mainly focuses on identifying factors that impact pricing, in machine learning and data mining research real estate price modeling mainly focuses on developing sophisticated predictive models beyond linear regression (Chopra et al., 2007; Fu et al., 2014).

A literature review on hedonic pricing models (Bartholomew &

Ewing, 2011) finds the structural characteristics typically include the age and the size of the house, the number of bedrooms, and the presence of different amenities such as a garage.

location of the house on housing prices is often captured by physical proximity to a central business district (CBD) or a regional center. The literature review finds evidence of an inverse relationship between pricing and distance to CBD in studies on various cities around the world.

access-related characteristic often used in hedonic models is the proximity of the house to a transit station, measured in air distance or walking distance. This attribute is used to capture the effect transit has on relative accessibility of a CBD or a regional center. Here the results are more mixed, with the majority of studies suggesting pricing premiums for housing located near to a transit station, and a higher premium for transit stations that provide a higher degree of relative proximity to a CBD. The era of big data provides access to new data sources, such as public transport, traffic and social mobility data, that potentially relate to real estate prices (at least intuitively we know that people consider mobility, and social factors when buying an apartment). Integrating such data could help to model residential real estate prices more precisely, and, as a result, better understand urban mobility patterns and activities. Such models can contribute to managing, coordinating and long term planning of mobility, and overall development of modern smart cities.

Our pilot study investigates to what extent accessibility of a neighborhood relates to residential real estate prices. This case study focuses on the Helsinki region. We model price per square meter as a linear function of apartment characteristics, and characteristics of the neighborhood, including accessibility by public transport and social activities. Our main hypothesis is that prices are more related to travel times than travel distances, and local centers of activities than the city center. The resulting models show good predictive performance, as compared to baselines not taking accessibility into account. We discover that an apartment price relates to the geographical distance from the city center, but accessibility by public transport to local centers of interest is more informative than just the geographical distance to those centers.

Our study introduces two conceptual novelties in modeling prices of residential real estate: (1) to measure accessibility, we consider travel times in addition to distances, and (2) we consider dynamic local points of interest, defined by 4square1 check-ins (people posting their location and activity on a social network), in addition to community centers at fixed locations.

The remainder of the paper is organized as follows. Section 2 describes data acquisition and feature engineering. Section 3 presents the results of the experimental case study, and Section 4 concludes the study.

The sales price data comes from a Finnish web portal Oikotie3, which is the most popular marketplace for residential real estates sales and rental. Our dataset consists of apartments in the capital region (Helsinki, Espoo, Vantaa and Kauniainen municipalities) advertised for sales on October 24, 2014. The pricing data is based on sales ads, as sales transaction prices are not available for the public. We exclude apartments that do not provide a street address (hence no coordinates), and for which size is not available. Moreover, we filter out very large apartments (size more than 300 m2), very old apartments (built earlier than 1850), far away apartments (distance to metro more than 20 km), extremely cheap (price pr square meter less than 1200 eur) and extremely expensive apartments (price per square meter more than 12000 eur), because we aim at focusing on modeling prices of mainstream apartments and avoiding extreme outliers. After filtering our dataset includes 8337 apartments. Figure 1 plots all the apartment locations.

We consider two types of location data: fixed location, and dynamic points of interest. Fixed location data includes the city center, for which the Stockmann department store is used as a proxy (coordinates found by hand via Google maps), and local community centers, approximated by H&M shop (a chain of clothing shops) locations in Helsinki region (also found by hand from Google Stockman

HM ● center (Stockmann). The black rectangular indicates the area from 6:00, violet 6:00-10:00, red 10:00-14:00, brown 14:00-18:00, orwhich point of interest data is collected. ange 18:00-22:00. maps). Stockmann is a well-known location in the centre of Helsinki. H&M shops are typically present in larger shopping malls. Shopping malls are local centers of attraction. We hope that H&M serves as a proxy for local centers in the neighborhoods. Figure 2 plots the community centers and the city center location.

Dynamic points of interest are obtained from an existing dataset of 4square check-ins (Le Falher et al., 2015). Each check-in in the dataset corresponds to one user’s visit to one venue (restaurant, cafeteria, store, etc) with known geographic location, at a particular time. The data cover user activity between March and July 2014 in the inner Helsinki city. To extract points of interest, we perform k-means clustering on the geographic locations of check-ins, using k = 20. Each of the k centroids identified defines one point of interest. Note that we extract points of interest both on top of all check-ins contained in the dataset, regardless of the the time of the day they occur, as well as separately for check-ins that occur at separate time intervals in the day (five 4-hour intervals from 2am to 10pm ). Figure 3 plots the points of interest for each time interval.

Accessibility data connects apartments with point of interest.

We consider two types of accessibility features: air distance from an apartment to the location of a point of interest, and travel time by public transport from an apartment to the point of interest (including walking time). Air distance is measured in kilometers from coordinate of the apartment to coordinate of the point of interest, as D s1 s2 = = =

Re · arccos(s1 + s2), where cos(lat 1) ∗ cos(lat 2) ∗ cos(lon2 − lon1), sin(lat 1) ∗ sin(lat 2), where Re is the radius of Earth (set to Re = 6371km), (lat 1, lon1) are the coordinates of the apartment, and (lat 2, lon2) are the coordinates of the point of interest. Travel time by public transport between two coordinates is measured using a freely available tool Reititin4, developed by BusFaster Ltd and researchers at University of Helsinki.

We model price per square meter. An alternative would be to model the total price. We choose the former as the target variable, because price per square meter is easier to interpret and compare across neighborhoods.

We limit our analysis to linear regression, which is easily Ne interpretable. Note, however, that some of the features are expressed as non-linear functions of simpler features (e.g. fyear is a non-linear function of a building’s age, as explained above). The ordinary least squares procedure (the standard implementation in R) is used for estimating the model parameters.

For assessing the performance we use two common accuracy measures: coefficient of determination (R2) and mean absolute error (MAE). Coefficient of determination is a relative accuracy measure, where 1 means the best possible performance, and 0 means the performance is equivalent to random. Mean absolute error indicates error in the units of the target variable, 0 is an ideal performance, the higher the

Base models do not use any accessibility information, and use only very basic location information. The first base model (Size-year) does not use location at all, and is based only on size of the apartment and its construction year (fyear ). The second model in addition uses basic location information, encoded as raw geographical coordinates, centered in the old town of the city.

The resulting models for price per square meter are: price =

3722 − 4.97 × size + 0.91 × fyear , and = + price 5643 − 5.14 × size + 0.78 × fyear + 38.9 × east − 147.7 × north.

The models are consistent with common intuition: the larger the apartment, the cheaper the price per square meter; older or newer apartments with respect to 1970 construction year are more expensive; the further to the north from the sea and the city center, the cheaper. Easterness has a positive effect, which is somewhat inconsistent with a common intuition that cheaper neighborhoods are in the east. However, this can be explained by the range of data (see Figure 4). Data extends further to the west than to the east, therefore, western apartments are on average further from the center, and thus cheaper.

Table 2 reports predictive accuracies of the base models. We can make two observations. First, Size-year-location model already performs quite well with the cross-validation of determination (the higher, the better), MAE - mean absolute error (the smaller the better). location model with one additional accessibility feature at a time. formance differs only a little, which suggests that there is no notable overfitting, and the model could use more informative input features.

Next we test whether adding accessibility information helps to predict more accurately. We test accessibility to the city center (Stockmann), local centers (HM), and dynamic centers of interest (4square check-ins) overall and at morning peak times (from 6:00 to 10:00). We compare informativeness of using air distance as a feature to using the total travel time by public transport.

We use the base model Size-year-location as a starting point, add one feature at a time to it, and measure the accuracy. Table 3 reports the results.

From the resulting accuracies we can see that accessibility has some predictive power, as in all cases the predictive performance improves as compared to the base model. The results indicate that the distance to the city center (Stockmann) is more informative than the travel time by public transport. However, accessibility to the local centers (fixed centers H&M and dynamic centers 4square) by public transport is more informative than just the air distance to those centers. In other words, it seems that an apartment price relates to the overall geographical location, but accessibility to local centers of interest is more important than just the geographical distance to those centers. This is an interesting finding for exploring in detail in future studies. We report selected models. Metro distance is intuitive - the = − = − = + = + ment: price apartment: price closer to metro, the more expensive is the apartment: price 5300 − 3.94 × size + 0.77 × fyear − 62.2 × east − 50.8 × north − 158.4 × metro. Adding metro distance shrinks other coefficients, which suggests that earlier this feature was indirectly captured. More importantly, adding metro distance changes the direction of the easternness coefficient from positive to negative. Now it is more intuitive keeping in mind peculiarities of Helsinki residential neighborhoods, where overall the east is considered cheaper than the west.

Stockmann distance is as well intuitive - the closer to the center, the more expensive is the apartment: price 5698 − 3.78 × size + 0.72 × fyear + 3.3 × east − 59.8 × north − 117.8 × dstock .

Shortest H&M travel time is intuitive - the shorter the travel time to the local center, the more expensive is the apart5681 − 5.00 × size + 0.78 × fyear + 37.0 × east − 139.6 × north − 39.3 × thm .

Shortest 4square travel time is intuitive - the shorter the travel time to a center of interest, the more expensive is the 5659 − 3.55 × size + 0.77 × fyear + 13.5 × east − 103.3 × north − 31.4 × t4sq . price 5729 − 4.06 × size + 0.71 × fyear + 31.6 × east − 94.5 × north + 73.0 × metro − 139.0 × dstock + 21.6 × thm − 12.5 × t4sq2 = + + + We can see some interesting relations, reflecting peculiarities of the Helsinki region. First, the longer the metro distance, the higher the price, while one could expect the opposite. Our interpretation is that the metro distance captures what was not very successfully captured by the easternness.