An investigation of the temporality of OpenStreetMap data contribution activities

ABSTRACT

OpenStreetMap (OSM) is a dataset in constant change and this dynamic needs to be better understood. Based on 12-year time series of seven OSM data contribution activities extracted from 20 large cities worldwide, we investigate the temporal dynamic of OSM data production, more specifically, the auto- and cross-correlation, temporal trend, and annual seasonality of these activities. Furthermore, we evaluate and compare nine different temporal regression methods for forecasting such activities in horizons of 1–4 weeks. Several insights could be obtained from our analyses, including that the contribution activities tend to grown linearly in a moderate intra-annual cycle. Also, the performance of the temporal forecasting methods shows that they yield in general more accurate estimations of future contribution activities than a baseline metric, i.e. the arithmetic average of recent previous observations. In particular, the well-known ARIMA and the exponentially weighted moving average methods have shown the best performances.

KEYWORDS:

• Volunteered geographic information
• time series analysis
• temporal forecasting
• OpenStreetMap

1. Introduction

For well more than a decade, OpenStreetMap (OSM) has been the world’s most successful volunteered geographic information project. Founded in 2004, the geographical coverage, geometric accuracy, semantic completeness, and overall reliability of the data have increased immensely since then (Arsanjani et al. 2015). Consequently, OSM has been a fundamental dataset in numerous geospatial research and applications, like pedestrian and motorized routing (Neis and Zipf 2008; Novack, Wang, and Zipf 2018), urban change modeling (Zhang and Pfoser 2019), land use and cover monitoring (Schultz et al. 2017), and fine-resolution population mapping (Bakillah et al. 2014), to name a few. However, geospatial research and applications based on OSM data frequently assume and rely on the stability of the data, neglecting the fact that it is constantly evolving and changing (Sieber and Haklay 2015). Even in large cities in the Global North, where data has been contributed and edited by larger numbers of contributors since longer date, OSM is a dataset in constant change.

One of the reasons for this is that the world itself is dynamic. Venues change their names, buildings are erected and extended, urban green areas are implemented or re-designed, etc. Also, OSM enables an always changing number of active volunteers to tag (i.e. to semantically annotate) features without any constraints. Although tag contributions and editions are usually intended to enhance the semantic completeness of map features (Hecht, Kunze, and Hahmann 2013) and to achieve tagging consistency across geographically, culturally, and politically related areas (Davidovic et al. 2016; Zia and Cakir), because volunteer contributors often have different worldviews and are motivated by different agendas (Anderson, Sarkar, and Palen 2019; Grinberger et al. 2021; Gardner et al. 2019), disagreements and negotiations may occur on which tags should be used or become deprecated (Mocnik, Mobasheri, and Klonner 2018), leading to map features having their tags edited, deleted, and extended. Other more exceptional reasons for OSM features being created and edited are disruptive (intentionally or not) mapping (Ballatore 2014; Juhász et al. 2020) and the aim of contributors to assist disaster managers in areas affected by, for example, earthquakes and floods (Ahmouda, Hochmair, and Cvetojevic 2018; Zook et al. 2010).

Because OSM data will continue to expand and to be essential for an increasing number and variety of geospatial applications, it is important to better understand its dynamic processes of change and evolution. This will enable researchers and practitioners behind OSM-based applications and services to assess the instability of the data, plan maintenance and updates, and design improvements to their tools and services more effectively. Accordingly, the motivations of and the research questions (RQs) addressed in this work are the following:

RQ 1 -

Better understand the temporal dynamic of OSM data contribution activities. What is the most consistent time interval for understanding such activities? In other words, how far in the past previous activities seem to affect present ones? How strong are those effects?

RQ 2 -

Uncover temporal correlations (i.e. apparent influences) between OSM data contribution activities. For example, what is the strength of correlation between the amount of new volunteers contributing data within a certain time span and the amount of tag editions occurring in a certain time span after that?

RQ 3 -

Investigate the extent to which we can forecast contribution activities in OSM. What is the prediction accuracy achievable with statistical and machine learning forecasting methods? How far in the future can we make such predictions? How the different prediction models compare in terms of prediction accuracy for different contribution activities?

For addressing these questions, we explore different time series statistics and forecasting methods. The remainder of this paper is structured as follows. The next section provides an overview of previous works related to temporal analysis and evolution of OSM data. Section 2 describes our experiment set up, namely, the data, considered variables, and test-sites. Section 3 describes the methods explored in this work. Section 4 presents the results obtained and Section 5 concludes the paper with a summary and outlook.

1.1. Related work

Due to the crowdsourced aspect of OSM data, numerous works have proposed practical and theoretical approaches to assess its quality (Sehra, Singh, and Rai 2017). A multidimensional notion, quality may refer, for example, to semantic veracity and completeness, as well as to geometrical consistency and accuracy, or to the usefulness (i.e. fitness) of the data to a specific purpose, such as pedestrian routing (Novack, Wang, and Zipf 2018). Generally, OSM data quality is assessed extrinsically, based on comparisons with authoritative and trustworthy data, or intrinsically, based on different characteristics and dynamics of the data itself (Degrossi et al. 2018; Fogliaroni, D’Antonio, and Clementini 2018; Mocnik, Mobasheri, and Klonner 2018; Senaratne et al. 2017). Intrinsic quality measures are typically applied when no authoritative data is available (or is comparable) or when the intention is to assess the fitness of the data to specific purposes. Substantial research efforts have focused on analyzing the temporal dynamics and historical evolution of OSM data as a way to intrinsically infer and assess its fitness and reliability. Raifer et al. (2019), for example, developed the robust and flexible OpenStreetMap History Database (OSHDB) tool and application programming interface, which can support intrinsic data quality analyses based on the historical evolution of the data within user-defined polygons or administrative areas. The authors also provide a thorough overview of the characteristics and functionalities of other similar tools, such as Tag Info and OSM Tag History.

Other works have proposed quantitative ways of assessing the maturity and stability (reflecting completeness) of certain OSM features (e.g. roads, hospitals) based on the temporal cumulative function of a certain attribute of the data (e.g. the total length of roads in a given region). Barrington-Leigh and Millard-Ball (2017) approximated this cumulative function with a sigmoid shape and detected saturation (representing stability) in ways emerging from the model, i.e. from the asymptote of the sigmoid. Previously, Grinberger et al. (2021) had detected saturation simply through empirically defined saturation threshold. These and other related works have conducted analyses on OSM historical data not for understanding the dynamics, processes, and patterns through which the data evolves, but rather to infer the trustworthiness and completeness of the data.

The maturity or completeness of OSM data has been analyzed not only temporally but also spatially. Maguire and Tomko (2017), for example, proposed metrics based on the temporal trends of the geometric definition of features to assess the spatially variable maturity of the data. Their approach is able to identify areas where mapping communities have reached consensus in the geometric definition of certain features as well as areas in need of more intense editorial activity in order to enhance the homogeneity of the data. Also aiming to better understand the spatio-temporal dynamics of the data contribution evolution of OSM, Arsanjani et al. (2015) developed a cellular automata model. The model could also be used to predict potential future states of the data. So far though, the authors tested their model only in the medium-size city of Heidelberg (Germany). Furthermore, no validation of the results has been provided for their one-year ahead predictions. In a related paper, Arsanjani et al. (2015) proposed a contribution index encompassing metrics of node quantity, interactivity, semantic completeness, and the ability to attract contributions. Besides analyzing the spatio-temporal evolution of the index for grid cells in Stuttgart (Germany), they also applied a cellular automata model to project the state of OSM data for that city up to the year of 2020. Zia and Cakir studied the spatial distribution of OSM road features contributions across time within Turkey. Similarly to the work of Corcoran, Mooney, and Bertolotto (2013), they reported the two-phase evolution tendency of exploration, where features are discovered, followed by a densification phase, where features get connected to each other and their semantic information are deepened.

Other works have focused on the temporal evolution of the semantic information of OSM features, which is formalized as so-called tags. Mocnik, Zipf, and Raifer (2017), for example, studied the temporal dynamics with which tags emerge, get consolidated, and finally documented in the OSM Wiki webpage, the OSM folksonomy portal serving as a catalog of generally accepted and suggested tags. By analyzing the temporal chart on the number of documented keys and tags since 2008 and fitting an exponential function to it, the authors also projected near future scenarios on the number of new documented tag keys. Along these lines, a number of tools have been developed and made available online that enable users to obtain temporal charts on the use of specific tags in OSM worldwide or for a given geographic area. These tools include TagInfo, OSM Tag History, and the Ohsome Dashboard.

Lastly, part of the OSM research community has focused on spatio-temporal patterns of OSM data contribution in areas affected by natural disasters, and where data had been typically scarce previous to the calamity (Ahmouda, Hochmair, and Cvetojevic 2018; Xu, Li, and Zhou 2017). Xu, Li, and Zhou (2017) investigated the temporal and spatial correlation between the creation of road and building features after the 2016 hurricane Matthew in Haiti. Ahmouda, Hochmair, and Cvetojevic (2018) focused on short- and long-term changes in mapping community composition and behavioral due to earthquake events in Nepal and Italy.

2. Preliminaries

2.1. Data acquisition and sampling

The aim of this paper is to propose simple quantitative ways of investigating the temporality of OSM data contribution activities. More specifically, we focus on contribution and edition activities of points-of-interests (POIs), which we define as OSM nodes containing tag keys “name” and “amenity”. Readers unfamiliar with the concept of OSM tags and with OSM’s feature types are referred to its Wiki page (Novack et al., 2017).

For conducting our experiments, the complete POI dataset at January 2020 from 20 cities worldwide was collected. The aspects considered for selecting these cities, shown in Table 1, were their cultural and socio-economic diversity, their national importance, and their well-established community of active OSM mappers. Next, the editing history of each POI in each of the 20 cities was extracted. This historical record describes how the POI has changed over time since its creation, which we denote as its first entry. All subsequent entries are modifications and/or addition of data, that is, tag deletions, tag insertions or tag editions, as well as modifications of the POI’s geographical location. (A POI can also be completely deleted at some point in time. However, since only existing POIs by January 2020 were considered in our experiments, only POIs creations and modifications were detected and considered in the construction of the POIs’ historical records.) More formally, a historical record is comprised of a set of entries $\{e_1,e_2,\dots ,e_n\}$, where $e_1$ represents the creation of the POI. Each entry has an associated timestamp. Extracting the edition variables we consider simply required comparing the states of a POI at entries $e_i$ and $e_{\mathit{i}-1}$, extracting the timestamp of $e_i$, and associating the change of state from $e_{\mathit{i}-1}$ to $e_i$ to its respective indexed month, as discussed below. At each point in time, a POI can be created or modified. Although in reality, both actions co-occur at a POI’s $e_1$, an exclusive distinction was made for the convenience of modeling. Therefore, an entry can refer to either a POI creation or modification. In the latter case, an entry can entail more than one type of edition. Table 2 gives the description of the variables computed at each entry $e_i$ of each POI from each of the 20 cities we consider in this study. Thus, an entry is a vector of seven binary elements, each referring to one of the variables in Table 2. From now on, we refer to the variables through their alias, also presented in Table 2.

Table 1. The 20 cities whose entire POI dataset at January 2020 and its editing history were considered in this study.

City	Approx. population (in Mio.)
Heidelberg	0.1
Washington DC	0.7
San Francisco	0.8
Oslo	1
Dublin	1.2
Stockholm	1.6
Berlin	3
Los Angeles	4
Montreal	4
Rome	4
Barcelona	5
Sydney	5
New York	8
London	9
Paris	11
Moscow	12
Mumbai	20
Mexico City	21
Sao Paulo	21
Shanghai	26

Table 2. Variables computed at each entry from each POI. The variables were computed by comparing two subsequent states of the POIs’ historical record.

Alias	Explanation	Values
create	Was the POI created at entry $e_i$?	$\{0,1\}$
modify	Was the POI modified at entry $e_i$?	$\{0,1\}$
tag addition	Was at least one tag added to the POI at entry $e_i$?	$\{0,1\}$
tag deletion	Was at least one tag deleted from the POI at entry $e_i$?	$\{0,1\}$
tag edition	Was at least one tag of the POI edited at entry $e_i$?	$\{0,1\}$
positional change	Was the POI re-located at entry $e_i$?	$\{0,1\}$
new mapper	Was the POI modified or created by a mapper not active at this city before entry $e_i$?	{0,1}

Following, the time series of each variable and city was derived from the entry vectors of all POIs of that city. The time series were sampled, i.e. discretized, into time slots of one month. The value of a variable for a specific month was computed by simply summing all respective elements from all entry vectors whose timestamps are within that month. In this way, a time series was created for each city and each of the variables presented in Table 2. All time series originally spanned from January 2007 to January 2020. However, for modeling purposes, the year of 2007 was omitted from all time series, as they contain very little data points for most of the cities. Also, time slots with values above the 99% quantile for any of the seven variables were considered outliers and had theirs values substituted by the value of its immediately preceding slot. In OSM, these outliers are caused mainly by mapping parties or major data imports (Juhász and Hochmair 2018), which we regard as exceptional events.

For the sake of reproducibility, and in accordance with the spirit of open science, all data processing procedures described in this paper are reproducible with a library coded in Python and made openly available at https://github.com/le0x99/OSMEvolution. This Python library works just as well with other OSM geometries, namely, ways and relations, and for any given city or OSM-mapped geographical boundary. At the ”How it works” section of the repository, the reader will also find a detailed technical description of how the OSM data was queried and structured into the time-series analyzed in this study. A description of this workflow is also given in Figure 1.

Figure 1. Data querying and structuring workflow for generating the time-series used in this study.

3. Methods

In this section, we introduce the methods used for addressing the RQs presented at the introduction of this paper. The methods applied to tackle RQ 1 are described in Sections 3.1 and 3.2. RQ 2 was approached with the method described in Section 3.3. Lastly, the methods addressing RQ 3 are described in Sections 3.4 and 3.5.

3.1. Rolling window

For addressing RQ 1, related to the most consistent time interval with which OSM data contribution activities take place, the simple rolling window method was applied. Let $y_t^i$ be an observation $\mathit{y}$ of variable $\mathit{i}$ at time slot $\mathit{t}$. As explained above, for each time slot and variable, the element referring to that variable in all entry vectors whose timestamp is within that slot are summed to yield the observation y. The rolling window method estimates this observation as $\hat{y}\mathit{ti}=\frac{1}{W}\sum \mathit{l}=1\mathit{W}{y}_{\mathit{t}-\mathit{l}}$, in words, as the average of the observations of $\mathit{i}$ at previous time slots $\mathit{t}-1,\mathit{t}-2,\mathit{t}-\mathit{W}$, where $\mathit{W}$ denotes the size of the window. The squared error metric $(y_t^i-\hat{y}\mathit{ti}{)}^2$ can be used to measure the difference between an observation at time $\mathit{t}$ and the average of its $\mathit{W}$ previous observations. After computing the squared error for all observations of a time series, we can compute its mean square error (MSE). The MSE metric was computed for all seven variables, all 20 cities, and for different $\mathit{W}$ window sizes. Given a time series of a variable $\mathit{i}$ and a certain city, the $\mathit{W}$ for which the lowest MSE is obtained is the most consistent time span with which that variable changes in time. That gives us valuable insights into that variable’s temporal dynamic. For example, if $\mathit{W}=4$ yields the lowest MSE, we can conclude that the data generating process of variable $\mathit{i}$ is, in average, most correlated with and influenced by activities occurring in the last four time slots, whether these are days, weeks, or months.

3.2. Time Series Decomposition

Also related to RQ 1’s motivation to better understand the temporal dynamic of OSM data contribution activities, time series decomposition was applied. As the name implies, this is a procedure for decomposing a time series into different components, namely, trend, seasonality, and residuals. The first two components relate to two underlying properties of the data we aim to analyze. These are, respectively, the strength of increase in data contribution and edition activities in OSM, and how cyclical these activities are.

In this work, an additive decomposition technique was adopted, such that any observation $y_t^i$ can be recomposed through the sum of its three components. Formally,

(1) $y_t^i=T_t^i+S_t^i+R_t^i,$(1)

where $T_t^i$ represents the trend component, $S_t^i$ the seasonal component, and $R_t^i$ the residuals. In order to compute the components, the cycle length $\mathit{m}$ must be defined. In our case, for monthly aggregated data and an assumed yearly cycle, we defined $\mathit{m}=12$. The trend component $T_t^i$ was computed as the $2\ast \mathit{m}$ (i.e. 24-month) moving average of the data. For estimation of the seasonal component, the de-trended time series $y_t^i-T_t^i$ was averaged for every month in the cycle, meaning that, for a given month, we obtain all values of the de-trended time series that lie within that month and take their average. The outcome of this are 12 values, which are repeated for every year and express the time series seasonality component. The third component, $R_t^i$, is the residual between the underlying original time series and the trend and seasonal components, such that $R_t^i=y_t^i-(T_t^i+S_t^i)$. This component expresses all remaining properties of the time series, but it can also be viewed as the deviation from a simple model, based on which each time series is only characterized by trend and seasonality in an additive way.

Following the approach proposed by Wang, Smith, and Hyndman (2006), the strength of the trend $F_T$ and seasonality $F_S$ components of the variables’ time series can be quantified, respectively, according to the equations below:

(2) $F_T=max\left(0,1-\frac{\mathrm{Var}\left(R_t\right)}{\mathrm{Var}\left(T_t+R_t\right)}\right)$(2)

and

(3) $F_S=max\left(0,1-\frac{\mathrm{Var}\left(R_t\right)}{\mathrm{Var}\left(S_t+R_t\right)}\right),$(3)

where, as before, $T_t$, $S_t$, and $R_t$ stand for the trend, seasonality, and residuals components extracted as discussed above. In time series with strong trend, the variance of the trend component is significantly larger than the variance of the residuals; therefore, $F_T$ will be close to 1. Likewise, in time series with strong seasonality, the variance of the de-trended data is larger than the variance of the residuals, leading to $F_S$ closer to 1.

3.3. Temporal linear correlation

For uncovering temporal correlations between OSM data contribution activities, (which is the rationale of RQ 2), the Pearson’s correlation coefficient $\mathit{\rho }$ was used. Besides measuring the linear correlation between two different data contribution variables, $\mathit{\rho }$ was also used for measuring the correlation between observations $y_t^i$ of a variable $\mathit{i}$ at time $\mathit{t}$ and their temporally lagged values $y_{t-T}^i$. Formally, this autocorrelation is given by

(4) $\mathit{\rho }(y_t^i,y_{t-T}^i)=\frac{\mathrm{c}\mathrm{o}\mathrm{v}(y_t^i,y_{t-T}^i)}{{\sigma }_{y_t^i}{\sigma }_{y_{t-T}^i}},$(4)

where $\mathit{T}$ is the temporal lag, the nominator is the covariance between $y_t^i$ and $y_{t-T}^i$, and the denominator is the product of their standard deviations.

This simple metric enables inspecting, for different $\mathit{T}>0$, how temporally auto-correlated a variable $\mathit{i}$ is. It also enables, and was used for, as mentioned, investigating the temporal correlations between different data contribution variables. For example, we can measure the correlation of tag insertions at $\mathit{t}-1$ and tag editions at $\mathit{t}$. Note that we can consider in this analysis different $\mathit{T}>=0$ for all pairs of $\mathit{i}$ and $\mathit{j}$ variables.

3.4. Temporal Forecasting Methods

To address RQ 3, the temporal forecasting methods presented in Sections 3.4.2 to 3.4.6 below were applied. In the next section, the notation used for presenting these methods and the metric to evaluate their performance is introduced.

3.4.1. Adopted notation

For each of the 20 cities considered in this study, four multivariate time series were generated, each for all seven variables presented in Table 2 and discretized into time slots of 1–4 weeks. Thus, given city $\mathit{c}$ and time sampling $\mathit{h}$ (in 1–4 weeks), we denote the respective time series as ${\mathbf{X}}^{\mathit{c},\mathit{h}}$. The series contains $\mathit{T}$ observations $X_t\in {\mathbf{X}}^{\mathit{c},\mathit{h}}$, which are row vectors containing the values of the seven variables for time slot $\mathit{T}$. Note that the size of $\mathit{T}$ depends on $\mathit{h}$. This vector is referred to as the objective vector, as it holds the seven target variables we aim to forecast. A specific target variable will be denoted as $x_{\mathit{t},\mathit{i}}\in X_t$, where $x_{\mathit{t},\mathit{i}}$ is the column vector of the specific target variable $\mathit{i}$ with length $\mathit{T}$. Each of the methods explored and compared regarding their performance in forecasting the objective vector $X_t$ will be introduced in the following sections. If the method iteratively approximates each variable $x_{\mathit{t},\mathit{i}}$ separately, instead of the joint $X_t$ vector, the target variable $x_{\mathit{t},\mathit{i}}\in X_t$ is then notated as $X_t$.

3.4.2. Moving average methods

The first and most simple time series forecasting method explored in this study is referred to as the naive method (NM). It approximates the unobserved value of variable $\mathit{x}$ at time $\mathit{t}$ as its previous observation $x_{\mathit{t}-1}$. Thus, this method can be formalized as follows:

(5) $\mathit{NM}\leftarrow x_t\approx x_{\mathit{t}-1}.$(5)

Despite its simplicity, the NM is often used in time series forecasting and is in fact hard to be outperformed by more complex methods. This is due to the often existing temporal correlation of time series observations.

The next three forecasting methods we present in this section can be generally regarded as moving average methods. The first of these is the simple moving average (SMA) method, which is an extension of the naive baseline method introduced above. It estimates an observation $x_t$ as the arithmetic mean of its previous $x_{\mathit{t}-1},x_{\mathit{t}-2},\dots ,x_{\mathit{t}-\mathit{W}}$ observations, where $\mathit{W}$ is the size of the lagged window. The linearly weighted moving average (LWMA) method is a derivation of the SMA method in that it assigns to the observations within the lagged time window $\mathit{W}$ linearly decreasing weights, such that more recent observations receive higher weights than less recent ones. Given a window $\mathit{W}$ and lag $\mathit{l}\in [0,\mathit{W}]$, the linear weight for observation $x_{\mathit{t}-\mathit{l}}$ is defined as

(6) $w_l=\frac{2(\mathit{W}-\mathit{l}+1)}{\mathit{W}(\mathit{W}+1)}.$(6)

Alternatively to a linear decay of the weights $w_l$, these can also decay exponentially. The exponentially weighted moving average (EWMA) method implements this idea. Thus, the exponential weight for a lag $\mathit{l}$ can be approximated by

(7) $w_l=\frac{{(1-\mathit{\alpha })}^{1-\mathit{W}}{\alpha }^l}{{\sum }_{l=1}^W{(1-\mathit{\alpha })}^{1-\mathit{W}}{\alpha }^l},$(7)

where $\mathit{\alpha }$ controls the initial weight of the first lag.

3.4.3. Ordinary Least Squares Autoregression

A widely used method in univariate time series forecasting is the ordinary least square autoregressive model (AR). It estimates an unobserved objective vector $x_t$ as a linear function of its own lagged values $x_{\mathit{t}-1},x_{\mathit{t}-2},\dots ,x_{\mathit{t}-\mathit{l}}$, where $\mathit{l}$ denotes the maximum incorporated lag. The assumption of the AR model is that a time series variable can be estimated as a linear function of its $\mathit{l}$ lagged values. Formally, the AR model is a linear regression one and has the following form:

(8) $\mathit{AR}\leftarrow x_t\approx w_0+\sum _{\mathit{l}=1}^L{w}_l{x}_{\mathit{t}-\mathit{l}}+{\text{isin}}_t,$(8)

where ${\text{isin}}_t\sim \mathcal{N}(0,{\sigma }^2)$ is irreducible white noise and $w_l$ is the ordinary least square coefficient of the $\mathit{l}$th lagged observation.

Before the AR can be correctly applied, it is necessary to address the assumed stationarity of the underlying data. Stationarity refers to when the mean and variance of the data are constant over time and it is assumed by all models within the AR-family. As expected from crowdsourced data production processes, however, a certain seasonality (non-uniform variance over time) and trend (non-uniform mean over time) can be observed in our time series. In order to address this, the first-order difference $\mathrm{\Delta }{x}_t=x_t-x_{\mathit{t}-1}$ was applied to our data. With that, Equation 8(8) $\mathit{AR}\leftarrow x_t\approx w_0+\sum _{\mathit{l}=1}^L{w}_l{x}_{\mathit{t}-\mathit{l}}+{\text{isin}}_t,$(8) was altered to

(9) $\mathit{AR}\leftarrow \mathrm{\Delta }{x}_t\approx w_0+\sum _{\mathit{l}=1}^L{w}_l\mathrm{\Delta }{x}_{\mathit{t}-\mathit{l}}+{\text{isin}}_t,$(9)

which is trivial to re-transform for later prediction. Please consider that the first-order difference is also applied to the other models from the AR-family presented below.

3.4.4. Autoregressive Moving Average

The Autoregressive Integrated Moving Average Model (ARIMA) is an extension of the AR model above and is extensively used in the modeling of time-varying processes. Like the AR model, ARIMA entails an autoregressive part. Additionally to the AR part though, the ARIMA model includes a moving average (MA) term that models $x_t$ as a linear function of the current and previous white noise error terms ${\text{isin}}_t,{\text{isin}}_{\mathit{t}-1},\dots ,{\text{isin}}_{\mathit{t}-\mathit{l}}$, where $\mathit{l}$ parameterizes the model, such that the model $\mathit{MA}(\mathit{l})$ is formalized as $x_t\approx \mathit{\mu }+{\epsilon }_t+{\beta }_1{\epsilon }_{\mathit{t}-1}+\cdots +{\beta }_l{\epsilon }_{\mathit{t}-\mathit{l}}$, where $\mathit{\mu }$ is the mean of the series. In contrast to the AR part of the model, fitting the MA term cannot rely simply on the Ordinary Least Square measure, since the lagged white error terms are not directly observable. The error terms are therefore fitted iteratively using Maximum Likelihood Estimation. Combining the AR and MA terms, before applying first-order differencing, leads to the formalization of the ARIMA model as:

(10) $\mathit{ARIMA}\leftarrow \mathrm{\Delta }{x}_t\approx \mathit{\mu }+{\epsilon }_t+\sum _{\mathit{l}=1}^p{\alpha }_l\mathrm{\Delta }{x}_{\mathit{t}-\mathit{l}}+\sum _{\mathit{l}=1}^q{\beta }_l{\epsilon }_{\mathit{t}-\mathit{l}}$(10)

3.4.5. Vector Autoregression

Similarly to the AR and ARIMA models, the Vector Autoregression (VAR) model is a multivariate statistical time series forecasting method based on the idea that a set of variables $x_t\in X_t$ can be estimated as a function of its lagged values $X_t=\mathit{f}(X_{\mathit{t}-1},X_{\mathit{t}-2},\dots ,X_{\mathit{t}-\mathit{l}})$, where $\mathit{l}$ represents the maximum lag in time. In contrast to both AR and ARIMA though, VAR estimates a variable $x_t\in X_t$ not only as a linear combination of its lagged values but as a linear combination of all other lagged variables $x_t\in X_t$. Technically, the VAR model solves a set of linear equations, each of which being an Ordinary Least Square linear regression with multiple inputs (i.e. the lagged values of $X_t$ are the input and $X_t$ is the output). The VAR model is formulated as

(11) $\mathit{VAR}\leftarrow \mathrm{\Delta }{X}_t\approx w_0+w_1\mathrm{\Delta }{X}_{\mathit{t}-1}+w_2\mathrm{\Delta }{X}_{\mathit{t}-2}+\dots +w_L\mathrm{\Delta }{X}_{\mathit{t}-\mathit{L}}+{\text{isin}}_t,$(11)

where each $w_l$ is a $7\times 7$ weight matrix (7 is the size of our objective vector) and ${\text{isin}}_t$ is irreducible white noise, which in case of VAR is a vector with seven elements.

3.4.6. Random Forest

The last model we experimented with in this paper is the Random Forest (RF) method (Breiman 2001). Known for its efficacy in modeling highly non-linear relations in the data, RF is a method based on an ensemble of bootstrapped fully grown regression trees. Each split at each node is defined based on the criterion of the mean squared error. As recommended by Breiman (2001), the number of features considered at each tree’s split was of $\frac{N_x}{3}$, where $N_x$ is the total number of input features. For prediction, the mean value of the set of fully grown trees is then used. A deeper understanding on the underlying tree-building algorithm can be obtained at Breiman’s seminal work (1984).

Although not commonly applied for time series data forecasting, we decided to experiment with the RF regression method because it works fundamentally different than the statistical methods introduced above and may be effective in forecasting non-linear time-varying processes. In contrast to VAR and ARIMA, RF does not assume any distributional properties of the underlying data other than representative sampling.

In order to improve the forecasting ability of the RF model, temporal indicator features were added to the input feature vectors. Specifically, the following modal features were added: week of the year, in range $[1,52]$, and day of the month, in range $[1,31]$. Also, the non-modal feature month of year was added, yielding a dummy variable, i.e. in range $0,1$, for each of the 12 months. Thus, we are assuming that time-specific properties of the observations, like the month or the week, contain information that would be otherwise lost without these additional features. We experimented with two kinds of RF models, namely, the Univariate Random Forest (URF), which considers only the past values of the variable it predicts, and the Vector Random Forest (VRF), which considers the entire vector of past observations. The motivation for applying and comparing these two models is that, similarly, the AR and VAR models also consider, respectively, uni- and multivariate lagged observations, assuming, however, linearity of the data, differently from the RF models, as noted.

3.5. Forecasting models training, evaluation, and test

This section presents the procedure and metrics adopted to evaluate the performance of the forecasting methods presented above and implemented to address RQ 3.

3.5.1. Data partitioning

The time series generated as presented in Section 2 were divided into three parts. The first part, spanning from January 2008 to January 2018, was used for the training of the models. The second part of the data, spanning from January 2018 to January 2019, was used for evaluating the parameters of the models, as will be discussed below. After fitting the parameters, based on the criterion of performance maximization, the third part of the series from January 2019 to January 2020 was used for testing the performance of the models. The total number of observations of each of the data parts is the same for all the 20 cities, but depending obviously on the time sampling and forecasting horizon, which we henceforth note as $\mathit{h}$. Table 3 shows the number of observations per city of each of the data partitions and time sampling rate forecasting horizons (in weeks). Note that, for example, when $\mathit{h}$ = 1, there are 524 observations for training and 52 for testing for each of the 20 cities.

Table 3. Number of observations per city of the three data partitions and for the four time sampling rates and forecasting horizons (in weeks).

	h = 1	h = 2	h = 3	h = 4
Model Training	524	262	176	121
Parameter Evaluation	52	26	17	12
Model Testing	52	26	17	12

By distinguishing between evaluation and testing data, hard-coded parameters are avoided, as it is always possible to find a set of parameters that maximize any metric when the data they are evaluated on stays fixed. Although in this particular scenario, this may not be the case, even without an additional testing set, since we already cross-validate over the cities, we consider that this partition is still useful, as it further increases the reliability of the obtained results.

3.5.2. Model parameters evaluation

For each of the methods presented above, parameters were set based on a parameter evaluation analysis. The statistical models AR, VAR, and ARIMA require setting the maximum lag $\mathit{L}$, which essentially defines the model. For that, the evaluation dataset from each of the 20 cities was used to compute the average error and its standard deviation for each considered value of $\mathit{L}$. This procedure was undertaken independently for all four time sampling rates of 1–4 weeks. Likewise, concerning the ARIMA model, the value of $\mathit{L}$ was defined based on the evaluation dataset. Regarding the methods based on rolling statistics, i.e. SMA, LWMA, and EWMA, the value of $\mathit{w}$, that is, the lagged window from which the moving average is calculated, was set. Concerning the EWMA model, the $\mathit{\alpha }$ parameter was set.

3.5.3. Method performance metric

Different performance metrics have been proposed in the literature of time series forecasting, each having its pros and cons (Armstrong and Collopy 1992; Makridakis 1993; Makridakis and Hibon 1979). The metric used in this work is based on the squared error of the predicted objective vector, given city $\mathit{c}$ and time sampling $\mathit{h}$. Given the true vector $X_t$ and the predictions ${\hat{X}}_{\mathit{t}}$, this metric is defined as:

(12) ${\text{isin}}_t^{c,h}=(X_t^{c,h}-{\hat{X}}_{\mathit{t}}^{\mathit{c},\mathit{h}}{)}^2,$(12)

where $\text{isin}$ represents the squared error vector containing the squared errors of all seven objective variables within $X_t$. Based on this metric, the conditional RMSE vector, meaning the RMSE given time sampling $\mathit{h}$ and city $\mathit{c}$, was computed. The conditional RMSE is formalized as:

(13) $\mathrm{RMS}{\mathrm{E}}^{\mathit{c},\mathit{h}}=\sqrt{\frac{1}{T_h}\sum _{\mathit{t}=1}^{T_h}{\text{isin}}_t^{c,h}},$(13)

where $T_h$ denotes the total amount of test observations given $\mathit{h}$ (e.g. $T_{\mathit{h}=1\mathrm{week}}=52$ observations per city). The RMSE was used instead of the plain MSE in order to get interpretable results when analyzing the errors. Since $\mathrm{RMS}{\mathrm{E}}^{\mathit{c},\mathit{h}}\in {\mathbb{R}}^7$, we are able to inspect each objective vector element by element. By using this conditional error metric, we can compare the RMSE vectors of all target variables within $X_t$ conditioned on city $\mathit{c}$ and horizon $\mathit{h}$. For any model $\mathit{M}$, we now can inspect ${\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}_M^{c,h}$, the models main performance criterion. However, using the conditional RMSE in a comparative analysis is not trivial, as we observe different value ranges for (i) the different cities (e.g. Berlin has a larger value range than Heidelberg), (ii) the chosen forecasting horizon $\mathit{h}$ (monthly indexed data has obviously another range than the weekly one), and, most importantly, (iii) the objective variable themselves (e.g. tag additions has a higher value range than locational change, for example). Now, comparing the conditional performance of the models is hampered by the arbitrary scaling of the RMSE, which prevents a meaningful comparison across the different objective variables. Although there exists a number of methods to normalize the RMSE, all of them have drawbacks. In this work, we chose to simply divide a model’s RMSE by the RMSE of the naive baseline model $\mathit{NM}$ with respect to horizon $\mathit{h}$, city $\mathit{c}$, and the objective variable $\mathit{i}$. With that, a formally consistent and easily interpretable error metric is obtained. Thus, given a model $\mathit{M}$ and its conditional error vector ${\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}_M^{c,h}$, the normalized error vector $\mathbf{E}$ for any model is given by

(14) $\mathbf{E}(\mathrm{M},\mathit{c},\mathit{h})=\frac{{\mathrm{R}\mathrm{MSE}}_{\mathrm{M}}^{c,h}}{{\mathrm{R}\mathrm{MSE}}_{NM}^{c,h}},$(14)

such that

(15) $\mathbf{E}(\mathit{NM},\mathit{c},\mathit{h})=[1,\dots ,1]\mathrm{\forall }\mathit{c},\mathit{h}.$(15)

Accordingly, ${\mathbf{E}}_i$ <1 indicates for any of the models a better performance than the baseline model $\mathit{NM}$ and ${\mathbf{E}}_i$ >1 a worse performance concerning variable $\mathit{i}$.

4. Results

In this section, we present the results obtained in our analyses. Subsections 4.1, 4.2, and 4.3 relate, respectively, to RQs 1, 2, and 3. Reflections on the findings to be presented and their utility for the OSM community and practitioners are discussed in Section 5.

4.1. The temporal dynamic of OSM data contribution activities

Referring to the rolling window method presented in Section 3.1 and related to RQ 1, Figure 2 shows for different window sizes (in months) and for all seven variables the mean and 95% confidence interval of the RMSE metric computed from the time series of the 20 cities considered in this study. In order to make the results comparable, as the variables have different ranges across cities of different sizes and across themselves, the values plotted in Figure 2 were all normalized to the mean RMSE, across all 20 cities, of each variable for the window size of 2 months. Aiming a better interpretation and a more structured discussion of the results, these variables were grouped into activity and modification variables and shown separately in Figure 2. We maintain this grouping for most of the discussions below.

Figure 2. For all seven variables, regarding the 20 cities considered in this study, the figure shows the normalized mean and 95% confidence interval of the rolling window metric RMSE (Section 3.1).

The window size for which the normalized mean RMSE is the lowest can be interpreted as the most consistent length of time each variable’s evolution, i.e. changes in time, can be tracked. In the formulations of RQ 1: as the most consistent time interval for understanding OSM mapping activities and as how far in the past such previous activities seem to affect present ones. One can observe from Figure 2 that the minimum normalized mean RMSE for all variables lies between 4 and 6 months, with the exception of variable tag deletion (around 13 months). In other words, these activities happening in any given month correlate most strongly with such activities happening, in average, in the previous 4–6 months. This uncovers the temporal ”rhythm” of these OSM data contribution activities. That tag deletion has a different temporality, i.e. a slower pace of change, is not surprising. Its minimum normalized mean RMSE of approximately 13 months indicates a reference of time for tags to become deprecated and for mappers focusing on data correction to become more active. It is also noticeable, and expected, that the variance of the normalized mean RMSE, as indicated by the 95% confidence intervals, increases consistently with larger window sizes.

Referring to the time series decomposition method presented in Section 3.2, Figure 3 shows the mean and 95% confidence interval (across the 20 cities) of the decomposed trend of each variable for each month of the time series. For computing the decomposed trends, a moving average window size of 12 months was considered. The decomposed trend values on the y-axis of Figure 3 are standardized according to the equation below:

(16) $\mathit{stand}.(y_t^i)=\frac{y_t^i-{\mu }_{y^i}}{{\sigma }_{y^i}},$(16)

Figure 3. Mean and 95% interval of the trend component of the time series of the 20 cities for all seven variables. The trend component was computed with a 12-month average window. The values on the y-axis are standardized according to Equation 12.(12) ${\text{isin}}_t^{c,h}=(X_t^{c,h}-{\hat{X}}_{\mathit{t}}^{\mathit{c},\mathit{h}}{)}^2,$(12)

where, as before, $y_t^i$ is an observation of variable $\mathit{i}$ at time slot $\mathit{t}$. ${\mu }_{\mathit{\hspace{0.17em}}}$ and ${\sigma }_{\mathit{\hspace{0.17em}}}$ are, respectively, the mean and standard deviation of all observations from the time series. Besides enabling the graphical presentation of all variables together, the normalization allows for statistical aggregation of the decomposed trend of cities of different sizes as well as the comparison of the decomposed trend of variables with very different value ranges. It can be seen, with the exception of variable new mapper which exhibits an outstanding pick on year 2017, that all variables exhibit a similar mildly linearly increasing trend with constant confidence intervals. The decomposed trend lines serve as evidence that a linear model is adequate for projecting OSM data contribution activities for future years.

Table 4 presents the descriptive statistics of the R-squared indexes computed by fitting, for each variable and city, an ordinary least squares regression model in which the independent variable is the time-indexed months of the series and the dependent variable is the respective decomposed trend of the contribution variables. The R-squared of such models is a reliable metric of the strength of linearity of the trends. It can be seen from Table 4 that the mean of the R-squared values obtained from the 20 cities is for all seven variables high (above 0.58 for four out of seven variables). The maximum R-squared values are all above 0.80 and variable new mapper exhibits a particularly strong linear trend, with an average R-squared value above 0.70 for the 20 cities. That further supports, with quantitative evidence, the argument that OSM data contribution activities evolve, in general, linearly, thus shedding light on the nature of temporal dynamic of OSM data contribution activities.

Table 4. Descriptive statistics of the R-squared values obtained by linearly regressing, for each variable and city, the time-indexed months of the series with their respective decomposed trend values.

	create	modify	tag ins.	tag del.	tag ed.	pos. change	new mapper
mean	0.44	0.59	0.58	0.43	0.63	0.35	0.72
std	0.31	0.20	0.18	0.21	0.17	0.30	0.17
min	0.00	0.10	0.13	0.09	0.26	0.00	0.30
25%	0.09	0.53	0.49	0.23	0.58	0.04	0.63
50%	0.56	0.63	0.61	0.49	0.66	0.27	0.76
75%	0.66	0.74	0.69	0.57	0.72	0.66	0.84
max	0.81	0.83	0.83	0.84	0.92	0.84	0.94

We also analyzed the intra-annual dynamic of each variable based on the time series’ seasonality component, extracted with the time decomposition method presented in Section 3.2. Figure 4 shows, for each of the seven variables, the box plot distributions, across the 20 cities, of the mean seasonality of each month of the year. As before, to account for the different variable ranges and city sizes, the seasonality values are standardized according to Equation 16.(16) $\mathit{stand}.(y_t^i)=\frac{y_t^i-{\mu }_{y^i}}{{\sigma }_{y^i}},$(16) It can be seen that the activity variables have a stronger intra-annual contribution cycle, similar to a sine wave. Such cyclical pattern is less prominent among the modification variables.

Figure 4. Box plot distributions of the mean seasonality component for each month and variable across the 20 cities. The seasonality component values are standardized, according to Equation 12(12) ${\text{isin}}_t^{c,h}=(X_t^{c,h}-{\hat{X}}_{\mathit{t}}^{\mathit{c},\mathit{h}}{)}^2,$(12) , for allowing comparison.

Figure 5 shows the box plot distributions, across the 20 cities, of these components’ strength for all seven variables. In line with the results from Table 4, the trend strength for all variables, with the exception of tag deletion, is high, specially for the variable new mapper. The seasonality strength, on the other hand, is comparatively lower for all seven variables. That variables create and positional change exhibit the strongest seasonality is also reflected in Figure 4, where, for these two variables, a stronger intra-annual variance across the monthly distributions of the standardized seasonality can be observed.

Figure 5. Box plot distributions, across the 20 cities, of the trend and seasonality strength for all seven variables.

The results presented in this section uncover interesting temporal patterns of OSM data evolution. In summary, for most variables considered, changes occur in a pace of 4–6 months and in linear way. Although some strength of seasonality is observed, the linear trend, throughout more than 10 years, is what stands out. That constant linear increase identified in our data contests the previously adopted S-shaped function to model the growth of OSM data (Gröchenig, Brunauer, and Rehrl 2014, 2014).

4.2. Temporal correlations among OSM data contribution variables

In order to uncover temporal correlations between OSM data contribution activities (RQ 2), cross auto-correlations (see Section 3.3) were computed between all possible pairs of activity and modification variables in time lags of 0–8 months. The rationale of this analysis is to provide evidence on possible causal relations between OSM mapping activities. Figure 6 shows the box plot distributions of these correlations between the activity variables across the 20 cities considered in this study. Figure 7 shows the same for the modification variables.

Figure 6. Box plot distributions, for all 20 cities, of the autocorrelation between observations from all pairs of activity variables in time lags of 0–8 months.

Figure 7. Box plot distributions, for all 20 cities, of the autocorrelation between observations from all pairs of modification variables in time lags of 0–8 months.

In Figure 6, one sees that new mapper is the variable with strongest autocorrelation. Also, and although subtle, it is noticeable that there is less variance in the correlations computed between modify and new mapper than in other pairs of so-called activity variables. That indicates a stronger and more stable relation of influence between new mappers and feature modification than feature creation activities, meaning that these new mappers initial activities tend to be to edit as opposed to create map features. In Figure 7, it can be seen that tag insertion is the variable with strongest autocorrelation and that a stronger mutual influence is observable between variables tag insertion and tag edition. This indicates that mappers inserting tags might be also editing tags at the same and possibly other features. In both figures, as one would expect, the correlations tend to decrease, and variances tend to increase, with longer time gaps.

4.3. Forecasting OSM data contribution activities

Following the procedures introduced in Section 3.5, the forecasting methods presented in Section 3.4 were evaluated and compared. In Figure 8, the forecasting performances obtained for each contribution variable, by each forecasting method, and for forecasting horizons $\mathit{h}$ of 1–4 weeks are shown. The box plot distributions refer to the performances obtained across the 20 cities. The red line where the normalized error is 1 refers to the performance of the baseline method $\mathit{NM}$ (see Equation 3(3) $F_S=max\left(0,1-\frac{\mathrm{Var}\left(R_t\right)}{\mathrm{Var}\left(S_t+R_t\right)}\right),$(3) ). The fact that the forecasting performance metric is relative to the baseline method enables the aggregation of cities of different sizes and magnitude of contribution activities. The models' absolute errors can be obtained by referring to Tables A1–A4 in the Appendix, where the descriptive statistics of the absolute errors of the baseline method for all variables, cities, horizons, and samples considered in this study are shown.

Figure 8. Performance of the forecasting methods for the seven variables and four forecasting horizons (in weeks). The box plot distributions refer to the 20 cities and the red-dotted line refers to the naive baseline method.

It can be seen that as the forecasting horizons increase from 1 to 4 weeks, the average performance of each method for each variable decreases and the standard deviation thereof increases. In other words, predictions are less reliable the further ahead we attempt to forecast the activities. However, performances are in general better than the baseline model, leading us to the conclusion that forecasting methods give us a better prediction of contribution activities than the baseline approach. The ranking of the performance of these methods is very similar for the seven variables and for the four different forecasting horizons. Most often, the best performance method is the ARIMA, followed by EWMA and LWMA. Also noticeable is that variables “new mapper” and “tag deletion” are frequently better forecast than the other variables across the different models and horizons. Due to the differences and complexities of the models, it is hard to pinpoint the reasons for this, but they may have to do with the fact that “new mapper” is notably the variable with strongest autocorrelation (Figure 7) and “tag deletion” has the lowest mean normalized RMSE (Figure 2). On the other hand, “create” and “tag insertion” are the variables for which the models are least accurate. This might be related with “tag insertion” having the highest mean normalized RMSE (Figure 2) and “tag deletion” the strongest seasonality (Figure 5) and variation thereof (Figure 4) across the cities.

Finally, Figure 9 shows the mean and standard deviation of the normalized error metric (Equation 14(14) $\mathbf{E}(\mathrm{M},\mathit{c},\mathit{h})=\frac{{\mathrm{R}\mathrm{MSE}}_{\mathrm{M}}^{c,h}}{{\mathrm{R}\mathrm{MSE}}_{NM}^{c,h}},$(14) ) of all eight forecasting methods for each of the 20 cities and the four forecasting horizons considered in this study. It can be noticed that the trend of higher errors for longer horizons holds somewhat consistently for all cities. Importantly, the size of the city does not seem to affect the prediction accuracy of the models.

Figure 9. Mean (a) and standard deviation (b) of the normalized error metric of all eight forecasting methods for each of the 20 cities and the four forecasting horizons considered in this study.

5. Summary and outlook

OSM is a constantly changing crowdsourced dataset representing a constantly changing world. It is maintained by a dynamic community of volunteers that define and redefine, not without negotiations and conflicts, how new and persisting features should be mapped and edited. In this work, we explored time series analysis methods and metrics to shed light on the temporal dynamics of different OSM data contribution activities. The trend of linear increase of these activities, their moderate but perceivable intra-annual cycle, and their temporal auto- and cross-correlations are identified patterns that help us better understand the nature of this valuable dataset and the community behind it. These patterns may be considered when planning maintenance and updates of geospatial applications and services based on OSM data, as they enable estimating how much the data will change in a given time (in terms of spatial coverage and semantic redefinition of geo-concepts). The OSM community of engaged mappers and moderators also benefit from evidence-based hints on when and to what type of activities it should pay attention to, indicated by the seasonality graphs and the identified temporal correlations between different data edition and contribution activities. Furthermore, the community can get valuable warnings on significant deviations from the edition patterns identified by the temporal trend and the rolling window graphs, thus enhancing its situation awareness and data quality control efficacy. Importantly, all the graphs generated and used metrics in this study can be reproduced for specific regions and for specific types of features, such as roads, buildings, parks, etc.

We also investigated the extent to which OSM data contribution activities can be forecast. Besides applying a variety of established time series regression methods to forecast seven different OSM data contribution activities in prediction horizons of 1–4 weeks, we proposed an interpretable metric to compare the performance of the models in forecasting these different activities. The Python code developed for extracting and structuring historic OSM data into time series, as well as for applying the compared forecasting methods, is as mentioned, readily accessible to anyone aiming to reproduce this forecasting analysis in other areas and on any set of OSM objects.

Although large data imports and data contribution parties can be expected to negatively affect the accuracy of the forecasting models and the reliability of temporal correlation metrics and patterns, previous studies have reported that such events have long-term influence on the mappers activities and on data contribution dynamics (Ahmouda, Hochmair, and Cvetojevic 2018; Gröchenig, Brunauer, and Rehrl 2014; Juhász and Hochmair 2018). Thus, these events do not hamper the applicability of the analyses and methods explored in this study.

While our work addresses the gaps in current OSM literature of forecasting contribution activities and investigating large-scale temporal data development patterns across cities from different cultural contexts, this effort is far from complete and this paper can be considered a first exploratory investigation. A particularly interesting follow-up study is to apply the approaches presented in this work to non-urban areas. Also, it is relevant to investigate how groups of cities of different cultural contexts, sizes, national importance, and levels of developed OSM community compare in terms of the patterns uncovered in our work. Furthermore, many possibilities are open in terms of considering other attributes of the OSM features. These include their spatial context, semantic categories, individual edition history, and characteristics of the mappers acting on them. Besides capturing important nuances of the data temporal development, these mapper- and feature-related attributes may also increase the forecasting accuracy of the models and extend their applicability to temporal horizons beyond 4 weeks. We acknowledge that predicting data contribution activities, somewhat reliably, for a horizon of a few weeks only calls for improvements. In this regard, besides these spatial, semantic, and historical attributes, arguably more powerful forecasting methods, although hardly interpretable, may yield longer-term and more accurate predictions. Specifically, Long Short-term Memory models have shown impressive performance in time series forecasting in different domains (Hua et al. 2018; Lindemann et al. 2021).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings in this study, as well as the code to process it with the methods presented in this paper, are available in Github at https://github.com/le0x99/POI-Evolution-Forecasting.

Absolute error statistics of the baseline forecasting method

The descriptive statistics of the absolute errors of the baseline forecasting method for horizons of 1 to 4 weeks are shown in Tables A1–A4 below. The absolute error was calculated, as introduced, with the RMSE metric. For each of the four forecasting horizons, the statistics were computed for all 20 cities considered in this study and their respective test samples (see Section 3.5).

Table A1. Descriptive statistics of the absolute errors of the baseline method for a forecasting horizon of 1 week. The statistics were computed from all test samples from all 20 cities considered in this study.

	create	modify	tag ins.	tag del.	tag ed.	pos. change	new mapper
mean	12.6	37.5	24.1	5.2	12.8	8.0	2.4
std	6.8	33.6	21.1	5.4	10.0	5.7	0.9
min	2.1	7.5	5.3	1.1	2.5	1.3	1.4
25%	8.4	15.0	9.8	2.1	5.6	4.7	1.8
50%	10.9	26.7	15.0	2.8	8.8	6.0	2.0
75%	16.8	44.3	28.7	5.9	16.3	10.8	2.9
max	25.8	119.4	78.0	23.2	36.7	19.0	4.5

Table A2. Descriptive statistics of the absolute errors of the baseline method for a forecasting horizon of 2 weeks. The statistics were computed from all test samples from all 20 cities considered in this study.

	create	modify	tag ins.	tag del.	tag ed.	pos. change	new mapper
mean	20.7	75.1	41.3	9.8	25.0	12.7	3.5
std	11.5	84.2	36.2	8.8	21.0	9.5	1.7
min	3.0	13.2	8.8	2.2	2.4	2.6	1.8
25%	12.6	30.5	17.8	3.5	9.5	6.3	2.2
50%	20.0	51.4	25.8	5.6	14.6	8.9	2.8
75%	29.8	71.4	51.6	12.3	39.1	18.5	4.8
max	42.0	388.4	124.7	34.0	71.6	34.5	7.1

Table A3. Descriptive statistics of the absolute errors of the baseline method for a forecasting horizon of 3 weeks. The statistics were computed from all test samples from all 20 cities considered in this study.

	create	modify	tag ins.	tag del.	tag ed.	pos. change	new mapper
mean	28.3	115.9	75.0	12.6	35.3	18.2	4.8
std	16.1	117.5	88.9	11.4	28.5	15.3	2.9
min	3.1	27.6	13.7	2.4	5.2	3.0	1.8
25%	18.0	47.4	20.4	4.1	13.4	7.8	2.9
50%	25.0	64.2	30.9	8.4	28.1	12.4	3.4
75%	45.0	134.0	71.8	17.5	53.7	26.7	6.1
max	56.4	478.0	332.3	38.6	102.1	60.9	11.1

Table A4. Descriptive statistics of the absolute errors of the baseline method for a forecasting horizon of 4 weeks. The statistics were computed from all test samples from all 20 cities considered in this study.

	create	modify	tag ins.	tag del.	tag ed.	pos. change	new mapper
mean	40.7	148.8	92.6	24.4	50.6	23.7	6.4
std	26.3	138.6	95.2	25.6	50.2	16.5	3.5
min	3.3	24.1	11.8	1.9	8.9	4.2	2.4
25%	25.9	61.1	27.2	6.0	18.0	10.6	4.2
50%	33.4	100.7	46.1	17.0	29.2	20.1	5.3
75%	48.0	143.4	132.5	32.0	64.4	33.9	8.0
max	101.9	529.4	316.4	103.3	202.0	59.9	15.8