from the entrance, real relative asymmetry (RRA), and relative difference factor (H*) as the explanatory variables (Zako, 2006) (see Appendix S2 in the supplementary material). The latter three features were used in the Space Syntax analysis. The maximum depth from the entrance indicates the degree of privacy from outside. RRA indicates the degree of isolation of each node in the entire graph, with larger values indicating greater isolation. H* indicates the diversity of the RRA distribution for each node in the graph, with larger values indicating more diversity in the RRA for each node, that is, a deeper space. The larger the value, the more diverse is the RRA of each node, that is, the deeper is the space.

In this study, the RRA was obtained for each node as a starting point, except for the closets. However, the node with the highest value was used when there were multiple rooms of the same type. The value was set to zero if there were no corresponding nodes. Owing to the large number of prepared variables, only the variables employed in the GF model after variable selection are listed in Table S3 in the supplementary material.

Pearson's product-moment correlation coefficients between the main variables used in each model are listed in Tables S4 and S5. Although the correlation coefficients between F_Building and F_Room, Num_cl, and Num_edge exceed 0.7, we checked the variance inflation factor (VIF) of the models described below and found that multicollinearity did not occur among the numerical variables (Tables S6 and S7).

Extracting floor plan values using the graph convolutional network

This section describes the method to extract FPVs using GCN.

Step 1: Definition of GCN

A GCN is used to estimate the real estate value of a floor plan by inputting the floor plan data represented as an access graph. To train this network, the rent of each property should be used as an objective variable; however, the rent is not determined solely from the floor plan, and therefore, the aforementioned table data are also used. Figure 3 shows the learning model that combines a GCN and the multiple regression model. PyG (PyG, 2022) is used to implement this model. There are several standard architectures for GCNs in convolutional layers. However, there is no typical architecture for their combination such as VGG (Simonyan and Zisserman, 2015) in CNNs for image processing. In this study, we employed a graph network (Zhao et al., 2018) that mimics the structure of VGG, which has a simpler structure; this GCN model performed comparatively well on many graph datasets. The main convolutional layer, ResGatedGraphConv (Bresson and Laurent, 2017), which performed well in the preliminary experiments, was also used. However, the first layer is only a more basic GCNConv (Kipf and Welling, 2016) because the calculation of the integrated gradient (IG) (Sundararajan et al., 2017) is the method used to explain the model described below, and it requires an edge attribute in the input layer for masking. However, ResGatedGraphConv does not allow for an edge attribute.

Figure 3.

Multiple regression model for training including GCN. Numbers in () are dimensions of (input, output) data.

Step 2: Training of GCN with all data

The mean squared error (MSE) loss was used as the loss function, and the training settings were optimizer = Adam, learning rate = 0.01, batch size = 1024, and epoch size = 2000. Figure S6 in the supplementary material shows the results of the convergence evaluation on the training data using all 15,323 data points. The root mean squared error (RMSE) of the training data at the end of 2000 epochs is 6657 Yen, which is approximately 8% relative to the average rent. The convergence of the model was judged to be satisfactory, and the parameters of the model were stored at every 50 epochs and the real estate value of each floor plan was estimated later.

Step 3: Determine the optimal epochs for GCN training using 10-fold semi-cross-validation

Next, 10-fold semi-cross-validation learning was performed to evaluate the prediction accuracy of the FPV estimation model for each of the 50 epochs. The model for the epoch with the highest prediction accuracy was used to estimate the FPV, and the prediction accuracy was verified. The 15,323 data points were divided randomly and equally into 10 segments, and each segment was divided into training and test data. Next, we trained the whole GCN model on the training data for each partition using the training parameters, and we saved the model for each of the 50 epochs. Only the GCN portion was extracted from each saved model to estimate the FPV of the test data and a multiple regression model consisting of that value, other variables, and a constant term created to determine the accuracy (i.e., RMSE). Unlike usual cross-validation, a multiple regression model is trained and validated with only FPV as the unknown data during accuracy validation, which we call semi-cross-validation.

The distribution of the RMSE obtained after repeating this process 10 times is demonstrated in Figure S7 in the supplementary material. The model with the smallest average RMSE was the FPV trained at the 1550 epoch. We evaluate the accuracy of the baseline and GF models using the same test data.

Step 4: Distribution of FPVs

The original values were converted to deviation values for facilitating their positioning because the FPV is a relative value and the absolute value is meaningless. The deviation value is obtained by converting the original data such that the mean is 50 and the standard deviation is 10, which is routinely used in Japan to compare test scores. Let $x, \bar{x}, a n d σ$ be the values of the FPVs before conversion, their mean, and standard deviation, respectively. Then, the deviation $F P V (x)$ of a given FPV of $x$ is defined by

F P V (x) = 10 \frac{x - \bar{x}}{σ} + 5 0

Figure S8 in the supplementary material shows a histogram of the deviation of the FPVs for the 7865 unique access graphs estimated by the model at 1550 epochs when all graphs were trained with the data. The minimum, maximum, and median values were 2.2, 226.9, and 48.6, respectively. The distribution was not normal; however, it was asymmetric with the maximum value having a base longer than the mean value. Hereafter, this deviation in the FPV is referred to as the FPV.

Comparison of the accuracies of the three hedonic models

To verify the validity of the hedonic model that considers the FPV model, a rent estimation model that uses only general variables as the baseline model and the GF model were compared in terms of their accuracy using the aforementioned 10-fold semi-cross-validation method. The accuracy was compared using the aforementioned semi-cross-validation method. In addition to the RMSE, the adjusted R² was used for accuracy. Figure S9 in the supplementary material shows the distribution of the accuracy for each model and the results of multiple comparisons (Bonferroni, 0.05 level of significance). The accuracy of the FPV model that had a mean RMSE of 11,280 Yen and a mean adjusted R² of 0.79 was significantly higher than that of the other two models.

Tables S6 and S7 in the supplementary material summarize the results of 10 and a half cross-validations on the test data of the model with FPV/graph features. The high VIF of Structure_RC is attributed to Structure_RC being a dummy variable created by decomposing a categorical variable of Structure. It is just correlated with other similar dummy variables such as Structure_S (see Table S4). In all models, except for the constant term, the most influential variables include surrounding land price, unit area, and year of completion, which is a general trend for Japanese real estate rent estimation models. For the FPV model, the FPV has the next highest influence. As shown in Figure 4, the logarithmic values of the variables from #6 declined significantly. The most influential variable in the GF model is real relative asymmetry of Japanese room (RRA_jp), but its logarithmic value is as small as 1/20 of the FPV. However, it is easily interpretable, for example, a floor plan with a Japanese room that has a high degree of isolation has lower rent, or a floor plan with many closets has a higher rent.

Figure 4.

Distribution of the log values of each variable in the FPV model.

Detailed analysis of the GCN model and its result

We obtained the FPVs of isomorphic access graphs using GCN at epoch 1550, which was learned using all 15,323 data points. We analyzed the relationship between the floor plans and the GCN model.

Analysis 1: Differences in floor plans by FPVs

The floor plans with the smallest, average, and largest FPVs are shown in Figure S10 in the supplementary material. The floor plans with the lowest FPV are unique because all living rooms are Japanese rooms, and all functions such as water supply are lined up in a row against the hallway. However, the average floor plan has features such as tatami mats facing a balcony and a separate kitchen, which provides the impression of being old-fashioned. The best floor plans are the most luxurious ones with two balconies, considerable storage space, and a high degree of spatial independence.

Analysis 2: Basis for estimating the FPV model for each access graph

The basis for estimating the FPV of the FPV model is determined. To this end, we visualized the access graphs of characteristic floor plans using IG implemented by Captum (2022), which is an explanatory method of deep learning models. Although there are several explanatory methods for deep learning models, IG was adopted because it has a clear theoretical foundation and is easy to implement.

First, the state in which there are no components in the access graph is set to 0, and the state in which the nodes and edges of the access graph to be examined are set to 1. The intensity of the graph is changed gradually from 0 to 1. IG expresses the contribution of each component of the access graph to the FPV as an integral value. The PyG graph model requires the input of nodes as a matrix of types, and the edges as a list of pairs of nodes at both ends of the matrix. The application of IG requires a simultaneous and continuous change in the strength of the components of the access graph. Edges are represented by neighbor lists; therefore, their strengths as edges must be set separately. This was achieved by setting edge weights in the first convolutional layer of the graph. During the training and testing of the model, the weights of nodes and edges are fixed at 1, and their weights can be varied continuously in the range [0, 1] by Captum only during the IG computation. The range of increments from 0 to 1 was set to 200 steps.

IG is applied to each unique access graph to determine the contribution of the components. The results are shown in Figure 5 for floor plans with low, average, and high FPVs visualized in a relatively easy-to-understand manner. Blue, gray, and red indicate a decrease, no change, and increase in the FPVs, respectively. The color scale is set for each property, and it is easy to understand that the connection of a Japanese room lowers the value of a floor plan with a low FPV. However, the result is similar for an average property. The difference is that balconies connected to Japanese rooms are rated lower for floor plans with low FPVs, whereas they are rated higher for floor plans with average FPVs. Nodes and edges around the dining room are evaluated positively in the floor plan with a high FPV, and this is consistent with the human evaluation of open-floor plans centered on the dining room. In contrast, the area around the water is rated as low. The dining kitchen-lavatory-hallway (dk_0-la_0-hw_0) loop seen in this floor plan is a looped flow line that has become popular in Japan in recent years. However, the FPV model does not recognize this loop as a good pattern, and there is a partial discrepancy between the loop and evaluations of the people.

Figure 5.

Visualization example of the contribution by the IG of access graphs for floor plans with low, medium, and high FPVs.

Analysis 3: Understanding the overall estimation basis of the FPV model

We characterized the estimation basis of the overall FPV model for all unique access graphs. IG is a relative value calculated for each floorplan, and it is not sensible to directly compare or aggregate the IG values of components with those of other floorplans. Therefore, the IG values of each floor plan component were standardized to have a mean of 0 and standard deviation of 1, and their distribution was tabulated for each component of all floor plans. The distributions were analyzed for significant differences from the overall mean at a significance level of 0.05 using the mean analysis method (ANOM) (Nelson et al., 2005). The results are shown in Figure 6. Each point represents the mean value, and if the value is outside the range of the confidence interval [lower decision limit (LDL), upper decision limit (UDL)], it is significantly different from the overall mean. The confidence interval decreases with an increase in the number of components.

Figure 6.

Distribution of node and edge contributions for all unique access graphs and confidence intervals for the mean analysis method.

The node with the largest positive contribution to the FPV is the balcony (0.463), whereas nodes with the largest negative contribution are the Japanese room (−0.267), dining kitchen (−0.216), and entrance (−0.165). The presence of a balcony may be interpreted as a guarantee of the minimum FPV because a balcony is an essential place to dry laundry in a family-oriented floor plan. As the popularity of Japanese rooms is declining in Japan, it is understandable that its presence has a negative impact. The dining room, kitchen, and entrance are common to all properties and are not involved in the differentiation factor if they are only present; therefore, it is difficult to interpret them as anything other than an overall adjustment factor.

For edges, the expression “bl-bt” for the edge type indicates that the edge connects the balcony and the bathroom. The edges with absolute values greater than 0.1 beyond the confidence interval are in the descending order from the highest positive contribution, closet-hallway (0.175), closet-dining kitchen (0.167), hallway-toilet (0.164), dining kitchen-Japanese room (0.152), and closet-entrance (0.121). The contribution tends to be higher when the closet is located at the hallway or entrance. The contribution is higher when the toilet is independent and entered from the hallway rather than that from the washroom. The Japanese room is entered from the dining room and kitchen rather than from the main hallway, which is the characteristic of modern layouts. Although these connections are convincing, the overall results suggest that the relationship between detailed accessory functions such as closets and toilets, instead of the relationship between rooms, tends to affect rent. The only significant edge with a negative contribution of −0.1 or less was the Japanese room-Japanese room (−0.138), which was less significant than the positive case. This result is easy to understand, although it suggests that the contribution of Japanese rooms tends to be lower when they are connected than when they stand alone, because of synergistic effects.

Although we evaluated the effectiveness of FPV using a simple ordinary least squares (OLS) model, we used a geographically weighted regression (GWR) model for determining the differences in the geographic effectiveness of each variable. The results are presented in Appendix S3 in the supplementary material, and they suggest that FPV has a strong effect on urban centers.

Discussion and conclusion

We discuss the accuracy of the access graph data. In this study, we improved the accuracy of access graph recognition by making detailed improvements to the methods used in previous studies; however, there are still cases of misclassification. In this method, the accuracy of semantic segmentation significantly affects the accuracy of neighboring graph extraction. Segmentation fails in small areas such as bathrooms and closets, when the text in the description is prominent and when the floor plan is black or white. In the future, it is necessary to improve the accuracy of segmentation, which is the basis for graph extraction.

Next, we explain the relationship between the FPV model and human evaluation. For example, the FPV and human evaluation may be similar in some respects and different in others, as seen in the aforementioned lack of detection of water circulation. The current GCN model does not appear to clearly detect the features of long flow lines beyond room pairs. However, this may be attributed to the visualization quirks of IG, which is a general-purpose method such as IG but can output more intuitive results. In this study, we used IG, which is theoretically superior and easy to implement; however, we believe that appropriate methods for explaining the GCN of floor plans need to be compared and investigated. The current access graphs represent only the connections between rooms with different uses. However, the presence or absence of openings was not considered except for the approach to the balcony. More basic features such as the size and shape of the rooms were not considered; it is highly possible that these points are the cause of the differences in human evaluations. This is a problem that needs to be improved from the graphing stage of floor plan images; however, we believe that it is an issue that needs to be addressed.

Finally, we discuss the use of GCNs and explicit graph features. Space Syntax indices such as RRA are related to the centrality of space, so they are appropriate for distinguishing flow lines and public/private spaces, but difficult to evaluate the relationship of connections between room uses. Although the graph features are easy to understand the meaning and are suitable for rough generalization of floor plans, they are not suitable for comprehensive evaluation of the real estate value. On the other hand, the GCN is groundbreaking in that it can combine FPVs into a single value, which improves the explanatory power of the hedonic model. Deep learning models have higher-order nonlinearities, and even if the model explains the rationale, it does not always provide a generalized feature as graph features. It is necessary to use different methods depending on whether the main objective is to evaluate the entire floor plan or specific features of the floor plan.

The study concluded that they proposed a new method for floor plan analysis and related fields. The results showed that GCN can inductively learn that room connectivity, that is, connectivity from dining rooms to multiple rooms, tends to increase the value of real estate. Although the modeling and analysis of floor plans using graphs have been conducted since the days of space syntax, these studies manually created graphs of floor plans, and only a relatively small number of graphs were analyzed. However, recent technological innovations centered on deep learning have made it possible to easily obtain a larger number of access graphs. This study proposed a method to model them using GCNs, estimated the real estate value of the floor plan, and showed that it is a powerful variable in the hedonic model. We showed that the GCN can provide a basis for estimation.

Supplemental Material

Supplemental Material - Extracting real estate values of rental apartment floor plans using graph convolutional networks

Supplemental Material for Extracting real estate values of rental apartment floor plans using graph convolutional networks by Atsushi Takizawa in Environment and Planning B: Urban Analytics and City Science.

Footnotes

Acknowledgments

We thank Professor Toshihiko Yamasaki (The University of Tokyo) for providing the code and trained models for extracting access graphs from the floor plan images. We used “LIFULL HOME'S dataset” provided by LIFULL Co., Ltd. via IDR Dataset Service of National Institute of Informatics.

Declaration of conflicting interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by a JSPS Grant-in-Aid for Scientific Research (C) (grant number: 20K04872).

ORCID iD

Atsushi Takizawa

Supplemental Material

Supplemental material for this article is available online.

Atsushi Takizawa, PhD., is Professor of Graduate School of Human Life and Ecology at Osaka Metropolitan University of Osaka, Japan. He has a PhD in Engineering from Kobe University. His research interests include spatial analytics in architecture and urban space, real estate analysis, evacuation planning, application of deep leaning, machine learning, and discrete mathematics in architecture and urban planning. He teaches architectural planning, data science, and computational design.

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