# On spatial variation in the detectability and density of social media user
protest supporters

Víctor H. Masías Corresponding author<EMAIL_ADDRESS>Department of
Computer Science and Applied Cognitive Science, University of Duisburg–Essen,
Germany  Fernando Crespo  Facultad Tecnológica, Universidad de Santiago de
Chile, Estación Central, Santiago, Chile  Pilar Navarro R  E.T.S. of Computer
and Telecommunication Engineering, University of Granada, Spain  Razan Masood
Department of Computer Science and Applied Cognitive Science, University of
Duisburg–Essen, Germany  Nicole C. Krämer  Social Psychology: Media and
Communication, University of Duisburg–Essen, Germany  H. Ulrich Hoppe
Department of Computer Science and Applied Cognitive Science, University of
Duisburg–Essen, Germany

###### Abstract

Although much has been published regarding street protests on social media,
few works have attempted to characterize social media users’ spatial behavior
in such events. The research reported here uses spatial capture-recapture
methods to determine the influence of the built environment, physical
proximity to protest location, and collective posting rhythm on variations in
users’ spatial detectability and density during a protest in Mexico City. The
best-obtained model, together with explaining the spatial density of users,
shows that there is high variability in the detectability of social media user
protest supporters and that the collective posting rhythm and the day of
observation are significant explanatory factors. The implication is that
studies of collective spatial behavior would benefit by focussing on users’
activity centres and their urban environment, rather than their physical
proximity to the protest location, the latter being unable to adequately
explain spatial variations in users’ detectability and density during the
protest event.

_Keywords_ Protest Event $\cdot$ Social Media $\cdot$ Circadian Rhythms
$\cdot$ Spatio–Temporal Behavior $\cdot$ Urban Environment

##  1 Introduction

Protest events are a social phenomenon that contributes to processes of change
in all political systems, whether democratic, non-democratic, or some hybrid
of the two. In the last years, massive demonstration events held in the USA
have generated renewed international attention from the scientific community
on the phenomenon of street protest (Fisher et al., 2019). They typically take
place in major urban centres and are inspired by a wide range of different
motives. Recently, it has been found that there is a causal relationship
between the moralization processes that occur in social media and the behavior
of individuals in an offline environment (Mooijman et al., 2018). Little is
known, however, about the spatial behavior of social media users who support
street protests and how the urban environment of a city influences it. This
paper focuses on examining in greater detail the spatial behavior of social
media user protest supporters at the city level.

Previous works have explored protest behavior in online environments and its
correlations with the spatial dimension of offline protest (Chen and Pirolli,
2012; Traag et al., 2017; Mooijman et al., 2018). Part of the contemporary
research which studies protests in natural settings argues that the physical
proximity to the protest location is an important explanatory of the spatial
behavior of supporters during protest events. For example, it has been found
that the place of residence, that is, if the social media user is frequently
observed in the center on the periphery of the city is correlated with the
level of support expressed in social media to a protest event (Chen and
Pirolli, 2012; Barberá et al., 2015). Also, studies based on socio-physical
models have proposed that physical distance to the protest location acts as an
impedance to attendance (Traag et al., 2017). Other studies have proposed that
the relationship between environmental characteristics and the distribution of
individuals across space is more complex and dynamic, prompting researchers to
investigate the relationship using simulation models (Davies et al., 2013;
Lemos et al., 2016; Pires and Crooks, 2017; Bacaksizlar, 2019), whose results
are, therefore, of unknown ecological validity.

In this context, it is relatively unexplored whether existing elements of the
urban environment influence the spatial behavior of social media user protest
supporters. For this reason, we propose to conduct an observational
interdisciplinary study that applies an ecological approach, known as spatial
capture-recapture, to test a series of alternative hypotheses that
theoretically have a better explanatory capacity in the context of social
media research. Within this scenario, our research question is whether
existing structures in the urban environment, such as street or subway
networks, or whether the rate of social media posting in a given geographic
area have significant ability to explain the detectability (i.e. the
probability of detecting a user in a given place at a given occasion) and
spatial density (i.e. the numbers of users divided by a spatial area) of the
social media users supporting the protest. Thus, the objectives of this study
can be summarized as follows:

  * •

Determine the factors that explain the variation in spatial detectability of
social media user protest supporters.

  * •

Determine the factors that explain the variation in spatial density of social
media user protest supporters.

  * •

Determine whether physical proximity to a protest location contributes to
explaining the detectability and density of social media user protest
supporters.

  * •

Compare different models and evaluate whether social media post rhythms in a
given geographical region, transport network structures, the proximity of the
users to the protest location, neighborhood-level socio-demographic variables,
and the day of observation, contributes to explaining the detectability and
density of social media user protest supporters.

To determine these subjects, we will use multiple types of information that
are generally difficult to use together under the same methodological
framework. Our focus will be on protests at the city level to explain
relationships between the spatial dimension and social media user behavior.
More specifically, we examine how protests events are reflected in the spatial
behavior of social media users who support a protest.

##  2 Conceptual-Analytical Framework

Although the relationship between environmental elements and social media
users’ spatial behavior has only recently attracted the attention of
researchers, earlier work on the field of animal ecology had already thrown
light on the impact of urbanization on species richness and diversity
(McKinney, 2008). Chronobiology research on cattle wandering the streets of
India’s cities has found that their activity patterns (i.e. lying down,
standing, walking, foraging) are correlated with environmental factors (Sahu
et al., 2019). In the case of human beings, there is a complex interaction
between land use and human activities that take place in the urban
environment. Other studies have proposed that socio-ecological systems
maintain reciprocal interactions between biophysical and socioeconomic
structures (Arnaiz-Schmitz et al., 2018). In short, those studies suggest that
there is a significant relationship between the environment and organisms’
spatial behavior.

In this context, research in the existing literature suggests that the spatial
behavior of individuals is influenced by factors related to both the
individuals themselves and the geographic area they live in. In particular,
numerous works have documented the way basic processes such as daily physical
activity, cognitive performance, and locomotion are regulated by circadian
rhythms (Valdez, 2018). In evolutionary terms, it has been suggested that
chrono-physiological processes control and facilitate the organization of
spatial and temporal behavior in living beings. As an example, animal behavior
studies indicate that wallabies follow circadian patterns in their search for
food and shelter to avoid dangers in their environment (Fischer et al., 2019).

Recently, in the field of social media research, it has been shown that daily
posting rates of users can be used as a proxy for the endogenous circadian
clock of individuals. For example, the daily use of social media has been used
to examine how the rate of collective posting varies seasonally and
geographically, and also to further demonstrate that social events and
pressures disrupt patterns of social media activity, as occurs in the so-
called “Twitter social jet lag” phenomenon (Leypunskiy et al., 2018). In
another research more consistent with chronobiology studies, empirical
evidence has been reported on the existence of the phenomenon of social
synchronization in Facebook Messenger (Diwan et al., 2020). Generally
speaking, research suggests that the behavior of posting social media content
can be used as a proxy measure for the endogenous circadian clock of users of
social networking sites (Murnane et al., 2015; Swain and Pati, 2019). In light
of the above, it seems plausible to consider that the daily posting rates of
social media content in a given geographical region can be a relevant factor
that can help explain variations in the spatial behavior of social media user
protest supporters.

A parallel line of research has focused on investigating how the transport
network configurations influence individuals’ spatial behavior. This research
has found, for example, that street centrality is positively correlated with
different types of land use (Rui and Ban, 2014) and can be a good predictor of
pedestrian flow (Bielik et al., 2018). Other authors have shown that street
network configurations can explain serious outdoor violence (Summers and
Johnson, 2016). These findings imply that street centrality may affect
individual spatial behavior, which in turn means it is reasonable to expect
that the centrality of such spatial structures would also have the potential
to explain variations, across a geographical region, of the spatial behavior
of social media user protest supporters.

Finally, neighborhood-level socio-demographic characteristics have been cited
as having an impact on the spatial distribution of individuals over time and
space. For example, a comparative study found that a set of geographical
characteristics of the built environment consistently accounted for the
greater part of the variability in population distribution in low- and medium-
income countries (Nieves et al., 2017). Other studies have determined that a
range of urban factors explain the density of mobile telephone activity within
cities (Nadai et al., 2016; Liu et al., 2020). In general terms, it seems
plausible that both neighborhood-level socio-demographic characteristics and
the built environment have the potential to explain variations of the spatial
behavior of social media user protest supporters.

With the foregoing in mind and to enhance our understanding of the spatial
behavior of social media user protest supporters, we designed an observational
study based on the spatial capture-recapture approach (Royle et al., 2013)
(see ‘Spatial capture-recapture analysis’ in the Methods section). More
specifically, our approach attempted to determine whether and to what extent
the physical proximity of the social media users (hereafter “SMUs” or simply
“users”) to the protest location, socio-demographic characteristics, street
network configurations, and the daily rhythms of social media posting in a
given geographical region, and the day of observation, contribute in
accounting for the variations in the detectability and density of SMUs at the
city level. The event used as a real case study is the 40th annual Mexico City
LGBT pride parade held on June 23, 2018. The organizers of the event proposed
a march that has a distance of $\approx$4km. The main meeting place was
planned to be in the Angel of Independence111This is a frequent starting point
for various demonstrations and not only for this case study (see,
https://en.wikipedia.org/wiki/Angel_of_Independence). at 10:00 a.m. From
there, different groups marched to reach the so-called Zócalo222This city
square has an area of 57,600m2 and is located in the downtown area of Mexico
City (see, https://en.wikipedia.org/wiki/Zócalo)., where a concert was held
during the afternoon, for concluding the whole event. This case is of
particular interest because the parade is one of the largest mass gatherings
held in the Mexican capital (Bosia et al., 2019). And unlike other types of
collective behavior such as riots, the events organized by the Mexican LGBT
movement are primarily of a collaborative, non-violent nature (Beer and Cruz-
Aceves, 2018).333This social movement has achieved in Mexico several successes
in the political sphere such as the legalization of same-sex civil unions and
LGBT adoptions, demonstrating its effectiveness in bringing about changes in
human rights law. These changes have not only increased the acceptance of LGBT
persons in Mexican society as a whole but have also improved their
perspectives for embarking upon and developing careers in the sciences
(Walker, 2014).

We used geotagged tweets to study the spatial behavior of users who supported
this protest event. The geotagged social media data for the study were
collected through the Twitter API, and the tweets were filtered based on
geolocation information and constrained to Mexico City. To operationalize
which SMUs supported the march, we coded 10,000 tweets by hand and used them
to train a logistic regression classifier that then identified supportive
tweets in our whole geotagged social media data sample (see ‘Identification of
users supporting the protest event’ in the Methods section). To organize the
data for the analysis of SMU’s spatial behavior during the march, we imposed a
spatial grid over Mexico City in which each grid cell, hexagonal and covering
1.18km2, represented a trap where SMUs could be captured or recaptured in time
and space (see Figure 1). For each such SMU capture or recapture, we indexed
in a 3–dimensional array who ($i$), where ($j$), and when ($k$). Thus,
$y_{i,j,k}$ $=$ 1 denoted an individual user who was captured in a given cell
on a given occasion, and $y_{i,j,k}$ $=$ 0 indicated that the individual was
not captured in that cell on that occasion. To identify each SMU ($i$), we use
the unique identifier already assigned to each user by the Twitter API (the
User ID field) and which was anonymized to maintain the user’s privacy. A
unique identifier was also assigned to each grid cell ($j$) and each of the 24
hours in a day ($k$).

${(1)}$${(0)}$${(1)}$${(0)}$${(0)}$${(1)}$${(0)}$${(1)}$${(1)}$${(0)}$${(1)}$${(0)}$${(0)}$${(1)}$${(0)}$${(1)}$${(0)}$${(1)}$${(0)}$${(1)}$${(1)}$${(0)}$${(0)}$${(0)}$${(0)}$${(1)}$${(0)}$${(1)}$${(1)}$${(0)}$${(1)}$${(1)}$${(1)}$${(0)}$${(1)}$${(0)}$${(0)}$${(1)}$${(1)}$${(1)}$${(1)}$${(0)}$${(1)}$${(0)}$${(0)}$${(1)}$${(0)}$${(0)}$Occasions
($k$ $=$ 1,…, $K$)Traps ($j$ $=$ 1,…, $J$)Users ($i$ $=$ 1,…, $I$)A social
media user was captured posting something today, here and now

$t-1$$t$$t+1$sessions Protest event day

Figure 1: Indexing social media users in a 3–dimensional array.

Besides, three sets of proxies were used to serve as metrics of the urban
environment factors and the SMU’s attributes hypothesized to influence the
spatial detectability and density of SMU protest supporters. The first set of
proxy measures corresponds to the concept of the physical proximity of the
SMUs to the protest location (see ‘Physical proximity to the protest location’
in the Methods section). The second set consisted of a single proxy, which was
the Twitter post rate of SMUs in the Mexican capital, which was measured using
the Tweetogram metric (Leypunskiy et al., 2018) that expresses the normalized
activity rate of users over 24 hours (see ‘Measuring the tweeting rhythm’ in
the Methods section). The third set measured was the centrality of the Mexico
City street and metro network. The network data were obtained from
OpenStreetMap using the automated approach developed by Boeing (2017, 2020).
The metro network was based on the official information published by the
Mexican metro system. The specific proxies used for quantifying street
intersection centrality were the degree, betweenness, and closeness measures
for weighted networks (Opsahl et al., 2010) (see “Measuring street and metro
networks centralities’ in the Methods section). The fourth set represented
socio-demographic and socio-economic characteristics based on an anonymized
data sample from the 2010 Mexican census of 58,064 blocks in Mexico City. One
of these proxies measured population density while the other was a relative
wealth index based on an aggregate measure of household assets, both
calculated at the city block level (see ‘Demographic and economic indices’ in
the Methods section). Our database consisted of $i$ $=$ 1,216 SMUs who
supported the march and who were captured by $j$ $=$ 158 traps over 3
consecutive observation days (i.e. sessions) encompassing the day of the march
and one day on either side.

The testing and evaluation of SMU’s detectability and density variations in
the sample were done using spatial capture-recapture methods (Royle et al.,
2013), which is an approach developed in the field of population and landscape
ecology. This approach has definite advantages for identifying patterns in
hard-to-find samples given that, even if the latter are small and incomplete,
it can provide estimates of their detectability and density over a given
geographical area. The method makes joint estimates of a pair of models, one
for SMU’s detectability and the other for SMU’s spatial density (see Table 1).
The detections decay as a function of the distance between the trap and the
detected SMU’s activity centre $d(s)$, the latter considered as a latent
variable (Royle et al., 2017). Thus, for the detection model, we use the so-
called half–normal detection function. It has two parameters: baseline
detection probability $p_{0}$, which determines the maximum detection
probability at the SMU’s activity centre, and spatial decay $\sigma$, which
controls how rapidly detection probabilities decrease with distance from it
(see ‘Spatial capture-recapture analysis’ in the Methods section).

Model | Parameter | Formula
---|---|---
Baseline encounter model | $p_{0}$ | logit$\left(p_{0}\right)=\alpha_{0}+\sum_{k}\alpha_{k}Cov_{k}$
Spatial decay model | $\sigma$ | $\log(\sigma)=\gamma_{0}+\sum_{k}\gamma_{k}Cov_{k}$
Spatial point process model | $d(s)$ |  $\log(d(s))$=$\beta_{0}+\sum_{k}\beta_{k}Cov_{k}$
Table 1: Parameters of the SMU’s detectability and density variation models.
$Cov_{k}$ are the different covariates affecting the parameters and
$\alpha_{k}$, $\gamma_{k}$, $\beta_{k}$ are the covariate coefficients.

These parameters are theoretically significant for understanding SMU’s spatial
behavior during protest events given that $d(s)$ allows us to estimate the
variation if any, in SMU’s spatial density, $p_{0}$ allows us to estimate the
maximum detectability of SMUs during a protest event, and with $\sigma$ we can
estimate any variation in the use of a space before, during and after the
protest day. The importance of estimating these parameters lies in the fact
that previous studies, especially those in sociology, have tended to focus on
estimating the local number (i.e. at the protest location) of persons
attending a demonstration (Rotman and Shalev, 2020) without also considering
the changing detectability, use of space, and density. This is relevant
because it is usually not possible to make a direct estimation of user spatial
density with geotagged social media data, and especially because the sampling
mechanism of social media APIs is generally unknown. Also, the user’s location
can only be observed when posting, so his or her activity centre is not
directly observable, and the estimation of space use needs to be addressed
differently. Also, given the understanding of SMU’s spatial behavior developed
here, observed changes in density, detectability, or spatial decay on the
protest day could be seen as an expression of the collective engagement. By
the same token, a lack of significant change in the group’s spatial parameters
could be said to indicate that there had been no change in its spatial
behavior and level of engagement during the protest event. The approach
proposed here is thus very powerful in its ability to identify behavior
patterns using observational samples of SMUs and spatial covariates.

Several candidate model configurations were used to test what factors explain
the detectability and density of the observed SMUs. First, a null model was
created, where the density of social media user, the baseline probability of
detection, and the scale parameter is kept constant over the city. Second, a
series of alternative models were created. For the baseline encounter model
($p_{0}$), the measures tested were demographic and economic indices of the
neighborhood, the centrality of the street and metro network, the Tweetogram
measure (which measures the rate of posting in the city for each hour), the
day of observation (i.e. session), and the physical proximity between the
endpoint of the protest march and the trap where the SMU was captured or
recaptured posting social media content. For the spatial decay model
($\sigma$) we tested whether observation day (i.e. session) contributed to
explaining variability in the use of space. Additionally, for the density
model ($d$($s$)), we include the demographic and economic indices of the
neighborhood, the centrality of the street and metro network, the day of
observation (i.e. session), and the physical proximity between the endpoint of
the march and SMU’s possible activity centres (i.e. represented by a regular
grid of points).

Maximum likelihood was used to jointly estimate the model parameters and
evaluate which candidate model best fit the data. Specifically, a likelihood
analysis of various models were conducted using the R package oSCR (Sutherland
et al., 2019), a type of generalized linear mixed model. As can be seen, this
methodological design is quite flexible given that maximum likelihood allows
us to compare multiple competing models and explanatory spatial and temporal
factors.

##  3 Methods

###  3.1 Spatial capture-recapture analysis

The following account of the spatial capture-recapture method is based on the
work of Sutherland et al. (2019) which was adapted to our research context. In
conceptual terms, an SMU is assumed to have an activity centre ($s_{i}$ $=$
[$s_{i,X}$,$s_{i,Y}$]) that can be regarded as a spatial coordinate. However,
an SMU’s location can only be known if it is captured in a trap, so $s_{i}$ is
considered to be a latent rather than an observable variable. SMUs are also
presumed to live within a geographic area represented by a state space ($S$).
In our methodological setting, the null model specifies that each SMU’s
activity centre is distributed uniformly in space:

$s_{i}\sim Uniform(S)$ (1)

To determine the activity centre values we use maximum likelihood estimation
with spatial capture-recapture (SCR) models. This approach is based on the
marginal likelihood that the unknown variable s is removed by averaging (or
marginalizing) over the possible values of s. Thus, we begin by identifying
the conditional-on-s likelihood. The user encounter model $y_{ijk}$ for
individual $i$ at trap $j$ on occasion $k$, conditional upon $s_{i}$, is

$y_{ijk}|s_{i}\thicksim Bernoulli(p(x,s_{i};\theta))$ (2)

where

$p(x,s)=p_{0}\;exp(-\|x-s\|^{2}/(2\sigma^{2}))$ (3)

is the detectability or probability of detection at trap x, which depends on s
and $\theta=(p_{0},\sigma)$ (see Table 1 for more details). The joint
distribution of the data for individual $i$ is the product of $J\times K$ such
terms (i.e., contributions from each of $J$ traps and $K$ occasions):

$[y_{i}|s_{i},\theta]=\prod_{j=1}^{J}\prod_{k=1}^{K}Bernoulli(p(x_{j},s_{i};\theta))$
(4)

This assumes that an encounter of individual $i$ in each trap and on each
occasion is independent of encounters in every other trap and occasion,
conditional upon $s_{i}$.

To compute the marginal likelihood, consider a regular grid of $G$ points
denoted $s_{u}$ that form cells of equal area and are indexed by
$u$=$1,2,...,G$. In our design, we use a grid of 479 points. The marginal
probability mass function (pmf) of $y_{i}$ is then approximated by

$[y_{i}|\theta]=\frac{1}{G}\sum_{u=1}^{G}[y_{i}|s_{u},\theta]$ (5)

The joint likelihood for the data from $n$ observed individuals, assuming
independence of encounters among and between individuals, is the product of
$n$ such terms and a contribution of the $n_{0}$ $=$ $N-n$ uncaptured
individuals. Each of these all-zero encounter histories (i.e., the capture
histories of individuals not encountered) will have the same marginal pmf
contribution in the likelihood given above, here denoted by $\pi_{0}$. Of the
$n$ observed individuals, there are $N\choose n$ = $\frac{N!}{n!n_{0}!}$ ways
to choose a sample of size $n$. A combinatorial term is therefore required,
the joint likelihood then being given by

$\mathcal{L}\left(\theta,n_{0}\mid\mathbf{y}\right)=\frac{N!}{n!n_{0}!}\left\\{\prod_{i=1}^{n}\left[\mathbf{y}_{i}\mid\theta\right]\right\\}\pi_{0}^{n_{0}}$
(6)

Our data are from distinct and more or less independent populations, referred
to as sessions, that correspond to the three days in June considered in the
study. The multi-session model integrates data from these different sessions .
If $N_{g}$ is the population size of group $g$, there are
$(\frac{N_{g}!}{n_{g}!\left(N_{g}-n_{g}\right)!})$ ways to choose a sample.
The multi-session model assumes that

$N_{g}\thicksim Poisson(\lambda_{g})$

where the $N_{g}$ are mutually independent random variables. We obtain the
marginal likelihood as a function of $\lambda_{g}$ by independently
marginalizing over this distribution of $N_{g}$ for the data from each group:

$\mathcal{L}(\lambda_{g},\theta)=\sum_{g=1}^{\infty}\mathcal{L}(\theta,n_{0_{g}}|\mathbf{y})Poisson(N_{g};\lambda_{g})$
(7)

Explicit models can be formulated for $\lambda_{g}$:

$log(\lambda_{g})=\beta_{0}+\beta_{1}Cov_{g}$

Spatial covariates can be obtained by raster data or by inverse distance-
weighted interpolation, as in this study, which also contributes to
maintaining offline the privacy of the studied geographical areas. For further
details on the assumptions of spatial capture-recapture modelling, see Royle
et al. (2013); Sutherland et al. (2019).

###  3.2 Identification of users supporting the protest event

The identification of SMUs who supported the protest was accomplished in two
stages. The first stage was to manually label the data using qualitative
coding in a small sample of social media data. The second stage utilized a
machine learning approach to search in a larger sample for protest-related
tweets.

####  3.2.1 Qualitative coding of data

The data coding procedure consisted of five steps that were applied to the
text of each tweet, as follows. Step 1: Determine whether it includes hashtags
relating to the march. Step 2: Determine whether it contains emoticons related
to this social movement. Step 3: Determine whether it has any other content
supporting the protest (e.g., photos, videos, maps, or any other media content
in the URL). Step 4: Read the entire text to determine whether it suggests
support for the protest. Step 5: Code each tweet based on the results of the
previous steps. This last step was carried out by two raters. If a tweet
contained references to the protest, it was coded YES, otherwise, it was coded
NO.444Additional details of the coding can be found in Masias et al. (2019).
The outcome of this procedure was that, of the 10,000 coded tweets, 796 users
supporting the march. The value of Cohen’s kappa coefficient for the two
raters’ coding results ($\kappa$$=$0,84) indicated a high level of agreement
between them. This initial codification was used for the next section.

####  3.2.2 Machine learning classification

Once the 10,000-item database was codified, the classification of the entire
sample using machine learning could be performed. The tweet texts to be
classified were first lemmatized and cleaned by removing stop words,
punctuation, URLs, and mentions. Hashtags were kept and emoticons were
replaced with code words given that they played an important role in
distinguishing related tweets. Logistic regression was used to classify the
tweets and a grid search was used to refine the model parameters. We then
applied a term-frequency transformer and performed a feature selection using
the chi-square test to choose the most significant 500 terms. Because the
dataset is unbalanced, we also employed combined under-sampling and over-
sampling techniques using SMOTE+Tomek as suggested in Santos et al. (2018).
The performance of the classifiers (see Table 2) was evaluated by 5-fold
cross-validation on the test dataset measured in term of ROC-AUC, as well as
the Macro-F1 score (M-F1) and the Matthews correlation coefficient (MCC), the
last two often used to measure performance with unbalanced databases. The
obtained model was then used to make predictions regarding the non-coded data
in the sample. Logistic regression obtained 2,605 protest-related tweets and
114,848 unrelated ones. After filtering the database, the number of users
identified as supporters on each of the three days covered by the data (i.e.
22, 23, and 24 of June) was 526, 846, and 539 respectively. Therefore, the use
of machine learning made it possible to identify additional users supporting
the protest march.

Classifier | M-F1 | ROC-AUC | MCC
---|---|---|---
Logistic regression | 0.95 | 0.98 | 0.91
Table 2: Summary of classification performance.

###  3.3 Measuring the tweeting rhythm

To measure SMU’s tweeting activity in the city we used the measure (A(t))
(Leypunskiy et al., 2018), defined as:

$A(t)=\frac{1}{N}\sum_{i}\frac{f_{i}(t)}{\sum_{\tau}f_{i}(\tau)}$ (8)

where $N$ is the number of observed users normalized to a unit weight, and
$f_{i}$ is the number of tweets posted by user $i$ during a time bin $t$, in
this case, 1 hour. The time series were then averaged across the 72 hours
(i.e., the three observation days, see Figure 2).

Figure 2: Normalized posting rate of users in Mexico City during three days of
observation. On June 23, the day of the planned protest event, the maximum
value of Tweetogram was reached at 3:00 p.m.

###  3.4 Measuring street and metro networks centralities

A graph of the Mexico City street network was generated that contained 112,188
nodes representing intersections and 164,586 edges representing streets. The
mean and standard deviation of the edge lengths were 88.91 meters and $SD$ $=$
128.12, respectively. To measure street centrality as an explanatory factor of
SMU’s density in the city, we used the centrality metrics
$\alpha\omega$-weighted degree, $\alpha\omega$-weighted betweenness, and
$\alpha\omega$-weighted closeness (Opsahl et al., 2010). These indices allowed
us to measure the centrality of street intersections, and metro stations (i.e.
nodes) depending on the “number” or the “strength” of the links, or both. A
tuning parameter $\alpha$ was incorporated to include additional information
in the centrality measures. The values used for this parameter were: $\alpha$
$=$ 0, which leaves the centrality measures in their traditional form;
$\alpha$ $=$ 0.5, which weights the measures by the number of edges and the
latter’s weights (the lengths of the streets in meters, and the distance
between pairs of connected metro stations); and $\alpha$ $=$ 1, which weights
the measures only by the street lengths.555Further information on how these
definitions of the weighted centrality measures compare with the original,
non-weighted definitions may be found in Masías et al. (2016). Network data is
publicly available from OpenStreetMap through OSMnx Package. See, Boeing
(2017, 2020).

###  3.5 Demographic and economic indices

The neighborhood-level socio-demographic indicators were created with
anonymized data from the 2010 Mexican census.666The anonymized census data of
Mexico City was made publicly available by Diego del Valle
(https://blog.diegovalle.net/2013/06/shapefiles-of-mexico-agebs-manzanas-
etc.html). Household and dwelling attributes were used to create indices at
the census block level, which were then normalized by census-block area.

####  3.5.1 Population density per census block

This indicator described the population density of each census block in terms
of its population density per dwelling and household. The information was
aggregated and normalized by census-block area. A principal components
analysis (PCA) was carried out to detect independent features characterizing
the population density per census block. We used the first two main components
(i.e. population density PC1 and population density PC2) that captured 64.3%
and 32.6% percent of the total variation to create a feature vector that
characterized the population density characteristics of each census block
(n=58,064) of Mexico City.

####  3.5.2 Relative wealth per census block

This index measured the relative wealth of a census block. It was constructed
from census data on two categories of assets. The first category was household
items such as information and communications technology devices (radios,
televisions, computers, landlines, and mobile telephones, etc.),
refrigerators, washing machines, and motor vehicles. The second category
included dwelling characteristics such as internet access, electricity,
running water, toilets, and connection to the city sewage system. The asset
counts were aggregated by census block and normalized by census-block area. In
the same way, a principal components analysis (PCA) was carried out to detect
independent features characterizing the relative wealth per census block. The
first two main components (i.e. wealth PC1 and wealth PC2) that captured 95.9%
and 3.1% percent of the total variation were used to construct a feature
vector characterizing the relative wealth of each census block (n = 58,064) in
Mexico City.

###  3.6 Physical proximity to the protest location

Finally, we created two spatial covariates to operationalize the concept of
physical proximity. The first one was the Haversine distance between the place
where the social media user was captured or recapture posting social media
content in a given trap and the centroid of the Zócalo. The second measure was
the Haversine distance between the centroid of the Zócalo and the and SMU’s
initial possible activity centres (i.e. for this, we used the regular grid of
479 points defined in section ‘Spatial capture-recapture analysis’). As can be
seen, these two distance measures will be used as covariates for the
detectability model, and the density model, respectively.

##  4 Results

In the following, we report the results on capture history, model fitting and
selection, and the main results obtained by studying the spatial behavior of
SMU protest supporters.

###  4.1 Capture history description

The number of SMU protest supporters who were captured on the three
consecutive observation days (Friday, Saturday, and Sunday) was 526, 846, and
539. The mean maximum distance moved (MMDM) was 7110.91 m (excluding cases
where the distance was zero). A visual representation of captured geotagged
social media data is given in Figure 3, which shows for each day where the
SMUs were captured in the grid cells imposed over Mexico City.

session 1 session 2 session 3

Figure 3: The capture history was constructed from the data collected on
social media in Mexico City. Each blue circle represents the cell/trap
centroid, and the directed arrows connect pairs of traps where SMUs were
captured and recaptured on the indicated observation day, where session 1
corresponds to June 22, session 2 corresponds to June 23, and session 3
corresponds to June 24. The circles with a dot at the centre indicate that the
user was captured only by that trap while those without a dot indicate that no
user was captured on that day.

From a qualitative point of view, it can be seen that during session 2 the
captures and recaptures are centered in the up center of the map and that it
corresponds to the downtown of Mexico City where the protest was planned.

###  4.2 Model fitting and selection

The conceptual and methodological approach developed allows generating
evidence–based comparative results. The statistic used to determine the best
model was the Akaike Information Criterion (AIC). The AIC values were
calculated for each candidate model and the differences ($\Delta$AIC) were
used to rank them, the model with the lowest value being the one with the
greatest explanatory power. The results for each obtained model are presented
in Table 3. To present the results, below are the results of 8 models (out of
a total of 100 configuration models tested): the best model obtained; the null
model used for comparison purposes; the models based exclusively on the
hypothesis of physical proximity to the protest location; a model that
explains the density and detectability exclusively from the day of observation
(i.e. only by session); and finally 3 models with the lowest performance
obtained.

Model | Density ($d(s)$ ) | Baseline detection probability ($p_{0}$) | Spatial decay ($\sigma$) | logL | K | AIC |  $\Delta$AIC | $\Omega$ | CumWt
---|---|---|---|---|---|---|---|---|---
Best | $\sim\alpha_{0}-\omega\texttt{weighted street degree}+\alpha_{0}\omega-\texttt{weighted metro betweenness}$ | $\sim\texttt{Tweetogram}+\texttt{session}$ | $\sim\texttt{session}$ | 16956.01 | 10 | 33932.01 | 0 | 9.999993e-01 | 0.9999993
Alternative | $\sim\texttt{session}$ | $\sim\texttt{session}$ | $\sim\texttt{session}$ | 19044.19 | 9 | 38106.38 | 4174.3708 | 0.000000e+00 | 1
Alternative | $\sim\texttt{Proximity to the protest location}$ | $\sim\texttt{1}$ | $\sim\texttt{1}$ | 19051.59 | 4 | 38111.18 | 4179.17055 | 0.000000e+00 | 1
Null | $\sim\texttt{1}$ | $\sim\texttt{1}$ | $\sim\texttt{1}$ | 19123.79 | 3 | 38253.58 | 4321.56967 | 0.000000e+00 | 1
Alternative | $\sim\texttt{1}$ | $\sim\texttt{Proximity to the protest location}$ | $\sim\texttt{1}$ | 19315.61 | 4 | 38639.23 | 4707.21099 | 0.000000e+00 | 1
Alternative | $\sim\alpha_{0.5}\omega-\texttt{street betweenness}$ | $\sim\texttt{Proximity to the protest location}$ | $\sim\texttt{session}$ | 19629.07 | 7 | 39272.14 | 5340.12337 | 0.000000e+00 | 1
Alternative | $\sim\alpha_{0}\omega-\texttt{street betweenness}$ | $\sim\texttt{Proximity to the protest location}$ | $\sim\texttt{session}$ | 19662.77 | 7 | 39339.53 | 5407.51729 | 0.000000e+00 | 1
Alternative | $\sim\texttt{population density PC2}$ | $\sim\texttt{Proximity to the protest location}$ | $\sim\texttt{session}$ | 19662.77 | 7 | 39339.53 | 5407.51942 | 0.000000e+00 | 1

Table 3: Summary of model selection for estimating variation in density
($d(s)$), baseline detection probability ($p_{0}$) and spatial decay
($\sigma$) of SMU protest supporters. Indicated are the Akaike Information
Criterion (AIC), the ranking based on AIC ($\Delta$AIC) and model weights
($\Omega$). Here, $\alpha_{0}$ refers to $\alpha=0$, $\alpha_{0.5}$
corresponds to a value of $\alpha=0.5$, and $\alpha_{1}$ refers to $\alpha=1$
for the weighted centrality measures.

Several observations can be made when comparing the models listed in Table 3.
First, Models using the proximity to the protest location performed similarly
or less than the null model. Second, if we fit a model to explain the density
and detectability exclusively from the day of observation (i.e. session), we
also obtain a model comparable to the null model. Third, the three lowest-
performing models have in common that they used the proximity to the protest
location for the baseline detection probability. In the following, the best
model obtained is described.

###  4.3 Description of the model

The comparative analysis of different models shows that density ($d(s)$)
varies with street degree centrality and metro betweenness centrality, the
baseline detection probability ($p_{0}$) varies with observation day (i.e.
session) and the Tweetogram variable, and spatial decay ($\sigma$) varies with
observation day. The AIC of the best model obtained was 33932.01 and the model
weights were $\Omega$ = 9.999993e-01. The results for the best model,
summarized in Table 4, indicate that all of these variables were statistically
significant.

Table 4: Summary of best model results (two-tailed $p$–value). Parameters | Estimate | SE | z | P(>$\mid$ z $\mid$)
---|---|---|---|---
p0.(Intercept) | -7.302 | 0.067 | -108.927 | 0.000
p0.session 2 | 0.170 | 0.074 | 2.301 | 0.021
p0.session 3 | -0.597 | 0.092 | -6.469 | 0.000
t.beta.Tweetogram | 20.520 | 0.385 | 53.318 | 0.000
sig.(Intercept) | 8.068 | 0.027 | 296.672 | 0.000
sig.session 2 | -0.062 | 0.036 | -1.700 | 0.089
sig.session 3 | -0.214 | 0.044 | -4.800 | 0.000
d0.(Intercept) | 0.907 | 0.495 | 1.832 | 0.067
d.beta.$\alpha_{0}\omega$-weighted street degree | -1.052 | 0.066 | -15.871 | 0.000
d.beta.$\alpha_{0}\omega$-weighted metro betweenness | 0.376 | 0.071 | 5.256 | 0.000

###  4.4 Spatial detectability and density variation results

The best model found evidence that the baseline detection probability
($p_{0}$) varied in accordance with the session (i.e., observation day) and
time-varying Tweetogram covariates. The latter case is shown in Figure 4(a).
In this figure, it is possible to observe that the baseline detection
probability of SMUs is higher, at different Tweetogram values, during the day
of the protest (i.e. session 2) in comparison to the day before or after the
protest event. It is observed that the baseline detectability is higher during
the day of the protest event compared to that of a weekday (i.e. session 1).
During Sunday (i.e. session 3) there was a noticeable decrease in baseline
detectability, as may be observed in the figure. The model thus demonstrates
that baseline detection probability varies with the daily post rate in Mexico
City and the observation day. Additionally, the model found evidence that
$\sigma$ varied with session (see Figure 4(c)).

The half-normal function, based on the estimates obtained for $p_{0}$ and
$\sigma$, shows that the detectability (i.e. detection probability) over space
of SMU protest supporters is higher during the day of the protest event.
Figure 4(b) describes how the detection probability decays with the distance
to the center of activity of the SMUs. As the figure indicates, the detection
probability decays at different rates. The model predicts that the highest
probability of detection of SMU protest supporters in Mexico City does not
occur at the beginning of the event, nor at the end of the event, but rather
at 3:00 p.m., when the Tweetogram obtained a value $\approx$ 0.116 (i.e. when
this measure reached its maximum during this day, see Figure 2).

22

Figure 4: Spatial variation in the detectability and density of SMU protest
supporters in Mexico City: a, Baseline detection probability ($p_{0}$). b,
Probability of detection ($p$($x$ ,$s$)) and use of space. c, Spatial decay
($\sigma$). d, Variation in SMU’s density ($d(s)$). In Figures a, c and d, the
error bar shows the lower and upper prediction intervals

Additionally, the model estimates that the SMUs had a different use of space
in the city during the three days of observation. Based on the $\sigma$ value,
the 95% home range radius was calculated as $r_{0.95}$ $=$
$\sigma*\sqrt{5.99}$ (where 5.99 is the chi-square critical value for the 95%
significance level) and the corresponding area used was calculated as
$A_{0,95}$ $=$ $\pi$ $r^{2}$ (Sutherland et al., 2016; Muñoz et al., 2016).
The day before the protest, $\sigma$ was found to be at its maximum,
suggesting that the radius from the SMU’s respective activity centres was the
largest of the three days ($\sigma$ $=$ 3189.74, SE $=$ 86.74; $r_{0.95}$ $=$
7806.74, $A_{0.95}$ $=$ 191465055). On the day of the protest, the radius was
marginally smaller than the previous day ($\sigma$ $=$ 2998.22, SE $=$ 73.45;
$r_{0.95}$ $=$ 7337.99, $A_{0.95}$ $=$ 169162767) while on the day after the
protest, $\sigma$ and therefore the radius was smaller still ($\sigma$ $=$
2576.51, SE $=$ 91.12; $r_{0.95}$ $=$ 6305.89, $A_{0.95}$ $=$ 124923079), what
is expected to be observed during a Sunday (i.e. during a non-working day).
These results show that there is variability in the use of space by SMUs and
that the use of space is different compared to the day before or after the
protest event.

The comparative analysis also uncovered evidence that the spatial density of
SMU protest supporters varied with metro and street centralities, as is shown
in Figure 4(d). In the case of street centrality there was an inverse
relationship, implying that the lower is $\alpha_{0}\omega$-weighted street
degree centrality, the higher is the SMU’s density per km2. An inverse
relationship between user density and the $\alpha_{0}\omega$-weighted metro
betweenness centrality was also found. To obtain a more conservative
representation of the functional relationship, we used a 10% quantile (i.e.,
$\alpha_{0}\omega$-weighted street degree $=$ 1.02;
$\alpha_{0}\omega$-weighted metro betweenness centrality $=$ 5.09 ) and a 90%
quantile (i.e., $\alpha_{0}\omega$-weighted street degree $=$ 3.98;
$\alpha_{0}\omega$-metro betweenness centrality $=$ 6.79) to define the
prediction range. This means that the centrality of the transportation
networks provides information and reference points from which the users’
activity centers can be found over space.

With these settings, the maximum estimated SMU’s density was found to be 5.72
SMUs per km2 (SE $=$ 0.62, lwr $=$ 4.62, upr $=$ 7.09), reached when
$\alpha_{0}\omega$-weighted street degree $=$ 1.02, and
$\alpha_{0}\omega$-weighted metro betweenness centrality $=$ 5.08. The minimum
estimated SMU’s density was found to be 0.47 SMUs per km2 (SE $=$ 0.08, lwr
$=$ 0.34, upr $=$ 0.67), reached when $\alpha_{0}\omega$-weighted street
degree $=$ 3.98, and $\alpha_{0}\omega$-weighted metro betweenness centrality
$=$ 6.79. These results show that the density of users supporting the protest
has a dependency on the existing structures of the urban environment of Mexico
City.

##  5 Discussion

The purpose of this study was to investigate spatial variability in the
detectability and density of SMUs in the context of a planned protest event.
The strategy consisted of comparing multiple models to find those that best
explain the case under study. Our set of hypotheses tested whether variables
representing street networks, neighborhood socio-demographic characteristics,
social media post rates, and the observation day could constitute a model that
fit the observational samples better than the null model or models based on
physical proximity to the protest location. In what follows we discuss the
main results and findings as they compare with those of the related
literature.

One of the most interesting aspects of the results was to find that the
detectability of SMUs is highly variable, and how we tested, it does not
depend on the physical proximity to the protest location. The results pointed
that the baseline detection probability ($p_{0}$) varied with the Twitter post
rate as measured by the Tweetogram metric. The inclusion of this variable
greatly improved the detection models compared to the null model. By measuring
the daily post rhythm we were able to identify when SMUs were more detectable
during the protest event (at 3 p.m.). We interpret that because the protest
march requires the participation of individuals in a certain place and time
(i.e., a target-driven user behavior), it results in reduced randomness of
movement and posting behavior over space, leading to an increased baseline
probability of being detected. To our knowledge, this empirical finding is one
of the first to explain variations in SMU’s detectability across space and
time in terms of the users’ collective posting rhythms. In a previous study
(Leypunskiy et al., 2018), the Tweetogram measure was used to show mainly that
there is a geographical and seasonal variation of user’s posting behavior, and
in our study, we have demonstrated that using our research design, this
measure can be used to predict, at a higher resolution level, where and when
users can be observed during the protest event in the city.

Also found by our study was evidence that the spatial decay parameter
($\sigma$) varied with observation day. Of particular interest was how SMU
protest supporters occupied space. On the day of the march, users made
significant use of the space. This result sheds considerable light on some key
aspects of SMU’s spatial behavior during the protest event. While the sigma
value was significantly different for the day of the protest, we can see that
its value was qualitatively similar to that obtained for the day before, a
weekday. On the other hand, the day after the event, SMU’s use of space did
decline, as is typical on a Sunday when people tend to stay close to home. Our
approach thus suggests, based on these empirical findings, that users’
activity centre and activity radius favored their participation in the protest
event. In other words, users made no extra "effort" to extend their radius of
action compared to a weekday. This can be interpreted to mean that the success
of the protest event was due to its location in the center of the city, which
is an area where users can reach.

Evidence was found on variations in the spatial density ($d(s)$) of SMUs who
supported the protest march analyzed in our case study. The results suggest
that the observed densities varied with the street network (i.e., street
intersection) degree centrality and metro betweenness centrality. As regards
the former measure, the model showed that there were lower densities in areas
where centrality was high. This makes sense given that streets in such areas
will often have a high confluence of vehicles, pedestrians, or both. In
ecological terms, they are not likely places for individuals to establish
their activity centre. Therefore, areas with a high street degree centrality
and with a high degree of metro betweenness correspond to places where
individuals commonly transit. These network structures can be interpreted as
reference points from which the centers of activity of SMUs can be found.

The comparative analysis also showed that the SMU’s spatial density did not
vary with session. Given that our study covered the entire area of Mexico City
and for a short observation period, it is reasonable to expect that the number
of SMUs who supported the protest was rather stable. This in turn implies that
during the observed period there was no sudden process of generation or
reduction of the number of social media supporters to the protest event. If an
increase or a decrease in their density had been observed over the three
sessions, a hypothesis on the generation of new activists could have been
formulated, but observing such change in a short period was unlikely. At best,
an observed increase in density could be interpreted to mean that the
individuals turning to social media during the event were already politically
active in the offline environment. This is feasible reasoning since a recent
repeated-wave panel study found that those individuals who are already
politically active are motivated to use social media for participating in
political life (Oser and Boulianne, 2020). In other words, the evidence
provided here and in previous research suggests that individuals who engage in
political activities become active users of social media, not the opposite. In
this sense, the best model obtained is showing that there is high variability
in the detection of social media users who support a protest, but that there
is no major change in density at the city level.777A clear example where the
centres of activity of social media users can change for a short time is the
Occupy Wall Street (OWS) protest movement, where hundreds of activists camped
out for weeks in Zuccotti Park, New York. An extreme example of how SMU’s
density can grow rapidly in an area under study is the case of the migrant
caravans (i.e. protesting asylum–seekers) along the U.S.-Mexico border. In
that type of collective action, density changes can be attributed to the
(temporary) changes in the activity centres of highly engaged individuals.

The results regarding spatial elements and other user-related factors could,
we believe, make a significant theoretical and methodological contribution to
human behavior studies. Previous research on protests has stressed the
importance of understanding the behavior of SMU protest supporters in terms of
their distance from the protest location (Wallace et al., 2014; Cortina,
2019). Also, previous work has shown that the local (i.e. at the protest
meeting location) number of individuals participating in a protest can be
interpreted as an indicator of the event’s magnitude (Biggs, 2016; Sobolev et
al., 2020; Opp, 2009). For example, some studies on social media have adopted
a quasi-experimental approach and difference-in-differences analysis for
comparing a group of users exposed to a protest event with a group not so
exposed based on their physical distance to the event (Zhang, 2016; Zhang et
al., 2016; Karduni and Sauda, 2020). Other investigations assume that physical
distance is an impedance to participation in a protest (Traag et al., 2017;
Biggs, 2016). In those studies, they do not consider that in the geographical
space there are structures of the urban environment that can affect and
restrict the spatial behavior of individuals.

In contrast, our conceptual and methodological approach, inspired by concepts
of ecology, chronobiology, network science, and social media research, has
pointed up the importance of the spatial dimension in SMU’s behavior. The
results reveal a completely different picture in which the urban environment
and the behavior of social media users have a rich interplay. In the present
investigation, we have focussed on the users themselves, or more specifically,
their activity centre as the fundamental factor in modeling their
detectability and density. Our results show that variations in these two
phenomena depend on structural elements of the city as well as SMU’s Twitter
post rhythms. The present study suggests that density is a key factor in that
it serves as a global indicator of SMU participants’ collective behavior at
the city level. But our most theoretically interesting finding is that
physical proximity to the protest event location did not prove to be an
explanatory variable. This means that generating a theory of physical exposure
to the location of the event to explain the behavior of users during the day
of the protest event has no empirical support. Therefore, this research offers
a comprehensive analytical framework for generating new insights into spatial
user behavior in the context of social media research.

Thinking reflectively, and from a conservative approach, our search for
empirical evidence also suggests that there is no general model that can be
applied to all cases of protest events, as there is variability in the
behavior of individuals and also in the environment they live in. We believe
that future research may consider other potentially relevant factors (e.g.
such as gender and age structure of the population, as well as other spatial
and geographic covariates or detection functions) would certainly contribute
to a better understanding of the sources of variation in the spatial behavior
of SMUs. The approach also can help to characterize the factors that delimit
spatial behavior of SMUs while protecting the geoprivacy of the user, an
increasing requirement for conducting research based on geotagged social media
data as discussed by Hu and Wang (2020).

To sum up, the evidence-based comparative models generated by our study, have
identified the patterns of variation in spatial detectability and density
determined by transport networks and the users’ own internal cognitive
mechanisms as represented here by the Tweetogram measure. It was found that
the rate of daily social media posts and the observation day are more powerful
in detecting social media users than street network centralities or measures
based on relative wealth or population density indexes. On the day of the
protest, users exhibited maximum detectability and significant use of space.
Evidence was also found that the density of social media users who supported
the protest can be explained by metro and street network centrality measures.
It was further demonstrated that information relating to physical proximity to
the protest location, taken by itself, performed worse than the null model in
modeling the spatial detectability and density of SMUs.

Overall, our study provides consistent evidence that the information embedded
in the geographic space where users post social media content does matter. The
built environment and the collective posting rate are significant explanatory
factors of the variations in their spatial detectability and density of social
media user protest supporters. Changes observed in these two elements may be
interpreted as indicators of users’ level of engagement during protest events.
Finally, we encourage other researchers, especially those focused on the
problem of ecological validity, to explore and propose new hypotheses on the
rich and complex behavior of individuals in their online and offline
environments.

## Funding

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) under
grant GRK 2167, Research Training Group “User-Centred Social Media" (UCSM).

## Declaration of conflicting interests

The author(s) declared no potential conflicts of interest concerning the
research, authorship, and/or publication of this article.

## Acknowledgements

We acknowledge the support of the National Laboratory of High-Performance
Computing (NLHPC), hosted at the Center for Mathematical Modeling (CMM,
Universidad de Chile).

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# Predicting the spectrum of UGC 2885, Rubin’s Galaxy with machine learning.

Benne W. Holwerda Physics & Astronomy Department, University of Louisville,
40292 KY, Louisville, USA  John F. Wu Space Telescope Science Institute, 3700
San Martin Drive, 21219 MD Baltimore, USA  William C. Keel Department of
Physics and Astronomy, University of Alabama Box 870324, Tuscaloosa, AL
35487-0324, USA  Jason Young Mount Holyoke College, 50 College Street, South
Hadley, MA 01075, USA  Ren Mullins  Physics & Astronomy Department, University
of Louisville, 40292 KY, Louisville, USA  Joannah Hinz Steward Observatory,
University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721- 0065, USA
MMT Observatory, P.O. Box 210065, Tucson, AZ 85721-0065, USA  K.E. Saavik Ford
Dept. of Science, Borough of Manhattan Community College, City University of
New York, New York, NY 10007 USA  Dept. of Astrophysics, American Museum of
Natural History, New York, NY 10024 USA  Physics Program, CUNY Graduate
Center, City University of New York, New York, NY 10016 USA  Center for
Computational Astrophysics, Flatiron Institute, New York, NY, 10010, USA
Pauline Barmby Department of Physics & Astronomy, Institute for Earth & Space
Exploration, University of Western Ontario, 1151 Richmond Street, London,
Ontario, Canada  Rupali Chandar Department of Physics & Astronomy, The
University of Toledo, Toledo, OH 43606, USA  Jeremy Bailin Department of
Physics and Astronomy, University of Alabama Box 870324, Tuscaloosa, AL
35487-0324, USA  Josh Peek Space Telescope Science Institute, 3700 San Martin
Drive, 21219 MD Baltimore, USA  Department of Physics & Astronomy, Johns
Hopkins University, Baltimore, MD 21218, USA  Tim Pickering Steward
Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721-
0065, USA  MMT Observatory, P.O. Box 210065, Tucson, AZ 85721-0065, USA
Torsten Böker European Space Agency, c/o STScI, 3700 San Martin Drive, 21219
MD Baltimore, USA

(Received January 1, 2018; Revised January 7, 2018)

###### Abstract

Wu & Peek (2020) predict SDSS-quality spectra based on Pan-STARRS broad-band
grizy images using machine learning (ML). In this letter, we test their
prediction for a unique object, UGC 2885 (“Rubin’s galaxy”), the largest and
most massive, isolated disk galaxy in the local Universe ($D<100$ Mpc). After
obtaining the ML predicted spectrum, we compare it to all existing
spectroscopic information that is comparable to an SDSS spectrum of the
central region: two archival spectra, one extracted from the VIRUS-P
observations of this galaxy, and a new, targeted MMT/Binospec observation.
Agreement is qualitatively good, though the ML prediction prefers line ratios
slightly more towards those of an active galactic nucleus (AGN), compared to
archival and VIRUS-P observed values. The MMT/Binospec nuclear spectrum
unequivocally shows strong emission lines except H$\beta$, the ratios of which
are consistent with AGN activity. The ML approach to galaxy spectra may be a
viable way to identify AGN supplementing NIR colors. How such a massive disk
galaxy ($M^{*}=10^{11}$ M⊙), which uncharacteristically shows no sign of
interaction or mergers, manages to fuel its central AGN remains to be
investigated.

Galaxy nuclei — Disk galaxies — Giant galaxies

††journal: ApJ††software: Astropy (Astropy Collaboration et al., 2013)

##  1 Introduction

In recent years, astronomical machine learning has transformed from a niche
subject to a well-developed suite of accessible and interpretable algorithms.
Machine learning algorithms are used for catalogs, time series, imaging, and
unstructured data across a wide array of astronomy subdisciplines (e.g.,
exoplanets, Shallue & Vanderburg 2018; radio interferometry, Vafaei Sadr et
al. 2020; transient photometry, Villar et al. 2020; and studies of the
interstellar medium, Xu et al. 2020). For extragalactic imaging data, machine
learning is regularly relied upon for classifying galaxy morphology (e.g.,
Dieleman et al., 2015; Beck et al., 2018), quantifying observed properties
(e.g.; Smith et al., 2020), and predicting spectroscopic properties (e.g.,
Pasquet et al., 2019; Wu & Boada, 2019). These advances have enabled machine
learning to take on an outsized role in mitigating the observational disparity
between enormous survey imaging data sets and limited spectroscopic follow-up
campaigns (e.g, Wu & Peek, 2020). While machine learning results are robust
for estimating the properties of typical galaxies, it is less clear if
predictions are reliable for rare or unusual systems.

Spectroscopy surveys lag behind imaging ones in coverage and depth simply
because of the longer integration time per object (see Davies et al., 2018;
Driver et al., 2019, for a discussion on ongoing and near-future surveys).
Predicting spectra or spectral features based on imaging is therefore a
worthwhile endeavour for both scientific and planning purposes.

UGC 2885 (“Rubin’s Galaxy”) is the largest and most massive spiral galaxy
($R_{p}=38.1$ kpc, $M_{*}=2.2\times 10^{11}$ M⊙) in the local Universe (Rubin,
1980). It shows very regular rotation with a maximum rotation velocity of 298
km s-1 ($M_{tot}=1.50\times 10^{12}$ M⊙ Rubin et al., 1980; Roelfsema & Allen,
1985; Wiegert & English, 2014; McGaugh & Schombert, 2015), rising from the
center, indicating a substantial and extended dark matter halo (Marr, 2015).
The galaxy has star-formation throughout its disk (Hunter et al., 2013), four
spiral arms, and a specific incidence of globular clusters that hints at an
uneventful accretion history (Holwerda et al in prep.). It lies just outside
the Sloan Digital Sky Survey’s footprint and has no SDSS or DES spectra.

UGC 2885 defies easy classification: to the first order it is an Sc galaxy but
it is at the outermost edge of the mass and size envelope for its class. The
initial identification of UGC 2885 as the largest isolated spiral galaxy by
Rubin (1980) was confirmed by Romanishin (1983) for the whole Uppsala Galaxy
Catalog. We measure the Petrosian radius of Rubin’s galaxy at 38.1 kpc (97)̈
in sdss-r. Ogle et al. (2016, 2019) introduce “Super spirals,” a class of
massive disk galaxies at the utmost top of the stellar mass-star formation
rate ($M_{*}$-SFR) relation. Ogle et al. (2015) note that “Super spirals” are
almost never in an isolated environment and often show signs of a recent
interaction, e.g. perturbed morphology, dual nuclei, or other signs of
significant merger activity. Rubin’s galaxy does not meet these qualifications
as it has a lower SFR and does not show signs of recent interaction, which
appear to be typical for this class of galaxies. Saburova et al. (2020)
discusses giant low surface brightness (LSB) disk galaxies. Once again, UGC
2885 does not meet those specifications either: its star-formation is too high
and concentrated in a more typical brightness disk. These giant LSB galaxies
also often seem to be visibly disturbed from recent accretion or merger
activity. Yet Rubin’s galaxy is remarkably unperturbed.

A $\sim 10^{11}M_{\odot}$ stellar mass galaxy typically has an active galactic
nucleus and our question for this letter is: is Rubin’s galaxy exceptional
here as well? Keel (1983a) remains the only study to attempt to characterize
the nucleus of this galaxy and does not reach a firm conclusion. Does UGC 2885
show signs of an active nucleus? One would expect its spectrum to lie in the
categories of LINER or star-formation/AGN mix. Can this be predicted from
broad-band photometry using machine learning? How good is the ML prediction of
this galaxy’s spectrum? As a local extreme of size and mass, the lack of a
SDSS spectrum offered the opportunity for a direct test of this prediction.

The purpose of this paper is to report a “closed envelope” test of the ML
predicted spectrum for the center of Rubin’s galaxy from Wu & Peek (2020) and
compare it to spectra obtained from private archives and recent observations:
the prediction was made first and then compared to spectra of comparable
quality.

##  2 Machine Learning Prediction of Rubin’s Galaxy’s Spectrum

We generate the predicted spectrum for Rubin’s Galaxy using the method
described in Wu & Peek (2020). Briefly, the method uses a convolutional neural
network (CNN), trained on $56\arcsec\times 56\arcsec$ $grizy$ image cutouts of
galaxies from the Pan-STARRS $3\pi$ Steradian Survey DR2, and predicts the
galaxies’ optical spectra (3$\arcsec$ aperture, SDSS resolution and s/n).
Galaxy spectra are normalized, shifted to a common reference frame, and
rebinned in 1000 logarithmically spaced elements. A variational autoencoder
(VAE) represents each spectrum using six latent variables, which can be
robustly “decoded” back into SDSS spectra (Portillo et al., 2020). Wu & Peek
(2020) train a CNN to predict galaxies’ SDSS spectra solely using image
cutouts. Figure 1 shows the results of this ML approach applied to the Pan-
STARRS image of Rubin’s galaxy. In the comparisons this spectrum is shifted to
the galaxy redshift of $v=5802$ km s-1 (Canzian et al., 1993).

Figure 1: The prediction by the ML method of Wu & Peek (2020) for Rubin’s
Galaxy (top) and reference SDSS spectra for an example of an AGN, a quiescent
galaxy, and a star-forming galaxy, all shifted to the rest frame. The spectral
features of Rubin’s Galaxy fall between those of a quiescent and an AGN-
dominated galaxy.

##  3 Data

To verify the ML prediction, we obtained two archival spectra, extracted one
from the VIRUS-P IFU observation, and obtained new MMT/Binospec observations.
The apertures used in each observations is shown in Figure 2.

The first comparison spectrum is originally from Keel (1983a, b), who
conducted an aperture spectroscopic survey of nearby galaxies to search for
AGN activity. Keel (1983a) reported line strengths for H$\alpha$, [Nii] and
[Sii]. Their verdict on nuclear activity was inconclusive.

Archival data is a scan of a 4.7$\arcsec$ diameter circular aperture spectrum
from the Mount Lemmon 1.5 m (60 inch) telescope taken on 4/5 February 1981,
shown in the top panel in Figure 3, and a 6.1$\arcsec$ circular aperture
spectrum taken using the Intensified Image Dissector Scanner on the KPNO 2.1
m, shown in the second panel in Figure 3. The archival spectra are normalized
by the maximum value in the spectrum for ease of comparison to the ML
spectrum. The 60 Inch spectrum closely resembles an SDSS spectrum in aperture
and signal to noise but is limited in wavelength coverage. The KPNO spectrum
has a similar wavelength coverage but much lower signal-to-noise and a wider
aperture compared to SDSS spectra.

Recent VIRUS-P IFU observations of Rubin’s galaxy seek to reveal star-
formation and abundances (Young et al. in prep). A blue spectrum ($<$ 5800 Å)
was extracted using a 4.16$\arcsec$ aperture to compare with the ML
prediction, shown in Figure 3, third panel.

Figure 2: The nucleus of Rubin’s galaxy from the larger HST mosaic. A clear
dustlane partially obscures the central stellar cluster. The inset shows the
apertures of the spectroscopic observations are marked using the same color
scheme as in Figure 3: Mount Lemon 60inch (orange), 2.1 KPNO (green), VIRUS-P
(blue) and MMT (white for contrast).

A targeted $3\times 300$ s optical spectrum was obtained at the MMT
Observatory with the instrument Binospec (Fabricant et al., 2019) in November
2020 with a position angle = 35∘ using the 270 lines/mm grating with a central
wavelength of 6500 Å. The observations were taken at RA=3:53:02.4811,
DEC=+35:35:22.103 with a 1″slit. Data reduction was completed by the Binospec
automated pipeline, which is an open-source IDL software package distributed
under the GPLv3 license (Chilingarian et al., 2019,
https://bitbucket.org/chil_sai/binospec). This standard reduction resulted in
the spectrum in Figure 3, fourth panel.

Both the VIRUS-P and the MMT/Binospec spectra have been renormalized using the
maximum value in each spectrum’s bandpass (VIRUS-P $4000-5700$ Å, MMT
$4000-7000$ Å). This leaves a gradual difference in continuum between
normalized ML and either spectrum. Subsequently, we modeled this continuum
difference between the ML prediction and the observed spectrum as a third
degree polynomial to remove bandwidth-wide effects. We subtracted this
continuum difference to facilitate a direct comparison between spectra and
their features in Figure 3.

Figure 3: The ML-predicted spectrum (black line in top four panels) and the
observed spectra, from Keel (1983a) using the Mount Lemon 60 inch (top panel,
orange), the KPNO 2.1 m telescope (second panel, green), from the VIRUS-P IFU
instrument (third panel, blue), and the 2020 MMT Binospec observation (bottom
panel, gray). The bottom panel shows the residuals of each spectrum and the ML
prediction.  Figure 4: The BPT diagnostic diagram for nuclear activity. The
Galaxy And Mass Assembly Survey data is shown for comparison with the
Kauffmann et al. (2003) star-formation/AGN demarcation (dashed lines). The
observed line strengths reported in Keel (1983a) and the VIRUS-P observations
for Rubin’s galaxy put it in the active galaxies category. The ML predicted
spectrum puts it in the AGN category. None of the line ratios prefer LINER or
Seyfert classifications (Kewley et al., 2006). The MMT line ratios are
complicated as H$\beta$ is not well constrained, skewing the vertical position
of the nucleus on the y-axis.

##  4 Discussion

###  4.1 How well did ML perform?

Figure 3 shows excellent agreement between the ML predicted spectrum and the
observations. Discrepancies in the stellar continuum are easily attributed to
night sky lines (present in the 60 inch spectrum $>6800$Å but not preserved in
the SDSS vectorization). In the residual, one can identify a slight gradient
in the KPNO spectrum’s continuum ($<$5000 Å), which is a similar calibration
difference. Discrepancies in H$\alpha$/[Nii] and [Oiii] line strengths are
notable in Figure 3.

The 60 inch and VIRUS-P spectra have closely comparable but not identical
apertures to SDSS ($\sim 4$″ and 3″ diameters respectively, Figure 2), and a
slight offset is to be expected. Both archival spectra (Figure 3, top two
panels) show excellent agreement with the ML predicted spectrum within their
respective noise levels. The major differences are telluric features (e.g.
$>6800$Å in the 60 inch spectrum in Figure 3), not included in the original ML
prediction (telluric features are a source of noise in the training set, and
are therefore left out as much as practical).

The VIRUS-P spectrum broadly agrees well with the ML prediction. The only
deviations are the [Oiii] emission line and the Hei absorption, which are both
slightly under-predicted by the ML method (Figure 3, third panel). About a
third of the equivalent width in the [Oiii] emission and the Hei absorption is
missing (Figure 3, bottom panel).

The MMT/Binospec spectrum (Figure 3, fourth panel) focuses on the very central
region of Rubin’s galaxy. The [Oiii] and H$\alpha$/[Nii] emission line
strengths, as well as the [Sii] absorption features at 4000 Å, do appear to be
under-predicted by the ML in comparison to the MMT spectrum.

There are two factors resulting in differences between the ML predicted
spectra and those observed: the aperture of the observed spectra and the
aperture-distance effects in the SDSS training sample.

Figure 2 illustrates that the archival spectra and VIRUS-P are for a slightly
larger aperture and the MMT one for a smaller aperture than an SDSS spectrum
on this galaxy would have been. Stronger H$\beta$ and [Oiii] from the nucleus
can be explained by less dilution of the AGN signal. This can be seen as the
progression of stronger observed emission lines in Figure 3 with smaller
apertures.

Secondly, the ML algorithm was trained on SDSS with a known aperture-distance
effect (dilution of AGN signal in more distant galaxies), matching the spectra
of more distant galaxies to Rubin’s Galaxy’s nucleus with a wider aperture
diluting the AGN signal.

###  4.2 AGN?

Identifying lower-power AGN can be difficult because selection effects are the
most notable at the lower luminosities. Traditionally, one would select
obscured or low-power AGN from IR colors rather than x-ray or emission lines
in spectra. The ML approach offers an alternative, with Rubin’s Galaxy an
instructive example of one that could be identified using imaging alone.

Figure 4 shows where the observed and the ML predicted line strengths place
the nucleus of Rubin’s galaxy on the BPT diagram (Baldwin et al., 1981). The
line strengths implied by the ML predicted spectrum imply strongly that
Rubin’s galaxy is an AGN (blue triangle in Figure 4).

A combination of Keel (1983a) and VIRUS-P line strengths are more consistent
with a lower-power AGN, closer to the dividing line between active galaxies
and star-forming galaxies (red circle in Figure 4). The MMT/Binospec line
strengths put the nucleus of Rubin’s galaxy solidly in the AGN category (green
square in Figure 4). The MMT spectrum does not constrain the H$\beta$ well and
this skews the Oiii/H$\beta$ ratio. The observed or predicted line ratios are
not consistent with those of either a LINER or Seyfert according to the Kewley
et al. (2006) criteria.

Figure 5: WISE colors of sources in the GAMA Equatorial Fields (Cluver et al.,
2014). The WISE colors of the ALLWISE catalog sources at the position of
Rubin’s Galaxy are shown. The colors of the bright foreground star projected
on the disk of UGC 2885 are as would be expected. The colors of the nucleus
are located away from the bulk of normal galaxies (contours) but the
$[4.6]-[3.6]$ colour does not quite reach the AGN criterion of Assef et al.
(2018).

Figure 5 shows the WISE colors of the central region of Rubin’s galaxy for
comparison with the classifications of Jarrett et al. (2011) and Cluver et al.
(2014). The WISE colors are consistent with those of spiral, star-forming disk
galaxies. The source catalog entry corresponding to the center of Rubin’s
Galaxy is in the part of color-space where star-forming galaxies border on
obscured AGN and Seyfert galaxies, according to Figure 5 in Cluver et al.
(2014). However the WISE $[3.6]-[4.5]$ color criterion from Assef et al.
(2015, 2018) does not place Rubin’s galaxy in the AGN bracket (dashed lines in
Figure 5). Given the angular resolution of WISE, dilution of the AGN signal by
the PSF likely accounts for this lack of AGN identification i.e. the WISE flux
is dominated by the stellar population of Rubin’s galaxy. Based on the
spectroscopic line strengths, the center of Rubin’s galaxy is indeed an AGN.
WISE colors have the benefit of suffering less from dust obscuration allowing
for unbiased searches of AGN in the nearby Universe. However, the WISE color
section still misses AGN such as these and the ML approach may be a way to
fill in the missing population.

###  4.3 Discussion

It is exciting to see that the ML prediction of an SDSS quality spectrum of
this galaxy is so reliable, even when this galaxy resides in the space between
star-forming and AGN. The ML method outperforms WISE color selection, the
preferred method of identifying AGN in objects without a spectrum. A
successful ML prediction in the loci of galaxy populations is reassuring but a
tangible success for an extreme object is especially encouraging. How the ML
algorithm transfers from e.g. Pan-STARRS broad-band grizy images to the Rubin
Observatory’s LSST looks to be promising example of transfer learning in
astronomy.

The combined line strengths of Rubin’s Galaxy point to ongoing AGN activity.
Combined with the very extended star-forming disk, the presence of an AGN
makes this galaxy an interesting case: a massive disk galaxy, with no signs of
interaction, relatively normal star-formation activity, and very regular
rotation, yet using secular mechanisms only to fuel its central source.

##  5 Conclusions

The ML predicted SDSS-quality spectrum from Wu & Peek (2020) is remarkably
close to the observed spectra (Figure 3). Deviations can be attributed to
small differences in aperture or to residuals from telluric lines. The
emission lines in the ML prediction are under-predicting the [Oiii] and
H$\alpha$ and [Nii] doublet compared to [Oii]. The successful identification
of this galaxy’s spectrum is a promising development in the use of ML. It is
an encouraging development for future use on the Rubin Observatory data.

In order to supply gas to the central black hole, the gas must lose angular
momentum, and astronomers have long suspected that galaxy collisions (or at
least interactions) provide the requisite torque to bring that gas into the
nucleus (e.g. Hong et al., 2015; Dietrich et al., 2018; Gao et al., 2020;
Marian et al., 2020). However, interactions are not the only avenue for
fueling the AGN (e.g. McKernan et al., 2010; Marian et al., 2019). Rubin’s
galaxy is an example of an extremely isolated, undisturbed, and massive galaxy
which shows clear evidence of nuclear activity, it may prove a useful
laboratory to study the secular fueling processes on a grand scale. Further
dissection of the inner regions of the galaxy may shed light on the secular
mechanisms that supply fuel to AGN.

## Acknowledgements

The authors would like to thank the anonymous referee for their effort and
time improving the manuscript. Observations reported here were obtained at the
MMT Observatory, a joint facility of the University of Arizona and the
Smithsonian Institution. Support for this work was provided by NASA through
grant number GO-15107 from the Space Telescope Science Institute, which is
operated by AURA, Inc., under NASA contract NAS 5-26555.

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