# Context-aware demand prediction in bike sharing systems: incorporating
spatial, meteorological and calendrical context

Cláudio Sardinha  INESC-ID and IST, Univ. de Lisboa
<EMAIL_ADDRESS>1234-5678-9012 ,  Anna C. Finamore  INESC-
ID and IST, Univ. de Lisboa<EMAIL_ADDRESS>0000-0001-7182-2683
and  Rui Henriques  INESC-ID and IST, Univ. de Lisboa<EMAIL_ADDRESS>0000-0002-3993-0171

(2021)

###### Abstract.

Bike sharing demand is increasing in large cities worldwide. The proper
functioning of bike-sharing systems is, nevertheless, dependent on a balanced
geographical distribution of bicycles throughout a day. In this context,
understanding the spatiotemporal distribution of check-ins and check-outs is
key for station balancing and bike relocation initiatives. Still, recent
contributions from deep learning and distance-based predictors show limited
success on forecasting bike sharing demand. This consistent observation is
hypothesized to be driven by: i) the strong dependence between demand and the
meteorological and situational context of stations; and ii) the absence of
spatial awareness as most predictors are unable to model the effects of high-
low station load on nearby stations.

This work proposes a comprehensive set of new principles to incorporate both
historical and prospective sources of spatial, meteorological, situational and
calendrical context in predictive models of station demand. To this end, a new
recurrent neural network layering composed by serial long-short term memory
(LSTM) components is proposed with two major contributions: i) the feeding of
multivariate time series masks produced from historical context data at the
input layer, and ii) the time-dependent regularization of the forecasted time
series using prospective context data. This work further assesses the impact
of incorporating different sources of context, showing the relevance of the
proposed principles for the community even though not all improvements from
the context-aware predictors yield statistical significance.

Context-sensitive forecasting, spatiotemporal data, multivariate time series,
LSTMs, bike sharing system, regularization

††journalyear: 2021††copyright: none††conference: arXiv; CoRR; 2021††price:
0††isbn: NA

##  1\. Introduction

Transportation dynamics are changing in large cities worldwide (Creutzig et
al., 2012; Nieuwenhuijsen, 2020; Karlsson et al., 2020). Modes of shared
mobility are rising in popularity, particularly bike sharing modes propelled
by structural shifts in the culture and cycling infrastructures of urban
systems (Shaheen and Guzman, 2011; Campbell and Brakewood, 2017). Worldwide,
the total number of bikes is estimated to have increased from 700,000 bikes in
2014 towards over 18 million in 2018 (Richter, 2018). To reduce the carbon
fingerprint and meet this demand, over 1600 Bike Sharing Systems (BSS) are now
operating and rapidly expanding (Richter, 2018) as they offer a reliable, low-
cost and environmental-friendly mode of short-distance transportation. Most
public BSS support cycling traffic along a network of docking stations, as
opposed to dockless bike sharing systems (Shaheen et al., 2020).

In contrast with other modes of transportation, the operation and planning of
public BSS in metropolitan areas are hindered by unique challenges. First, the
demand is unevenly distributed both geographically and temporally, with
stations in residence and office areas being either frequently full or empty
during peak hours, thus preventing local check-ins and check-outs and
consequently hampering user trust (Frade and Ribeiro, 2015; Ren et al., 2020).
Second, bike sharing demand is affected by significant externalities,
including daily variations on the users’ profile and endeavors impacting their
preference towards a given mode of mobility (Kim, 2018). Balancing
initiatives, including the ongoing bike relocation or dynamic user incentives
for taking specific routes along certain time windows can be placed to
counter-act this effect (Ren et al., 2020). Yet, their efficacy is largely
dependent on the ability to model and forecast the demand of BSS stations.

In this context, predicting bike sharing demand at fine spatial and temporal
levels is essential for the proper operation and planning of public BSS.
Despite the large attention placed by the communities of urban computing,
machine learning, and intelligent transportation systems on this task (Lin et
al., 2018; Li et al., 2019; Lozano et al., 2018; Chen et al., 2020), BSS
demand prediction is recognizably a difficult task. State-of-the-art
predictors, whether grounded on classical, distance-based or neural processing
principles, show unexpectedly large forecasting errors in comparison with
other transportation modes (Leite et al., 2020). In addition to the
aforementioned challenges, the difficulty on predicting demand is linked with
the fact that bike sharing demand is significantly dependent on:

  * •

the situational and calendrical context. The occurrence of public events and
the presence of calendar-driven context – including academic breaks,
festivities and weekly-monthly-yearly seasonal factors – affect demand, and
can significantly alter expectations on station load (Leite et al., 2020);

  * •

the meteorological context. Weather factors, including precipitation, humidity
and significant deviations to the perceived temperature are known to condition
user decisions (Kim, 2018);

  * •

spatial context (station-wise interdependencies). States of full and empty
station load not only hamper the demand analysis on the stations subjected to
check-in and check-out impediments, but also affect the demand of nearby
stations, which will receive an indirect increase in the demand for bike
check-ins and check-outs that should be separated from their true demand under
normal conditions. In this context, variables such as distance between
stations, station capacity and other interdependence factors impact demand
(Fishman et al., 2014; Frade and Ribeiro, 2015).

Recent contributions have been proposed to consider calendrical constraints
(Kim, 2018); offer meteorological-based corrections by either segmenting data
(Cerqueira et al., 2020) or extending the learning process (Ashqar et al.,
2019); or model spatial dependencies using influence factors (Tomaras et al.,
2018) or graph neural networks (Pan et al., 2019a). Despite their relevance,
state-of-the-art contributions for predictive tasks generally fail to model
the joint impact that these multiple sources of context exert on bike sharing
demand.

In addition, existing work generally fails to separate the important role of
both historical and prospective sources of context. For instance, historical
weather data are important to assert the true impact of weather variables in
demand, while prospective weather forecasts essential to adjust predictions.
Context-sensitive models generally tackle one of these two modes, either
historical sources of context to consistently remove context-dependent factors
from predictions or prospective sources to embed context-dependent factors
throughout predictions.

This work proposes a predictive deep learning approach that is able to
incorporate heterogeneous sources of spatial, meteorological and calendrical
context – both historical and prospective – into the time series forecasting
task. To this end, we propose a new class of recurrent neural layering for
context-sensitive demand prediction. Motivated by the solid performance of
long-short term memory networks (LSTMs) in traffic data analysis, this work
proposes a serial composition of recurrent components using two major
principles:

  1. (1)

to take advantage of the inherent ability of LSTMs to learn from multivariate
time series data in order to model correlations between demand variables and
an arbitrarily-high number of context variables derived from the available
historical context. To this end, a set of simplistic yet effective masking
procedures are proposed;

  2. (2)

to include an additional LSTM or gated recurrent unit (GRU) layering for the
time-dependent regularization of the forecasted signal using prospective
context data collected along the horizon of prediction.

This proposal is motivated and assessed in the context of BSS demand
prediction given its paramount relevance in this domain. In particular, our
work further introduces a study case – GIRA, the public BSS in the Lisbon city
(77 stations, approximately 700 bikes and 700 to 1500 daily trips) – and
evaluates the impact of incorporating available sources of context in the
ability to predict the demand along the GIRA’s bike sharing system. The
gathered results show the role of specific sources of historical and
prospective context data in shaping demand forecasts, motivating the relevance
of the proposed principles to support BSS balancing and planning.

The major contributions of this work are three-fold: i) extension of LSTM-
based predictive models to incorporate heterogeneous sources of context data
from masking principles; ii) serial composition of LSTM components for the
time-dependent regularization of the forecasted signal based on prospective
context data; and iii) comprehensive assessment of the impact of the proposed
context-awareness forecasters against state-of-the-art forecasters at
different spatial and temporal granularities.

The manuscript is structured as follows. Section 2 provides essential
background on bike sharing systems, time series forecasting, and urban sources
of context. Section 3 surveys relevant work on context-sensitive prediction.
Section 4 introduces the proposed approach, describing principles on how to
incorporate historical and prospective context data within the learning
process. Section 5 assesses the impact of these principles. Finally,
concluding remarks and implications are synthesized in section 6.

##  2\. Background

### Bike sharing systems

Bike sharing systems (BSS) allow users to access bicycles on an as-needed
basis using docking or dockless infrastructure. BSS are constituted by two
entities: agents (users) and the environment (bikes and stations). A bike
station is described by the number of docks (station capacity) and number of
docked bikes (station load). Agents change the environment by performing
check-out acts (picking-up bikes) and check-in acts (dropping-off bikes).

In the context of this work, bike demand is defined as the number of check-in
and check-out acts that should be supported at a specific station in a given
time to fill the user’s needs.

BSS traffic data are the monitored check-ins and check-outs along the network
of stations per user, accompanied by information on the station capacity and
load.

Context data are data produced from alternative urban sources of interest,
including public events (situational), weather records (meteorological),
seasonal determinants (calendrical), among others.

Given a bike sharing system, the target task in this work is to forecast bike
demand at desirable spatial and temporal levels from available traffic and
context data.

### Time series modeling and forecasting

Traffic and context data are generally represented as time series, a set of
ordered observations $\mathbf{x}_{1..T}=(\mathbf{x}_{1},...,\mathbf{x}_{T})$,
each observation $\mathbf{x}_{t}$ being recorded at a specific time point $t$.
Time series can be univariate, $\mathbf{x}_{t}\in\mathbb{R}$, or multivariate,
$\mathbf{x}_{t}\in\mathbb{R}^{m}$, where $m>1$ is the multivariate order
(number of variables).

Given a time series $\mathbf{x}$, the modeling task aims at finding an
abstraction that describes $\mathbf{x}$, while the forecasting task aims to
estimate $h$ upcoming observations, $\mathbf{x}_{T+1..T+h}$, from available
observations $\mathbf{x}_{1..T}$. Descriptive and predictive tasks typically
aim at respectively modeling and forecasting a single variable (the target
variable).

In multivariate data settings, non-target variables are used to guide the
learning of descriptive and predictive models.

Classical approaches for time series analysis generally rely on statistical
principles, including decomposition, auto-regression, differencing and
exponential smoothing operations. Time series can be decomposed into trend,
seasonal, cyclical, and irregular components using additive or multiplicative
models (Jain, 2001). Although these models are inherently descriptive in
nature, the components can be projected along a time horizon for predictive
ends. Alternatively, auto-regressive and moving-average models can be combined
to either describe or forecast stationary time series (Wei, 2006). These
models can be extended with simplistic differencing operations for dealing
with non-stationarity, and their learning guided in the presence of seasonal
terms. Classical alternatives use exponential smoothing principles to describe
and predict time series (Wei, 2006). Holt-Winters offers a form of triple
exponential smoothing (at level $\ell_{t}$, trend $b_{t}$ and seasonal $s_{t}$
components). According to an additive model,

(1) $\displaystyle\hat{\mathbf{x}}_{t+h}$
$\displaystyle=(\ell_{t}+\mathbf{h}b_{t})s_{t+h-d(k+1)}\text{ where}$ (2)
$\displaystyle\ell_{t}$
$\displaystyle=\alpha\frac{\mathbf{x}_{t}}{s_{t-d}}+(1-\alpha)(\ell_{t-1}+b_{t-1}),$
(3) $\displaystyle b_{t}$
$\displaystyle=\beta^{*}(\ell_{t}-\ell_{t-1})+(1-\beta^{*})b_{t-1},$ (4)
$\displaystyle s_{t}$
$\displaystyle=\gamma\frac{\mathbf{x}_{t}}{(\ell_{t-1}+b_{t-1})}+(1-\gamma)s_{t-d}.$

Advances from machine learning aim at mitigating the challenges faced by
classical approaches. In this context, time series are generally segmented to
compose a dataset that guides the learning of the target descriptive and
predictive models under a specific loss criteria. Among the wide-diversity of
contributions on (multivariate) time series analysis, two major groups of
approaches are here highlighted. First, distance-based approaches for time
series description and prediction that rely on similarities between
(multivariate) time series (lazy learning) and expectations (barycenter
computation) (Cai et al., 2016). Second, neural network approaches rely on the
composition of simple linear functions (neurons) to learn complex mappings. In
the context of time series analysis, the mapping can either be descriptive
(e.g. auto-encoders) or predictive (e.g. regressors) (Bao et al., 2017).

Recurrent neural networks (RNNs) capture the temporal dependencies within a
time series, subjecting each observation to a neural network and feeding the
result to the successor observation (hence recurrent),

(5) $\mathbf{h}_{t}=f(\mathbf{h}_{t-1},\mathbf{x}_{t}),$

where $\mathbf{h}_{t}$ is the output produced at time point $t$ and $f$ is the
neural function. As neurons are linear functions of inputs $w_{i}$,
$\sum_{i}w_{i}$,

(6)
$\mathbf{h}_{t}=\text{tanh}(\mathbf{W}_{x,t-1}\mathbf{h}_{t-1}+\mathbf{W}_{t}\mathbf{h}_{x,t}),$

where $\mathbf{W}_{t}$ is a matrix of input weights at state $t$ and tanh is
the hyperbolic tangent (activation) function. The output state is defined as
$\mathbf{W}_{y,t}\mathbf{h}_{t}$, where $\mathbf{W}_{y,t}$ is the set weights
at the output state.

RNNs suffer from memory loss, the well-studied vanishing gradient problem
(Hochreiter, 1998), being generally unable to detect seasonal time series
aspects. Long Short Term Memory networks (LSTMs) are extended RNNs able to
learn long-term dependencies. LSTMs are composed by a memory unit (cell) and
three regulators (gates) that control the flow of information inside the LSTM
– the preserved information (forget gate), the updatable inputs (input gate)
and the candidate outputs (output gate). Gated Recurrent Units (GRUs) exclude
the output gate, providing a simpler network that generally yield improvements
in denoising tasks (Chung et al., 2014).

### Context

Diverse sources of urban context data are known to have soft-to-strong
correlations with traffic dynamics (Cerqueira et al., 2020), suggesting their
relevance to guide descriptive and predictive learning tasks. These sources
can be divided according to: i) calendrical sources, providing relevant
information associated with academic and holiday periods, as well as daily,
weekly, monthly and yearly seasonality; ii) situational sources, including
historical and prospective public events (such as conventions, festivals,
concerts, sport events) and road interdictions (including construction works);
iii) meteorological sources, comprising observed and forecasted weather
variables (such as perceived temperature, humidity, wind intensity,
precipitation, visibility); and iv) spatial sources capturing geographical
dependencies with potential value for traffic data analysis (Casas et al.,
2019).

##  3\. Related work

Recent attention has been paid on how to incorporate context factors to
understand mobility dynamics and support traffic data analysis (Cerqueira et
al., 2020; Leite et al., 2020). These factors are typically divided on whether
they can be planned (Latoski et al., 2003) – including football matches,
concerts, festivals, construction works, urban planning – or not (Soua et al.,
2016) – weather, air quality, traffic accidents, emergencies. The former
factors are often referred as planned special events (PSE) (Latoski et al.,
2003). Some of the challenges of integrating spatiotemporal context and its
role in developing smart cities are discussed by Sagl et al. (Sagl et al.,
2015).

In this paper, we are interested in three large family of studies: i) studies
that assess the correlation impact of context factors; ii) studies that place
general principles on how to use context for guiding forecasting tasks; and
iii) deep learning studies able to incorporate context factors within neural
network learning.

In the first category, Tomaras et al. (Tomaras et al., 2018) proposed the use
of a metric, influence factor, to measure the impact of social events in the
demand of nearby bike stations. The influence factor is a ratio between the
sum of the drop-off and pick-up when an event happens, and drop-off and pick-
up in a typical day. This factor can be used as a correction factor for
descriptive and predictive models. Kwoczek et al. (Kwoczek et al., 2014)
proposed a method to predict and visualize traffic congestions caused by
planned special events. Public events are generally characterized by two waves
of congestion: people arriving and leaving the event. Recognizing the
difficulty of estimating the impact of these waves (the popularity of event),
the authors developed a system to predict the waves using nearest neighbors
from past PSEs and showed that event-sensitive predictions yield improvements.
Soltani et al. (Soltani et al., 2019) conducted a web-based survey from public
BSS and private BSS users (OfO and O’Bike) at Adelaide, Australia, and
explored key findings to support policy makers. Context factors, including
relatively low car dependency; young user profile; large share of students,
visitors, and non-australian residents; safety concerns; and facility
conditions were shown to highly impact demand. Yang et al. (Yang et al., 2019)
studied the impact that a new metro line has in dockless bike sharing systems.
To this end, they considered around 80,000 dockless bikes in Nanchang, China
to capture changes in behaviours and patterns in the urban flow.

In the second category, studies that have considered context to enrich
forecasting, Gallop et al. (Gallop et al., 2012) explore complex serial
correlation patterns between weather and bike traffic and use this effect to
adjust the error terms of the classic autoregressive integrated moving average
(ARIMA) models. They further suggest that this correction can be used to
affect historical data in an effort to create context-independent models that
facilitate traffic data analysis tasks. El-Assi et al. (El-Assi et al., 2017)
provide a multi-level model considering the impact of land use, built
environment, and weather measures on bike share ridership. Similarly, Tran et
al. (Tran et al., 2015) consider the problem of predicting bike-sharing system
flow. To this end, they propose the use of a regression model and further
consider the effects from five categories of context variables: public
transport, socio-economic, topographic, bike-sharing network, and leisure
variables. Ashqar et al. (Ashqar et al., 2019) consider a data-fusion approach
towards the analysis of context-enriched bike demand. They propose the use of
random forests to rank context predictors and consider them to develop a
forecasting model using a guided forward step-wise regression approach. They
found that time-of-day, temperature and humidity are significant predictors.
Thomas et al. (Thomas et al., 2009) studied cycle flows from utilitarian and
recreational paths in the Netherlands. A bi-level model for predicting the
demand for cycling was used. The lower level describes how cyclists value the
weather. The upper level is the relation between demand and this weather
value. Most fluctuations are described by the model.

In the third category, studies that have used context to enrich forecasting
using neural networks, Thu et al. (Thu et al., 2017) propose multi-layer
perceptron regressors from multi-source context data to predict bike pick-up
demands from New York city BSS considering clusters of stations based on their
geographical locations and transition patterns. The proposed networks combine
weather factors (condition, temperature, wind speed, and visibility) and taxi
trip records. Despite its relevance, temporal dependencies between
observations are disregarded. Pan et al. (Pan et al., 2019b) incorporate
weather record data at input layer of LSTMs to improve the prediction of bike
sharing demand for balancing of distribution of bikes across stations. Results
evidenced improvements against context-unaware LSTMs. Recent contributions on
deep learning research also show the possibility of incorporating specific
forms of calendrical and spatial awareness (Pan et al., 2019a; Casas et al.,
2019).

##  4\. Solution: context-aware LSTMs

We propose a new recurrent neural network layering able to incorporate both
historical and prospective sources of context to guide forecasting tasks. The
proposed architecture is a sequential composition of two components, $C_{1}$
and $C_{2}$. $C_{1}$ is a LSTM that receives context-enriched multivariate
inputs and returns the forecasted series as the output. $C_{2}$ is a LSTM (or
a gated recurrent unit) that receives as input the forecasted series from
$C_{1}$ and prospective sources of context along the horizon of prediction and
returns the true forecasting. Sections 4.1 and 4.2 respectively describe how
historical and prospective sources can be fed into the proposed architecture,
and further discuss their significance.

###  4.1. Incorporating historical context: masking

To incorporate historical sources of context data, we take advantage of the
fact that LSTMs are inherently prepared to learn mapping functions from
multivariate time series into the target univariate time series (demand
variable along a prediction horizon). In this way, an arbitrarily-high
multiplicity of context variables can be combined at the input layer of the
$C_{1}$ component to guide the learning task. Sections 4.1.2 to 4.1.5 offer
important masking principles on how to compose the multivariate time series
from difference context sources. For the purpose of illustrating the
principles introduced along these sections, consider that the task at hands is
to learn a predictive model that forecasts the number of hourly bicycle check-
outs for the upcoming days at a given station using a two-year historical data
with an hourly aggregation,

.

$\displaystyle\mathbf{x}_{\text{example}}$
$\displaystyle=(\mathbf{x}_{0h:1/1/2018},\mathbf{x}_{1h:1/1/2018},..,\mathbf{x}_{23h:31/12/2019}),$
$\displaystyle=((9),(6),..,(10)),$

a series to be further segmented for the purpose of learning.

Under masking principles, sources of historical context are hypothesized to
guide the forecasting task in two major ways. First, by looking to the past
and modeling how a certain context variable affects bike demand at a given
station offers the possibility of removing context-dependent factors.
Considering wind intensity as an illustrative context variable, deviations
from regular wind ranges can be considered by the LSTM unit to better model
the co-observed demand.

Second, some sources of historical context can be correlated with future
context and/or demand. Therefore, this relation can be directly learned by the
LSTM unit to shape short-term forecasts. For instance, strong wind intensity
at a given hour may decrease the observed demand with effect lasting up to
three hours.

####  4.1.1. Station context

In addition to the target variable, complementary demand variables can be
inputted to guide the prediction. For instance, the analysis of check-ins can
be complemented with the volume of check-outs to account for correlated
deviations.

Another example is to consider the load state of the station as we know that
states of high-load (low-load) can impact check-outs (check-ins).
Illustrating, $\mathbf{x}_{\text{example}}$=((check-in=9,check-
out=6,load=0.9), ..,(check-in=10,check-out=12,load=0.3)), is an augmented
series with a multivariate order of 3.

####  4.1.2. Calendrical context

Four masks are suggested:

  * •

a day mask can be added to the time series with information pertaining to the
week-day of each observation,

$\mathbf{x}_{\text{example}}=((9,monday),(6,monday),..,(10,tuesday)).$

In this way, LSTMs are inputted with information that helps them internally
separating neural pathways in accordance with the week-day. This is a
simplistic yet essential guiding information whenever segmentation creates
instances starting at different timings.

In addition, this masking principle can act as way of augmenting data as it
allows for the combined inclusion of weekends and weekday periods in the
forecasting task, instead of learning separate forecasting models.

If weekdays show similar patterns of demand, simpler daily masks can be
applied using mappings of lower cardinality, such as {weekday, saturday,
sunday};

  * •

a holiday mask can be added as a separated binary variable in order to
indicate whether a given observation was produced or not within a holiday;

  * •

an hour mask can be added as an additional variable to guide the learning task
whenever the segmentation step does not guarantee that every data instance
starts at the same time step. As a result, daily seasonalities can be
implicitly captured within the LSTM as a non-linear function of the hour
within the day. If the time granularity of the demand series is finer
(coarser) than hour, a finer (coarser) mask can be produced. For instance, a
mapping {dawn, morning, afternoon, evening} is adequate for temporally
misaligned data instances and time windows with up to 6 hours;

  * •

other relevant masks, include academic period masks or festivity period masks
that may not necessarily coincide with the aforementioned holiday mask. In the
context of our work, the influence of these masks were found to be essential.

####  4.1.3. Situational context

Similarly to the masks produced from year and academic calendars, situational
masks mark periods where events of interest may impact the demand observed at
a given station. The major difference between these sources of context is the
fact that situational context is usually circumscribed to a specific
geographical area, therefore only impacting a subset of stations from a given
BSS. Given a station, the situational variables produced using these masking
principles generally correspond to public events (concerts, conventions or
sport events) that occur within a maximum distance from the target station.

Situated events can produce varying levels of impact on the demand at a given
station. For instance, stations nearby a stadium and a small concert hall
should be able to differentiate between sport events and concerts. In this
context, these masks can explicitly capture the magnitude of an event, as well
as variations on that same magnitude throughout the period where the effects
of the event lasts. Illustrating, $(0,0,1,3,3,1,1,3,3,1,0...)$ series may
correspond to a mask modeling the magnitude of a gathering that can be placed
as a complementary inputted series to guide the learning.

####  4.1.4. Meteorological context

Meteorological variables, including wind intensity and precipitation, can be
as well inputted to guide the learning. The closest meteorological station can
be selected or k-nearest stations to compute the weather series (under
distance-weighting schema). Additional weather variables can be produced from
the raw weather records produced by meteorological stations, including the
perceived temperature or integrative scores.

A high number of weather variables leads to high a multivariate order of the
inputted, which can hamper the learning if not enough historical observations
are available. In this context, variable selection can be considered to
guarantee that only the most informative weather variables are inputted.

####  4.1.5. Spatial context

In the context of station-wise dependencies, we propose a geographical mask,
referred as the nearby mask. The nearby mask is the occupation ratio of the
neighbouring stations. The algorithm to create the nearby variables, Algorithm
1, receives the target station or cluster of stations under analysis, $SS$, a
distance radius, $R$, list of all stations, $S$, and time series $TS$.
Algorithm 1 has three-steps: 1) computes the centroid of the selected
stations, line 3; 2) finds all the stations inside the $R$ radius using the
previous centroid as the centre (lines 4–8), and updates the time series with
the occupation ratio of the nearby stations (lines 10–12).

Under the nearby mask, the target LSTMs are now able to consider the impact
that stations with high- and low-load have on the demand of nearby stations.
Here, the occupation ratio is proposed in contrast with full-and-empty station
states to allow for more flexible learning (nearly full stations may be full
in the upcoming time steps). Still, alternative encodings can be proposed by
customizing line 11 of Algorithm 1.

1

2 Function  _create_nearby_mask(_$SS,S,R,TS$_)_:

3 nearby_station = []

4 lat_center, long_center = calculate_centroid($SS$)

5 foreach  _station $s_{i}\in S$_ do

6

7 distance = Euclidean((lat_center, long_center), ($s_{i}$.lati,
$s_{i}$.long))

8 if  _distance $<$ radius_ then

9 nearby_station.append($s_{i}$)

10 end if

11

12 end foreach

13

14 foreach  _station $s_{i}\in$ nearby_station_ do

15

16 $TS$ = update_series
($TS,\dfrac{s_{i}._{\text{num\\_bikes}}}{s_{i}._{\text{location\\_capacity}}}$)

17 end foreach

18

19

20End Function

Algorithm 1 Create nearby mask algorithm

###  4.2. Incorporating prospective context: time-dependent regularization

Prospective sources of context, including weather forecasts or planned events,
may be available along the horizon of prediction. In this context, their use
can further guide the learning. Recall that the proposed architecture is a
composition of two components, $C_{1}$ and $C_{2}$. $C_{1}$ is a LSTM that
receives multivariate inputs (in accordance with the principles introduced
along section 4.1) and returns the forecasted series as the output. $C_{2}$ is
a recurrent neural component that receives the forecasted series from $C_{1}$
and the prospective sources of context along the horizon of prediction as
inputs, and returns the true forecasting. In this context, $C_{2}$ can be
though as a context-aware denoiser or time-dependent regularizer of the
forecasts. Empirical analysis show optimal performance when $C_{2}$ is a LSTM
unit. Nevertheless, a gated recurrent unit (GRU) provides a competitive
alternative given the properties of this step.

Under the proposed architecture, masking principles – similarly to the ones
introduced along section 4.1 – can be considered to compose the multivariate
time series to be inputted to the $C_{2}$ component. In this context:

  * •

calendrical masks can be produced to regularize the forecasts whenever the
prediction horizon contains holidays or any other meaningful season (such as
academic break). In addition, and more generally, time and day masks can be as
well inputted for a calendric-guided revision of forecasts;

  * •

situational masks can be produced from planned events available from cultural
and sport agendas, as well as semi-structured repositories containing
information on the usage of public spaces. See section 4.1.3 for principles on
duration- and intensity-sensitive encodings for situational masks;

  * •

meteorological masks can be produced from weather forecasts. As weather
forecasts are typically produced under a coarse-grained time granularity,
upsampling may be necessary to guarantee the weather and demand series share
the same granularity. See section 4.1.4 for principles on station and variable
selection;

  * •

spatial masks can be derived from forecasts of nearby stations’ load (see
principles in section 4.1.5) when load forecasts are able to satisfy upper
bounds on the observed error.

By incorporating prospective sources of context, the $C_{1}$-forecasted demand
series can now be further subjected to context-dependent corrections, guiding
the forecasting task. For instance, periods with forecasts of high wind
intensity can suffer an adjustment on the $C_{1}$-based demand expectations by
capturing relationships between the multivariate input series and the true
forecast.

###  4.3. Learning schema

To guarantee the proper learning of the proposed neural networks,
considerations associated with both the segmentation and the learning setting
should be placed. Given a specific horizon of prediction $h$ and its time
resolution $\Delta$, the series should be segmented in a set of instances,
each instance being a pair (input, output) where the input is a series with at
least twice the length of the prediction horizon (by default $7\times h$), the
output is the subsequent $h$-length series, and both series have the same time
resolution, $\Delta$. Segmentation is further characterized by the presence of
a sliding window to compose the data instances. By default, the sliding window
corresponds to a single day (24 hours).

The above principles are applied to segment series in the context of a single
dataset. For a more robust validation of predictors, cross-validation is
suggested. Particular attention should be paid to guarantee the soundness of
the cross-validation setting given the inherent time frame of the series data.
Algorithm 2 shows how multiple datasets are produced. In this context, series
is the inputted (univariate or multivariate) time series with a time frame
$\Delta$ given by the user; window_size is the length in days of each dataset,
and step_size is the lag value between datasets in days. Figure 1 provides an
example of the algorithm 2, where window_size = $T-2$, step_size = 1 and
datasets is the resulting set of three datasets.

1 Function  _create_subdatasets(_dataset, window_size, step_size_)_:

2 datasets = {}

3 end_dataset_index = window_size - 1

4 while  _end_subdataset_index $\leq$ $|$series$|$_ do

5

6 begin_dataset_index = end_dataset_index - window_size

7 dataset = series[begin_dataset_index:end_dataset_index]

8 datasets = datasets $\cup$ {dataset}

9 end_dataset_index += step_size

10 end while

11 return datasets

12

13End Function

Algorithm 2 Split dataset algorithm  Figure 1. Example of algorithm 2 with
$step\\_size$ of 1

After applying Algorithm 2, we split each sub-dataset into train, validation
and test data, guaranteeing that training data instances always precede
validation and testing data instances in order to better mimic real-time
testing scenarios.

####  4.3.1. Hyperparameter otimization

Each dataset is scaled using a min-max normalization to improve the LSTM
performance. The min-max scaler parameters are learned from the training data
instances for each dataset. The test and validation segments are also
normalized using the scaler learned from the training segment.

Parameterizations associated with the proposed layering architecture were
empirically conducted using a sensitivity analysis on the number, size, type
and composition of layers, as well as on the results yield by different loss
functions (including cosine, mean absolute error, mean squared error) and
forms of regularization.

All the additional parameters – including activation functions, presence of
drop-out layers, optimizers, batch size and learning rates – were fixed using
Bayesian optimization. The optimized metric was the mean absolute error
produced over all the training segments. Early stopping from validation errors
is considered.

##  5\. Results

Results are organized in three major steps. First, we introduced background
considerations on the: i) target public BSS (GIRA) and considered sources of
context, ii) assessment setting, and iii) general exploratory statistics on
GIRA’s bike demand. Second, we provide a thourough comparison of state-of-the-
art forecasters against the proposed context-aware predictors. Third, we offer
a greater detail on the performance of the proposed context-aware predictors,
describing the impact that different sources of context have on the
forecasting residues.

The proposed context-aware predictors were implemented using tensorflow,
python. The remaining state-of-the-art predictors were implemented using
facilities from statsmodels, tslearn (barycenter calculus) and scikit-learn
packages in python. The parameters of the state-of-ther-art predictors (such
as smoothing factors in Holt-Winters or $k$ in $k$-nearest neighbor
regressors) were subjected to Bayesian optimization. .

### Case study: GIRA

To comprehensively assess the proposed contributions, we consider the Lisbon’s
public BSS, termed GIRA, under the joint responsibility of EMEL and the
Lisbon’s city Council. The data associated with the target GIRA network
contains all bike trip records from November 2018 until April 2019, with
timestamps for every change in stations’ state and the corresponding load
value. Structural changes to the stations’ capacity associated with the BSS
expansion are also considered. Given the station load data, the check-out and
check-in events within the Lisbon’s public BSS were inferred from the
differences on the load state of each station along time. .

### Lisbon’s urban context

Historical and prospective weather record data was sourced by Instituto
Português do Mar e da Atmosfera (IPMA) and Instituto Superior Técnico (IST).
Humidity, wind speed (km/hour), pressure, precipitation and temperature
(Celsius) weather variables were sourced. Four meteorology stations available.
The station closer to a station is selected for providing weather data. When
analyzing clusters of stations, the centroid of each centroid is computed in
order to identify the closest meteorology station.

Situational context data was derived from: the Lisbon’s cultural agenda, road
construction works, and the city Council’s records on the occupation of large
public spaces and stadiums. Finally, calendrical context data was sourced from
available civil and academic calendars, and spatial context data inferred from
the GIRA dataset.

.

### Station clusters

Bike demand analysis can be pursued at different spatial granularities in
accordance with the targeted aim, such as establishing balancing initiatives
(finer granularity) or general planning decisions (coarser granularity). To
this end, we predict bike demand at three distinct levels: i) station level;
ii) cluster of stations; and iii) BSS level (all stations). To help the city
Council understanding demand, we identify three clusters of interest: IST
cluster, Saldanha cluster and Oriente cluster, represented in Figure 2.

(a) Oriente cluster

(b) Saldanha cluster

(c) IST cluster

Figure 2. Selected clusters of stations (screenshot from ILU App)

Each of these clusters yield unique aspects of interest. The IST cluster has a
high share of students since its stations are close to the campus of Instituto
Superior Técnico’s faculty. Saldanha cluster has a high share of workers since
its stations are located within a well-known business district. Finally,
Oriente cluster has a high share of tourists since its stations are located
near Parque das Nações, a place with diverse cultural, expo and leisure
attractions.

The Oriente cluster is the larger cluster, encompassing 6 docking stations and
a total capacity of 144 bicycles. The Saldanha cluster has 3 stations with a
total capacity of 44 bicycles. Even though, IST cluster has only 2 stations,
it is capable of holding 51 bicycles. .

### Exploratory statistics

Figures 3 and 4 provide a high-level view on how the demand varies for the
GIRA’s BSS as whole (cumulative demand from all stations). Figure 3 offers a
view on how demand is distributed along a normal week, evidencing the
calendrical differences and the effect produced by public events at Saturday
night. Figure 4 captures the variability of demand along the targeted period,
where the bounds (standard deviation) confirm that bike sharing demand is
susceptible to diverse idiosyncrasies causing significant variability.

Figure 3. Half-hourly volume of check-outs/ins within GIRA. Figure 4. Daily
volume and variation of check-outs and check-ins at a single GIRA’s station
(November 2018 to April 2019).

### Comparison of state-of-the-art forecasters

Tables 1 and 2 gather the predictive performance of state-of-the-art
forecasters, focusing respectively on check-ins and check-outs at different
spatial granularities (system-, cluster- and station-wise levels). The
prediction horizon is 24 hours under a 30-minutes time step. The mean absolute
error (MAE) and root mean squared error (RMSE) were the selected forecasting
metrics. The average and standard deviation estimates for these metrics were
computed from the residues gathered from all testing data instances from each
one of the three data folds (according to section 4.3).

From the state-of-the-art predictors, a variant of existing kNN forecasters,
combining neighborhood search and barycenter computation from sets of $k$ time
series, is proposed given its superior performance. In this context,
barycenter forecasters can be though as kNN forecasters when $k$ equals the
number of training data instances. Dynamic time wrapping (DTW) is considered
as a similarity metric to tolerate temporal misalignments.

Five major remarks are observed. First, classical approaches, including Holt-
Winters, are unable to properly deal with the arbitrarily-high variability of
bike sharing demand as seasonal and trend modeling is generally insufficient
to handle the peculiarities of the targeted bike trip data. Second, distance-
based predictors yield slightly worse yet competitive results against the
proposed LSTM-based predictors. Third, the proposed context-aware LSTM-based
predictors generally offer slight improvements against context-unaware LSTM-
based predictors, yet the improvements do not yield statistically significant
differences111Residues normally distributed. Unilateral paired $t$-tests with
$p$-value above 0.01.. Fourth, from the different sources of context, the
individual use of meteorological sources and the joint use of meteorological-
and-spatial sources of context are the optimal settings. Finally, historical
and prospective sources of context have similar impact on the forecasting
performance.

Figure 5 provide a more detailed view on the performance of the proposed $k$NN
predictors, showing the impact of locality – $k\geq 5$ –, and tolerating
misalignments – DTW is comparable to Euclidean distance to compute both
neighborhoods and barycenters.

Figure 5. MAE performance of proposed $k$NN with varying $k$ and distance
(Euclidean vs DTW in neighborhoods and barycenters) to forecast demand for the
whole GIRA network.

### Context impact on demand predictors

Figures 6 and 7 provide two illustrative data instances that clearly show the
impact of incorporating meteorological context data on the forecasts. Figure 6
considers the check-in demand at the whole network level, clearly showing the
indisputable role of incorporating weather record data for improving
predictions. Figure 7 considers the check-in demand at the Oriente cluster
level, showing the impact from the integration of multiple sources of context.

Table 1. Comparison of forecasting errors (MAE and RMSE) of state-of-the-art predictors: check-in demand at 30 minutes granularity. | Senario 1: all stations |  Senario 2: Oriente cluster | Senario 3: single station
---|---|---|---
| MAE | RMSE | MAE | RMSE | MAE | RMSE
KNN - DTW |  16.57$\pm$ 2.27 |  23.52$\pm$ 3.84 |  2.42$\pm$0.23 |  3.81$\pm$0.48 |  0.35$\pm$0.06 |  0.79$\pm$0.14
KNN - Euclidean |  17.03$\pm$3.72 |  24.06$\pm$6.02 |  2.46$\pm$0.35 |  3.82 $\pm$0.64 |  0.34$\pm$0.06 |  0.78 $\pm$0.14
Barycenter - DBA |  19.81$\pm$3.32 |  27.87$\pm$4.86 |  2.47$\pm$0.43 |  3.82 $\pm$0.54 |  0.34 $\pm$ 0.05 |  0.85 $\pm$ 0.15
Barycenter - Euclidean |  17.01$\pm$3.42 |  24.81$\pm$5.35 |  2.11$\pm$0.25 |  3.25 $\pm$0.44 |  0.35 $\pm$0.05 |  0.70 $\pm$ 0.21
Barycenter - DTW |  18.57$\pm$3.28 |  26.87$\pm$4.92 |  2.16$\pm$0.26 |  3.35 $\pm$0.46 |  0.36 $\pm$ 0.05 |  0.71 $\pm$ 0.22
Holts-Winters |  24.11$\pm$6.19 |  33.94$\pm$14.88 |  3.17$\pm$0.45 |  4.64 $\pm$0.45 |  1.01$\pm$ 0.33 |  1.99 $\pm$ 0.73
LSTM check-in |  15.07$\pm$3.41 |  20.87$\pm$3.4 |  2.26$\pm$0.23 |  3.45 $\pm$0.23 |  0.24$\pm$ 0.05 |  0.72 $\pm$ 0.14
LSTM check-in and check-out |  14.49$\pm$3.14 |  20.48$\pm$3.15 |  2.17$\pm$0.22 |  3.38 $\pm$0.21 |  0.24 $\pm$ 0.05 |  0.72 $\pm$ 0.14
LSTM day mask |  13.97$\pm$3.97 |  20.35$\pm$3.97 |  2.24$\pm$0.23 |  3.51 $\pm$0.22 |  0.24$\pm$ 0.05 |  0.72 $\pm$ 0.14
LSTM nearby | - | - |  2.23$\pm$0.26 |  3.38 $\pm$0.26 |  0.36 $\pm$ 0.05 |  0.68 $\pm$ 0.14
LSTM all meteo |  14.75$\pm$3.80 |  21.01$\pm$3.80 |  2.31$\pm$0.19 |  3.62 $\pm$0.19 |  0.24 $\pm$ 0.05 |  0.72$\pm$0.14
LSTM all meteo and nearby | - | - |  2.12$\pm$0.27 |  3.45 $\pm$0.68 |  0.36 $\pm$ 0.05 |  0.68 $\pm$ 0.14
Table 2. Comparison of forecasting errors (MAE and RMSE) of state-of-the-art predictors: check-out demand at 30 minutes granularity. | Senario 1: all stations |  Senario 2: Oriente cluster | Senario 3: single station
---|---|---|---
| MAE | RMSE | MAE | RMSE | MAE | RMSE
KNN - DTW |  17.37$\pm$ 2.72 |  24.21$\pm$3.64 |  2.44$\pm$0.42 |  3.64$\pm$0.55 |  0.36$\pm$0.05 |  0.88$\pm$0.18
KNN - Euclidean |  17.20$\pm$3.15 |  23.78$\pm$4.43 |  2.54$\pm$0.33 |  3.77 $\pm$0.44 |  0.34$\pm$0.06 |  0.81 $\pm$0.21
Barycenter - DBA |  19.70$\pm$3.06 |  27.18$\pm$5.05 |  2.35$\pm$0.26 |  3.82 $\pm$0.56 |  0.36 $\pm$ 0.08 |  0.81 $\pm$ 0.14
Barycenter - Euclidean |  15.62$\pm$3.18 |  22.30$\pm$5.29 |  2.11$\pm$0.29 |  3.33 $\pm$0.55 |  0.36 $\pm$0.05 |  0.67 $\pm$ 0.14
Barycenter - DTW |  18.25$\pm$2.95 |  25.85$\pm$4.96 |  2.16$\pm$0.31 |  3.48 $\pm$0.56 |  0.36 $\pm$ 0.03 |  0.66 $\pm$ 0.12
Holts-Winters |  25.00$\pm$4.94 |  34.78$\pm$4.94 |  2.91$\pm$0.35 |  4.21 $\pm$0.35 |  3.10$\pm$ 1.48 |  4.14 $\pm$ 1.79
LSTM check-out |  15.73$\pm$1.59 |  22.31$\pm$3.59 |  2.32$\pm$0.29 |  3.37 $\pm$0.29x |  0.35 $\pm$ 0.05 |  0.71 $\pm$ 0.21
LSTM check-in and check-out |  16.08$\pm$1.84 |  23.00$\pm$3.22 |  2.24$\pm$0.22 |  3.46$\pm$0.41 |  0.35 $\pm$0.05 |  0.70$\pm$ 0.21
LSTM day mask |  16.60$\pm$4.50 |  23.35$\pm$4.50 |  2.34$\pm$0.32 |  3.48 $\pm$0.32 |  0.36 $\pm$ 0.05 |  0.71 $\pm$ 0.21
LSTM nearby | - | - |  2.16$\pm$0.22 |  3.30 $\pm$0.44 |  0.35$\pm$ 0.05 |  0.71 $\pm$ 0.21
LSTM all meteo |  16.02$\pm$1.70 |  23.14$\pm$3.40 |  2.42 $\pm$0.32 |  3.62$\pm$ 0.49 |  0.36 $\pm$ 0.06 |  0.72$\pm$ 0.23
LSTM all meteo and nearby | - | - |  2.16 $\pm$0.22 |  3.30$\pm$ 0.43 |  0.35 $\pm$ 0.05 |  0.71$\pm$ 0.21
Figure 6. Aleatory testing data instance: true observations vs. LSTM forecasts
vs. weather-aware LSTM-based forecasts considering check-ins for all GIRA
stations. Figure 7. Hard testing data instance: true observations vs. LSTM
forecasts vs. context-aware LSTM-based forecasts considering check-ins for
Oriente cluster of stations. Figure 8. Performance impact of historical and
prospective weather variables on the forecasted check-ins at GIRA’s network.

Figures 8 and 9 measure the impact from incorporating different context
variables, including historical and available prospective variables. Previous
experimental settings are preserved for this analysis. Three major
observations. First, from weather variables, wind intensity and precipitation
variables offer the largest guidance. Second, the use of complementary demand
series (section 4.1.1) and spatial masks (section 4.1.5) impact predictions as
well, although the differences on the averaged error are not statistically
significant. Finally, we observe that the incorporation of historical context
has slightly higher positive impact on predictions in comparison with
prospective context. We hypothesize that this observation is a result of the
inherent uncertainty factors associated with the sources of prospective
context.

Figure 9. Performance impact of joint prospective-and-historical context
variables on the demand forecasts at GIRA’s network.

### Context-aware forecasters: parameters

Figures 10 and 11 provide two illustrative analyzes of the impact of two
parameters – batch size and optimizer – on the performance of the target
context-aware predictors. These figures suggest the use of small batch sizes
and Adam optimization. Similar analyzes conducted for the parameters listed in
section 4.3.1 confirm the adequacy of the fixed architectural and learning
parameters. Additional illustrative parameters include the presence of drop-
out layers, $1E-5$ learning rate, and $L_{1}$ norm regularization.

Figure 10. Batch size impact on GIRA network check-ins prediction. Figure 11.
Optimizer impact on check-out forecasts at GIRA network.

##  6\. Discussion

This work proposed neural processing principles to leverage the performance of
prediction tasks in the presence of heterogeneous sources of context data.
Motivated by the intrinsic challenges associated with the operation and
planning of bike sharing systems, we show the relevance of the proposed
approach for demand analysis in this domain, particularly hampered by the
spatial dependencies between stations, amongst other significant
externalities.

Two major contributions were introduced to this end. First, we propose a
serial composition of LSTMs, taking advantage of their inherent ability to
capture cross-variable relationships from multivariate time series data. In
this context, we propose masking principles to derive complementary series’
variables from spatial, meteorological and calendrical sources of context.
Second, we propose a time-dependent denoiser of the forecasted series using
prospective sources of context data collected along the horizon of prediction.

In addition to these contributions, a new class of distance-based forecasters
is also introduced, combining the advantages of lazy learning with the
advances on the calculus of bary-centers from time series data. We show they
are competitive with context-unaware LSTMs, and use them to further confront
the performance and behavior of the proposed context-aware LSTMs.

Results gathered over the Lisbon’s public bike sharing system (GIRA) confirm
the role of the above contributions, even though not all improvements yield
statistically significant differences.

To our knowledge, this work provides the first attempt to systematically
combine diverse sources of context, as well as seize the benefits that can be
propelled by the use of both historical and prospective context data. The
proposed principles are simplistic, yet effective, thus being now accessible
for researchers worldwide as viable techniques to incorporate a wide diversity
of available sources of context data in neural-based predictive models. The
introduce principles also form a sound and comprehensive basis for the
assessment of future context-aware predictors.

###### Acknowledgements.

The authors thank Câmara Municipal de Lisboa for data provision, support and
valuable feedback, particularly Gabinete de Mobilidade and Centro de Operações
Integrado. This work is further supported by national funds through Fundação
para a Ciência e Tecnologia under project ILU (DSAIPA/DS/0111/2018) and INESC-
ID pluriannual (UIDB/50021/2020).

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