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Modeling the Dynamics of Hurricane Evacuation Decisions from Twitter Data: An Input
Output Hidden Markov Modeling Approach
Kamol Chandra Roy
Ph.D. Student
Department of Civil, Environmental, and Construction Engineering
University of Central Florida
12800 Pegasus Drive, Orlando, FL 32816
Phone: 321-318-2067
Email: roy.kamol@knights.ucf.edu
Samiul Hasan
Assistant Professor
Department of Civil, Environmental, and Construction Engineering
University of Central Florida
12800 Pegasus Drive, Orlando, FL 32816
Phone: 407-823-2480
Email: samiul.hasan@ucf.edu
(Corresponding Author)
[This is the pre-print version of the following article: Roy, K. C., & Hasan, S. (2021). Modeling the
dynamics of hurricane evacuation decisions from twitter data: An input output hidden markov modeling
approach. Transportation Research Part C: Emerging Technologies, 123, 102976, which has been
published in final form at https://doi.org/10.1016/j.trc.2021.102976].
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ABSTRACT
Evacuations play a critical role in saving human lives during hurricanes. But individual evacuation
decision-making is a complex dynamic process, often studied using post-hurricane survey data.
Alternatively, ubiquitous use of social media generates a massive amount of data that can be used
to predict evacuation behavior in real time. In this paper, we present a method to infer individual
evacuation behaviors (e.g., evacuation decision, timing, destination) from social media data. We
develop an input output hidden Markov model (IO-HMM) to infer evacuation decisions from user
tweets. To extract the underlying evacuation context from tweets, we first estimate a word2vec
model from a corpus of more than 100 million tweets collected over four major hurricanes. Using
input variables such as evacuation context, time to landfall, type of evacuation order, and the
distance from home, the proposed model infers what activities are made by individuals, when they
decide to evacuate, and where they evacuate to. To validate our results, we have created a labeled
dataset from 38,256 tweets posted between September 2, 2017 and September 19, 2017 by 2,571
users from Florida during hurricane Irma. Our findings show that the proposed IO-HMM method
can be useful for inferring evacuation behavior in real time from social media data. Since
traditional surveys are infrequent, costly, and often performed at a post-hurricane period, the
proposed approach can be very useful for predicting evacuation demand as a hurricane unfolds in
real time.
Keywords: Hurricane evacuation, Hurricane Irma, Social media, Input output hidden Markov
model, Twitter, Florida.
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1. INTRODUCTION
Extreme weather events have become more common these days due to climate change and other
related causes. These extreme events have caused significant physical and socio-economic losses
(Guha-sapir et al., 2017; Hasan and Foliente, 2015; Re, 2013; Tousignant Lauren, 2017). A real-
time demand-responsive evacuation system is essential to save human lives and minimize losses
(Murray-Tuite and Wolshon, 2013). Traditionally, post-hurricane surveys are conducted to collect
data to understand and predict the evacuation behavior of a population. Such surveys are costly,
time consuming, and not effective to manage evacuation when a hurricane unfolds in real time
(Chaniotakis et al., 2017). With the ubiquitous use of social media platforms (e.g. Twitter,
Facebook etc.), a massive volume of real-time data is available. Such data can provide valuable
insights on individual behavior during extreme events such as a hurricane (Sadri et al., 2017a;
Wang and Taylor, 2014; Xiao et al., 2015).
Thus, large-scale social media data can be used for a better understanding of evacuation
behaviors during hurricanes (Martín et al., 2017). However, one of the major challenges of using
social media data is to reliably model evacuation decisions from such data. To date, the studies
investigating social media data are limited to inferring evacuation choices. These studies
(Chaniotakis et al., 2017; Martín et al., 2017) have mainly adopted clustering approaches that
locate a user during pre-evacuation and evacuation periods. A recent case study (Kumar and
Ukkusuri, 2018) on hurricane Sandy Twitter data shows the relationship between social
connectivity and evacuation decision without specifically modeling the real-time dynamics of
evacuation decision-making. Using geotagged Facebook data from hurricane Irma, Harvey, and
Maria, another recent study (Metaxa-Kakavouli et al., 2018) has analyzed the influence of social
ties on evacuation behavior. Although these studies have demonstrated the significant potential of
using location-based social media data in an evacuation context, they have not developed any
modeling framework that can answer what, when, and where users participate in different activities
during a hurricane.
In this paper, we present a modeling approach for understanding the dynamics of hurricane
evacuation from social media data. In particular, we have developed an input-output hidden
Markov model (IO-HMM) to infer evacuation behavior from Twitter data. We have gathered
large-scale Twitter data during hurricane Irma and used the spatio-temporal and contextual
sequences from this data to run the proposed model. Hurricane Irma, the largest storm ever
recorded in the Atlantic Ocean, made its landfall on the southern coastal areas of Florida. The
storm generated a massive amount of social media posts nationwide, especially in Florida. This
paper has the following contributions:
• We implement a process to gather hurricane evacuation information from geo-tagged
Twitter data. We validate the results by manually checking locations and tweet texts of the
users. As traditional survey data is costly and often confined with small geographic region,
this type of data can be used for understanding evacuation behavior during hurricane to
complement traditional approaches.
• We develop a Word2Vec model to extract contexts based on the tweets collected from
multiple hurricanes (Sandy, Matthew, Harvey, and Irma). The model has been trained using
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more than 100 million tweets having about 882.54 million words (after filtering out the
stop words, punctuations, emoticon, URLs). This model can contribute in future research
to determine disaster contexts from Twitter data.
• We develop an input output hidden Markov model from the sequences generated from user
tweets. To the best of our knowledge, this is one of the first studies that use social media
data for modeling the dynamics of hurricane evacuation decisions. The model can capture
the dynamics of hurricane evacuation by answering what, when, and how users participate
in different activities during a hurricane.
2. LITERATURE REVIEW
During a hurricane, timely evacuation is critical to reduce hazard risks and save human lives
(Baker, 1979). Despite the importance of evacuation, some people choose not to evacuate
(Whitehead et al., 2000). Therefore, a thorough understanding of the determinants of evacuation
behavior is needed to protect the loss of lives, especially for the vulnerable communities (Hasan
et al., 2011b). Many studies have investigated population response during hurricanes from
different perspectives, particularly focusing on evacuation choices (Murray-Tuite and Wolshon,
2013). These topics include: evacuation decision making (Gladwin et al., 2001; Hasan et al.,
2011b; Kang et al., 2007; Yang et al., 2019), evacuation time (Hasan et al., 2013; Lindell, 2008;
Rambha et al., 2019), evacuation demand (Xu et al., 2016), destination choice (Mesa-arango et al.,
2013), and mode and route selection (Sadri et al., 2015, 2014). However, most of these studies are
based on post-disaster household surveys collecting information on population behavior instead of
real-time dynamics. Studies (Lin et al., 2009; Ukkusuri et al., 2017; Yin et al., 2014) have
developed high fidelity agent-based models to predict population responses in future hurricanes.
One of the major shortcomings of these models is that factors influencing evacuation decisions do
not change over time. Although a few models (Fu and Wilmot, 2004; Sarwar et al., 2018)
considered the dynamics of evacuation decision-making process, these models depended on post-
disaster surveys, mainly focusing on household characteristics with limited transferability (across
regions, communities, and disaster contexts) (Hasan et al., 2011a; Martín et al., 2017). Survey data
have limitations in capturing the dynamic nature of the evacuation decision‐making process
(Murray-Tuite et al., 2019).
However, hurricane response is a dynamic event with significant changes and uncertainties
involving parameters beyond household characteristics. During a hurricane, emergency agencies
and weather services issue frequent advisories providing information on the hurricane’s projected
trajectory and category, wind speed, rainfall, storm surge, evacuation warning etc. Local and
national news channels disseminate information on the present condition of the hazard and traffic
situation. Context awareness, considering all these dynamic factors, plays a critical role for a large
number of populations to decide whether to leave or not. Lee et al. explored the dynamics of
visiting patterns to the weather-related websites during Hurricane Katrina (Lee et al., 2009). Yabe
et al. developed a web-search query-based evacuation prediction model (Yabe et al., 2019). These
studies mainly focused on understanding risk perceptions without modeling the spatial-temporal
dynamics of evacuation behavior. As an alternative to relying on static post-disaster surveys,
dynamic predictive models can be built employing real-time information received from multiple
sources including individuals, transportation facilities, and emergency services. For instance,
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Meyer et al. studied the dynamics of risk perception by using survey data collected during an
approaching hurricane (Meyer et al., 2014). Studies also developed a physics-based hazard
modeling approach to simulate evacuation uncertainty considering the physical interaction among
multiple hazard components (Blanton et al., 2020; Davidson et al., 2020). However, these studies
were based on simulated environments and did not use real-time information available from
different sources. Evacuation models can utilize the vast amount of streaming data available from
social media, giving us real-time insights on individual actions during evacuations (Chaniotakis et
al., 2017; Kryvasheyeu and Chen, 2015; Martín et al., 2017; Sadri et al., 2017b).
Recently, the role of social media in a disaster management context has gained a significant
attention, mainly from the perspectives of crisis communication (Lachlan et al., 2016; Roy et al.,
2020; Sadri et al., 2017b, 2017a), human mobility analysis (Beiró et al., 2016; Pan et al., 2013;
Roy et al., 2019; Yanjie Duan et al., 2016), nowcasting damage assessment (Kryvasheyeu et al.,
2016), and event detection (Dong et al., 2015; Kryvasheyeu and Chen, 2015). However, its
potential in understanding evacuation behavior is still underexplored. Existing studies on inferring
evacuation decisions from social media data found home locations and displacements to determine
if a user has evacuated or not. Chaniotakis et al. (Chaniotakis et al., 2017) used a density based
clustering approach to identify home and geotagged tweet counts during an evacuation order to
identify evacuation decision. Using hurricane Matthew data, Martin et al. (Martín et al., 2017)
showed that Twitter data can be used to understand evacuation compliance behavior. This study
considered user median locations during a normal period as their homes and median locations
during a hurricane as their evacuation destinations. Using similar approach on hurricane Sandy
twitter data, Kumar and Ukkusuri (Kumar and Ukkusuri, 2018) studied the evacuation decision of
New York City residents in relation to the social connection of the users, distance from coastline,
and time to evacuation. They have found that higher number of social ties (number of friends,
followers) decrease the likelihood to evacuate. A recent study using Facebook data of hurricane
Irma, Harvey, and Matthew found a similar result that social ties decrease the likelihood to
evacuate (Metaxa-Kakavouli et al., 2018). However, these studies did not capture the dynamics of
individual evacuation decisions requiring a modeling framework that can infer evacuation choices
from geo-location data.
In this paper, we present an input output hidden Markov model to infer evacuation behavior
from Twitter data. Hidden Markov models (HMMs) relate a sequence of observations to a
sequence of hidden states that explain the observations (Ghahramani and Jordan, 1996). HMMs
have been widely used in speech recognition (Rabiner, 1989), protein topology (Krogh et al.,
2001), social science (Eagle and Pentland, 2006), and activity modeling (Yin et al., 2017). HMMs
have been used to classify activity categories considering spatiotemporal features (Ye et al., 2013)
and to determine activity-location sequence from geo-location data (Hasan and Ukkusuri, 2017).
Duong et al. (Duong et al., 2005) introduced a switching hidden semi-Markov model for online
activity recognition and abnormality detection. Input-output hidden Markov model is an extension
to the standard hidden Markov model for using the HMM in a supervised fashion (Bengio and
Frasconi, 1995). IO-HMM has shown the added advantages over HMM to map the output
sequences with the inputs in studies such as audio-visual mapping (Bengio and Frasconi, 1995),
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price forecasting (González et al., 2005), hand-gesture (Marcel et al., 2000) etc. Yin et. al (Yin et
al., 2017) proposed an IO-HMM based modeling framework to infer urban activity patterns.
3. DATA PREPROCESSING AND DESCRIPTION
In this study, for inferring evacuation choices from social media posts, we have used Twitter data
from hurricane Irma. Using its streaming API, we collected around 1.81 million tweets made by
248,763 users between September 5, 2017 and September 14, 2017. We collected the data using a
bounding box covering Florida, Georgia, and South Carolina. To obtain user activities during a
pre-disaster period, we also collected user-specific historical data using Twitter’s rest API which
allows to collect the most recent 3,200 tweets for a given user. We collected user specific data for
19,000 users who were active for at least three days between the day the first evacuation order was
issued and the landfall day, so that we have enough data for capturing the activity dynamics during
the evacuation.
For our analysis, we have considered only the tweets with geo-location information. The
geolocation information is provided either as a point (latitude, longitude) or a bounding box (area
defined by two latitude and longitudes pairs). The point location is the exact location whereas the
bounding box has different level of precision of where a tweet has been posted. We use the center
point of a bounding box as the latitude and longitude of that place. To convert all the locations to
a region under a geocoding system and to protect the privacy of the users, we have used geohash
geocoding system with a precision of ~5 kilometers. Geohash converts a latitude, longitude pair
into a short string of letters and digits depending on the precision (length of the strings) (Balkić et
al., 2012). In our study, we have used a geohash of length 5, which is equivalent to a region
surrounded by ~ area and has a reasonable resolution to capture the spatial dynamics.
3.1 Preparing Evacuation Data
From the historical tweets of a user, we extracted the most visited place during office hours (9:00
AM to 6:00 PM) on weekdays and the most visited place during nighttime (10:00 PM to 7:00 AM).
For each user, we assigned the most frequent office hour place and night hour place as office
location and home location, respectively. For some users, the office and home location can be
same because users may not be a worker or may have their offices within 5 km from home.
Every year Florida attracts millions of visitors from home and abroad. We adopt several
steps to remove the users who came from outside of Florida (international visitors and domestic
users coming from states other than Florida). Through the filtering steps, we consider only the
users whose home and office locations are within Florida, whose evacuation distance is less than
2,400 km (chosen based on the literature (Cheng et al., 2008; Han et al., 2019)), and who have
returned to their home after the landfall.
In this study, we have focused on capturing the evacuation demand that is most likely to
affect traffic flows on highways. Short distance evacuations (e.g., going to a nearby shelter) are
not likely to impact highway traffic. Also, previous studies found that short distance evacuations
are only a small percentage of the total evacuation count. During hurricane Floyd, very few
evacuations were found less than 50 miles (~80.5 km); about 3.5% of the respondents chose a
shelter or a church as an evacuation destination (Cheng et al., 2008). Based on hurricane Matthew
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Twitter data, a recent study (Han et al., 2019) has found that evacuees are likely to move more
than 200 km for an evacuation. During hurricane Irma, only 4% of the respondents were found to
evacuate to a shelter (Wong et al., 2018, 2020). Moreover, some of the geotagged tweets do not
have the necessary granularity (tweets with locations as a bounding box) to detect short distance
evacuation. Thus, we select a threshold of 200 km to identify evacuation. After returning home, a
user may not have any tweets posted from her home but may have posted from nearby locations.
Thus, we select a 20 km distance threshold from someone’s home to identify the return of an
evacuee.
Starting from the beginning (9 days prior to landfall) of the location sequence to the landfall
day, if a user has not tweeted from home or office but tweeted from somewhere else with a
displacement of at least 200 kilometers, we consider that the user evacuated and the corresponding
time as evacuation time. After landfall, a return is considered as the time when an evacuated user
is first seen within the 20 kilometers from her home or office. We collect the information on
evacuation orders from the official Twitter account of each county. We have considered the
timings of the evacuation orders issued by each county. So, if someone evacuates before the first
official order, it is considered as an evacuation without an official order. We have found that 252
users have evacuated among 2,571 identified Florida users.
We have manually checked the results of the above approach of identifying a user’s home
location and evacuation (if any), it’s destination, and timing. Please see the supporting information
section for details of the manual checking process. We compare the results from the manual
checking process with the results obtained from this approach. We find that both the results match
with respect to evacuation time and displacement traveled during evacuation. We use this resulting
data as labeled dataset for the purpose of model estimation and validation. After all the processing,
our final dataset contains 38,256 geotagged tweets, posted by 2,571 users from Florida. For each
user, we created a sequence of his/her tweets and the corresponding locations posted between
September 2, 2017 and September 19, 2017.
3.2 Data Exploration
Figure 1 shows the origins and destinations of the evacuated users. Here the identified home
location of an evacuee is considered as the origin and the evacuation destination place is considered
as the destination. Figure 1 shows the result of 252 Florida-based users after filtering out the
tourists/visitors. Residents of Florida evacuated to Georgia (Atlanta was one of the major
destinations), Alabama, South Carolina, and North Carolina. Some users (at right bottom of Figure
1, near coast) moved to places that are closer to the coast than before. This is reasonable as the
projected path of hurricane Irma changed overnight on September 8, 2017. Initially, Irma was
expected to hit from the east coast of Florida, but later it changed its path and was predicted to hit
from the west coast. These results seem plausible according to the news updates from different
sources during hurricane Irma (Luz Lazo, 2017; Marshal, 2017). The majority of the evacuees
were from Miami, Tampa, West Palm Beach etc. (see Figure 1), where mandatory evacuations
were ordered.
Figure 2 shows the distribution plot of evacuation time and return time of the users who
evacuated during Irma. Figure 2(a) shows the marginal and joint frequency distributions of
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evacuation time and return time; the top histogram along x axis shows the distribution of
evacuation count in 24-hour intervals; the right histogram along y axis shows the distribution of
return time in 24-hour intervals; each cell in the heatmap shows both evacuation count and return
count with respect to the corresponding 24-hour evacuation interval on x axis and return interval
on y axis.
FIGURE 1 Evacuation Origin and Destination
Figure 2(b) and 2(c) show the probability distributions of evacuation and return time
considering the type of evacuation order received. The evacuation time and return time are
expressed as the time difference from landfall time (September 10, 2017), a negative value
indicates a period before the landfall and a positive value indicates a period after the landfall. Most
evacuees left within 100 hours before the landfall (September 10, 2017); 18 to 42 hours before
landfall was the most frequently chosen evacuation time window. On the other hand, 78 to 102
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hours after the landfall was most frequently chosen return time window. People started evacuating
before the official evacuation order (see Figure 2 (b)). Although the pattern of evacuation time is
different for voluntary and mandatory orders, the patterns of return times are almost similar (see
Figure 2 (c)). The resulting distributions are aligned to the actual evacuation time and return time
according to the concurrent news reports during hurricane Irma (ABC News, 2017;
FLKEYSNEWS, 2017).
(a)
(b)
(c)
FIGURE 2 Distributions of Evacuation Time and Return Time during Hurricane Irma,
(a) Joint distribution of evacuation time and return time (b) Probability distribution of
evacuation time for mandatory and without mandatory evacuation order, and (c) Probability
distribution of return time for mandatory and without mandatory evacuation order.
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4. METHODOLOGY
We have used an Input Output Hidden Markov Model (IO-HMM) to identify activity sequence
during a hurricane. We compare the results with a standard Hidden Markov Model (HMM). The
model structures are shown in Figure 3. The IO-HMM is similar to HMM, but it maps the input
sequence to output sequences and applies the expectation maximization algorithm (EM) in a
supervised fashion.
In an HMM modeling framework, the system being modeled follows a Markov process with
unobserved (i.e., hidden) states. Figure 3(a) shows a graphical representation of an HMM. The
solid circles represent the observed information and the transparent circles represent the hidden
state latent variables, in our case the activity types of a user. Here, the hidden states,
are assumed to follow a Markov process that means a hidden state, the probability distribution of
depends only on the previous state, ; i.e., . On the other hand, for the
observations , an observation, the probability distribution of depends only on its
current hidden state, ; i.e., .
Unlike the standard HMM, in IO-HMM, the probability distribution of hidden state at time
, depends on the previous state and the input at time ; i.e., . The
probability distribution of observation at time depends on both the hidden state and at
time ; i.e., (see Figure 3(b)).
Here, is the input vector at time t. is an output vector, and is
a discrete state. Similar to HMM, IO-HMM has three set of parameters : initial probability
parameters (), transition model parameters (β), and emission model parameters (.
(a) HMM
(b) IO-HMM
FIGURE 3 Graphical Model Specifying Conditional Independence Properties (a) For a
Hidden Markov Model (b) For an Input Output Hidden Markov Model
The likelihood of a data sequence given the model parameters ( is given by:
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(1)
The model parameters are estimated by an expectation maximization algorithm
(McLachlan and Krishnan, 2007). For initial and transition models, we have used a multinomial
logistic regression model. If we assume that there are hidden states, the equation of initial
probability model becomes the following:
(2)
where is a coefficient matrix for initial probability model with represents the
coefficients for the initial state being at state
The transition from the state to the state can be modeled as:
(3)
where represents the transition probability matrices with the being the
coefficients for transitioning to next state given the current state is
For the output model, we have used a linear model for a continuous outcome:
(4)
where, represents the emission coefficient when the hidden state is . For a hidden state
, and denote the arrays of model coefficient and standard deviation of the linear model.
And a logistic regression model is used for a categorical outcome:
(5)
where, denotes the model coefficient when the hidden state is .
Detailed descriptions of HMMs and the associated inference algorithms can be found in
ref (Rabiner, 1989). The IO-HMM model architecture and its formulation can be found in this ref
(Bengio and Frasconi, 1995).
5. MODEL DEVELOPMENT
An IO-HMM model considers data as sequences of inputs and outputs for each user. For that
purpose, we need to process the data from raw tweets in that specific form. Figure 4 shows the
sequence generation process. For a user, represent the times of the tweets posted
at locations , respectively. We have collected hurricane related information for
each of the location (county level) such as whether the location had a mandatory evacuation order
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or not, whether the location had a voluntary order or not, whether the time is before landfall or
after landfall. This information is encoded as a binary variable in the sequence. Other information
associated with each location is distance from home and time difference from landfall, similarity
score of the posted tweet text with the evacuation context words. For simplicity, all information is
not shown in Figure 4. We calculate the similarity score by training a word to vector model using
tweets from 4 hurricanes (Irma, Matthew, Harvey, and Sandy).
FIGURE 4 Schematic diagram of sequence generation. Here, =location of the user when
posting tweet ; = texts of the tweet ; = time of the tweet ; and total number of
tweets posted.
5.1 Inferring Evacuation Context from a Tweet
In general, the text of a tweet may reflect the underlying context such as hurricane awareness,
evacuation intent, information sharing/seeking, power outage etc. We use a similarity score to
quantify how similar a tweet is to an evacuation context (e.g., words such as ‘evacuate’,
‘evacuating’, ‘sheltering’). We have used a vector space model called word2vec to learn the word
vectors of an evacuation-related tweet.
Vector Space Model (D. E. Rumelhart, G. E. Hinton, 1986) is a natural language processing
tool to represent texts as a continuous vector where words that appear in the same contexts share
semantic meaning (Sahlgren, 2008),(Baroni and Dinu, 2014). A detailed description of how the
model works is given in the supporting information. Once a model is trained, every word in the
vocabulary will have a vector representation of a length equal to the vocabulary size (see
supporting information). We train a word2vec model using CBOW architecture (please see the
supporting information for details) on a corpus of 100 million hurricane-related tweets, collected
during multiple hurricanes (Hurricanes Sandy, Harvey, Matthew, and Irma). We calculate the
cosine similarity (Huang, 2008) between two word vectors by the following
equation:
(6)
Here, , . In
our study, to calculate the similarity of a word to an evacuation context,
and . If a window size
of is selected, then score of a tweet is calculated by summing up to top score for the words
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present in the tweet. We have used the top one score to represent the similarity of a tweet with
respect to an evacuation context. Similarity scores of the tweets posted at locations
are denoted by .
6. MODEL ESTIMATION
As we obtain the sequences of all the information needed, we need to specify the inputs and
outputs. In IO-HMM, both inputs and outputs are available at the training stage; but after training,
the model should infer the outputs given its inputs. In general, the inputs are known before the
start of a transition to a new state/activity, but the outputs are not known. In our model, we choose
input variables that are likely to influence the decision of a user’s next activities. We select 5 input
variables including: the time difference from landfall in hours represented as negative to positive
where negative means a pre-landfall period , a binary variable representing a pre-landfall or a
post landfall period , an interaction variable representing the time difference from landfall only
for a pre-landfall period , a binary variable representing if the user’s home location is under a
mandatory evacuation order , and a binary variable representing if the user’s home location is
under a voluntary evacuation order . As outputs, we choose two variables such as: current
location’s distance from home and evacuation similarity score (word2vec score) of the tweets
posted in the location .
We make several assumptions for selecting the dependencies among the initial, transition,
and output models of the IO-HMM structure. We assume that the transition (see Figure 3b)
between the hidden states depend on the current state and the input variables (time difference
from landfall), (post landfall), (user’s home is under mandatory evacuation), (user’s home
is under voluntary evacuation). We did not explicitly study the research question of what factors
impact an individual’s evacuation behavior. Rather we model this behavior as part of an activity
dynamics process, where evacuation is considered as an activity type. The coefficients of these
five input variables corresponding to an evacuation activity transition indirectly capture the factors
impacting evacuation behavior. Existing literatures have also found that variables like mandatory
evacuation order, voluntary evacuation orders, time of landfall significantly affect people’s
evacuation decisions (Pham et al., 2020; Whitehead et al., 2000; Wong et al., 2018). We also
assume that output variables include (home distance) and (word2vec score). These output
variables depend on the current state and the input variables including (time difference from
landfall), (time difference from landfall during pre-landfall), (user’s home is under mandatory
evacuation) and (user’s home is under voluntary evacuation). Moreover, no input is chosen for
the initial probability model and thus parameters will be learned by the EM algorithm only.
Multinomial logistic regression is used as the transition and initial models. Since both the outputs
distance from home and word2vec evacuation similarity score are continuous, linear
regression models are used as output models.
In the given setting of IO-HMM, to unfold the dynamics of hurricane evacuation, we
choose four types of activities as hidden states: home activity, office activity, evacuation, and other
activity. Home activity and office activity represent the activities when the user stays at home and
office, respectively; any activities participated at other locations are defined as “other” activities.
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Considering these four states would allow us to better capture the dynamics in user activities as a
hurricane approaches to make a landfall. For instance, it would enable us to capture the differences
between activity transitions in a zone with a mandatory evacuation order and those transitions in
other areas without a mandatory order (e.g., in a mandatory order zone, an individual is likely to
end office activity earlier).
Starting from the first evacuation order to the landfall day, if a user has only other activity
but no home/office activity and is found at a location of 200 kilometers or more away from home,
we labeled it as an evacuation activity. We train the IO-HMM model using the labeled sequences
of 80% (n=202) of the evacuated users and 80% (n=1855) of the non-evacuated users. To validate
the model, we use the data from the 20% (n=50) of the evacuated users and 20% (n=463) of the
non-evacuated users. We implement the models in Python programming language using the IO-
HMM package developed by (Yin et al., 2017), available at https://github.com/Mogeng/IO-HMM.
7. RESULTS
In this section, we present the results of our evacuation dynamics model. First, we apply a standard
HMM model to find the learned distributions of the selected outputs. Then we interpret the results
of IO-HMM.
7.1 HMM Results
In the HMM structure, we have four latent states/activities considering the output variables as
mixtures of gaussian distributions. Table 1 presents the posterior distributions of home distance
and word2vec score for each latent activity. Mean distances from home are 0, 22.64, 129.18,
699.97 kilometers for home activity, office activity, other activity, and evacuation, respectively.
The model has estimated higher average distance of 699.97 kilometer for evacuation activities.
Average distance for office activity is 22.64 kilometers with dispersion of 32.64 kilometer. We
choose other activities as a broad category for simplicity of the model; it may include grocery
shopping before hurricane, eating at restaurants, short or long trips etc., thus 129.18 kilometer of
average distance with the highest dispersion of 340.44 kilometer seems reasonable.
We are interested in learning how users respond to evacuation warning in their tweets. We
find the word2Vec evacuation similarity scores as 0.54, 0.48, 0.48, and 0.50 for home activity,
office activity, other activity, and evacuation, respectively. Although the difference is not that
much, we see a higher score during home activity and evacuation activity. This means that users
have tweeted about evacuation more during evacuation or home activity (0.54 and 0.50 word2vec
similarity score). It is expected since evacuated users are more likely to share posts about
evacuation. Also, during a hurricane, people are more likely to share evacuation related updates
from their homes.
15
Table 1 Posterior Distributions of Output Variables. Here () represents a normal
distribution with mean and standard deviation of .
Latent States
(Activity Types)
Distribution of Output Variables
Distance from Home
Word2Vec Score
Home
(0.00,0.00)
(0.54, 0.2)
Office
(22.64, 32.64)
(0.48, 0.19)
Other
(129.18, 340.44)
(0.48, 0.2)
Evacuation
(699.97, 444.5)
(0.5, 0.22)
7.2 IO-HMM Results
Although an HMM can learn the latent activities from the observed tweets, it does not allow to
incorporate contextual input variables to infer the latent activities and their relationship with the
outputs. Table 2 shows the coefficients of the output model when applied an IO-HMM structure.
We have considered other variables such as friends count and follower count; but the estimated
coefficients for these variables are not significant. We have excluded these variables from our final
model. The output variable, distance from home, given the current state is a home activity has no
coefficient. This is plausible since, for any user at home, distance from home is always zero. As
expected, among all activities, the evacuation activity has the highest intercept for the distance
from home output variable. The coefficients of , for an evacuation activity, are found
statistically insignificant, indicating a lack of evidence in the data that evacuation distance depends
on the time difference from landfall. However, negative values of these coefficients indicate that
an increase in the time difference from landfall (e.g., a time closer to the landfall in a pre-landfall
period) would decrease evacuation distance. Positive coefficients for both mandatory and
voluntary order indicate that evacuated users from mandatory and voluntary evacuation zones
will travel longer than a user from a zone with no evacuation order. Furthermore, users from
voluntary evacuation zones would travel longer than the users from mandatory evacuation zones.
TABLE 2 Coefficients of the Output Models for IO-HMM
Output
Variables
Latent
Variables
Input Variables
Intercept
Time
difference
from
landfall
(hour),
Time
difference
from
landfall*Pre-
landfall
period
(hour),
Home
location
under
mandatory
evacuation
order,
Home
location
under
voluntary
evacuation
order,
Distance
from
Home
Home Activity
0
0
0
0
0
Office Activity
22.565***
0.015***
-0.021*
1.893*
-5.724***
Other Activity
111.639***
0.189***
-0.457***
-24.910***
10.991***
Evacuation
585.724***
-0.125
-0.572
160.968***
176.748***
word2vec
Score
Home Activity
0.667***
-0.0006***
0.002***
0.035***
-0.0272***
Office Activity
0.577***
0.0005***
0.001***
-0.030***
0.019**
Other Activity
0.571***
-0.001***
0.011***
0.015***
-0.013***
Evacuation
0.563***
-0.0005***
0.002***
-0.040***
-0.036*
*Note: ~p*<0.1; **~p<0.05; ***~p<0.01;
16
For word2vec evacuation similarity score, home activity has the highest intercept value. It
means that if all the independent variables are equal to zero (equivalent to the landfall day and no
evacuation order has been issued), users are more likely to post about evacuation from their homes.
This is reasonable as users who are not required to evacuate are more likely to stay at home and
may post evacuation related tweets. For evacuation activity, a negative coefficient of (-0.0005)
and a positive coefficient of (0.002) indicate that evacuated users post more about evacuation
during a pre-landfall period as time approaches to landfall compared to a post-landfall period. In
other words, an evacuated user posts more about evacuation before landfall, probably because they
have already evacuated and expressing concerns who are yet to evacuate. These variables (, )
have similar effect for home activity and other activities, indicating that in general users are
expected to post more about evacuation before the landfall than in a post-landfall period. For home
activity and other activity, mandatory evacuation order has a positive coefficient and
voluntary evacuation order has a negative coefficient for word2vec evacuation similarity
score. It means that if all other variables remain constant, while staying at home or participating
in other activity, compared to a user from no evacuation order zone, a user from a mandatory
evacuation order zones is likely to post more about evacuation whereas a user from voluntary
evacuation order zones is likely to post less about evacuation. On the other hand, for evacuation
activity, variables representing mandatory order zone and voluntary order zone have negative
coefficients for word2vec evacuation similarity score. This indicates that evacuated users from a
mandatory or voluntary order zone post less about evacuation compared to evacuees from a zone
with no evacuation order. This is plausible since evacuated users may have less time to tweet while
traveling.
Table 3 shows the coefficients of multinomial logistic regression (MNL) models for the
transition models of IO-HMM. Given the current state, there are 4 MNL models to capture the
transition among the hidden states (activity types). Here, any positive coefficient means that an
increase in the associated variable will increase the probability to make a transition between the
corresponding states. We have 80 different coefficients to capture the dynamics of transition
between any two states. We mainly focus on interpreting the coefficients associated with
evacuation. For instance, if we observe the coefficients of home: evacuation (see Table 3), a
negative sign of the variable (i.e., a post landfall period) represents that if a user’s current state
is a home activity, in comparison to a pre-landfall period, a post-landfall period decreases the
likelihood to evacuate if all other variables remain constant. It is also same for office: evacuation,
other: evacuation and evacuation: evacuation transitions (see Table 3). These results are quite
expected as individuals are less likely to evacuate after the landfall.
The coefficient of the variable time difference from landfall () is insignificant for the
evacuation: evacuation transition; but it is significant and has negative coefficients for other 3
transitions (i.e., home: evacuation, office: evacuation, other: evacuation). This means that if
everything remains constant, with increase in time difference from the landfall (as time becomes
closer to landfall or away from landfall) these transitions are less likely to occur. The input variable
(home location under mandatory evacuation order) has positive coefficients for home:
evacuation, office: evacuation, and other: evacuation but it has a negative coefficient for the
evacuation: evacuation transition. A plausible explanation is that a user may evacuate directly from
17
home/office (some user’s home and office are same) or may perform some other activities
(distance < 200 km) and then evacuate. The positive coefficient of indicates that compared to
the users from zones with no or voluntary evacuation order, users from mandatory evacuation
order zones are more likely to evacuate. A negative coefficient of for evacuation: evacuation
transition means that users who evacuate from mandatory evacuation zone are less likely to remain
in the evacuation state. It might be because due to their concerns about the damage of their home
caused by the hurricane. The input variable (home location under voluntary evacuation order)
has positive coefficients for home: evacuation, office: evacuation transition and negative
coefficients for other: evacuation and evacuation: evacuation transition. The positive coefficient
of indicates that compared to the users from no evacuation order, the users from voluntary
evacuation order are more likely to evacuate given their current activity is home or office. The
negative coefficient of indicates that given the current state is other or evacuation, compared to
the users from zones with no evacuation order, users from voluntary evacuation zone are less likely
to evacuate or continue to maintain evacuation state.
TABLE 3 Coefficients of the Transition Models for IO-HMM
From Activity: To
Activity
Intercept
Time
difference
from
landfall
(hour),
Whether
time is
post
landfall,
Home
location
under
mandatory
evacuation
order,
Home
location
under
voluntary
evacuation
order,
Home: Home
0.034***
0.253***
0.0001***
0.521***
0.051
Home: Office
0.037***
-0.084
0.002***
-0.032
0.083
Home: Other
0.121***
0.521***
-0.001***
0.088*
0.067
Home: Evacuation
-0.191***
-0.691***
-0.0003
0.401***
0.201***
Office: Home
0.174***
0.061
0.001***
-0.062**
-0.293***
Office: Office
0.393***
0.450***
0.002***
0.588***
0.391***
Office: Other
0.282
0.364***
-0.001***
0.196***
0.069*
Office: Evacuation
-0.242***
-0.875***
-0.003***
-0.722***
0.167***
Other: Home
0.159***
0.023
0.001***
0.228***
0.065
Other: Office
-0.062***
-0.157
0.002***
0.111*
-0.088
Other: Other
0.103***
0.957***
-0.004**
0.187***
0.233***
Other: Evacuation
-0.165***
-0.734***
-0.0002
0.236***
-0.177*
Evacuation: Home
-0.099
0.103
0.010***
-0.072
0.137
Evacuation: Office
-0.132
-0.460
0.0008
0.049
0.237
Evacuation: Other
-0.053
0.025
-0.0009
-0.372***
0.147
Evacuation: Evacuation
0.283***
0.332
-0.010***
-0.394***
-0.523***
*Note: ~p*<0.1; **~p<0.05; ***~p<0.01;
18
Figure 5 shows the combined effect of different variables contributing to the transition
probability from one activity to another. The color of each cell represents the probability of making
a transition from the associated row activity to the associated column activity. The sum of each
row equals to 1 indicating that from the current state/activity type, it will make transition to any of
the four activity types. Figure 5 (a) and 5 (b) show the transition probabilities 100 hours before
landfall, whereas Figures 5 (c) and 5 (d) show the transition probabilities 100 hours after the
landfall. Overall, before the landfall, given a current state, it has higher probabilities to make a
transition to evacuation state compared to the post-landfall period. Figure 5 (a) and 5 (b) show the
differences in transition probabilities between voluntary evacuation order and mandatory
evacuation order at the home location, 100 hours before the landfall. Given the current state is a
home activity, compared to the voluntary evacuation order, a mandatory evacuation order has a
slightly higher probability of evacuation (0.25 vs. 0.24) and a lower probability of transitioning to
the office (0.16 vs. 0.21). In both cases, we see that given that the current state is a home activity,
the probability to participate in other activity is high (0.30 under a voluntary order and 0.26 under
a mandatory order). Given the current state represents other activity, the probability to evacuate
increases from 0.16 to 0.21 from zones with a voluntary evacuation order to zones with a
mandatory evacuation order, respectively. Moreover, given the current state represents an office
activity, the probability to evacuate decreases from 0.28 to 0.12 from a voluntary evacuation zone
to a mandatory evacuation zone, respectively. Besides, the probabilities that an evacuated user will
continue to remain evacuated for voluntary and mandatory evacuation zones are 0.45 and 0.56,
respectively.
Similarly, Figure 5 (c) and (d) show the transition probabilities after 100 hours of the
landfall for users under voluntary and mandatory evacuation zones, respectively. Given any state,
the probabilities to evacuate, 100 hours after the landfall, are very low. For an evacuated user, an
individual from a voluntary evacuation zone has a lower probability (0.076) to remain evacuated
(see Figure 5c), compared to an individual from a mandatory evacuation zone (0.11) (see Figure
6d). In both Figures 5 (c) and 5(d), the highest probability values are observed for the transition
from evacuation to home. However, there is not much difference in the probability of returning to
home for users, 100 hours after hurricane landfall, from a voluntary evacuation zone (0.59) or a
mandatory evacuation zone (0.60).
19
Using the trained IO-HMM model, we predict the activity sequences for the test data (20%
of the labeled dataset). Figure 6 shows the performance of activity recognition of IO-HMM. The
confusion matrix reports the numbers of predicted labels and the ratio of correctly predicted label
to actual label. IO-HMM has 100 %, 98.17 %, 28.62% and 77.03% accuracy for recognizing home,
office, other, and evacuation activities, respectively (see Figure 6(a)). Using the standard HMM,
we obtain 100%, 92.38%, 29.01%, and 62.51% accuracy for home, office, other, and evacuation
activity recognition, respectively. Thus, using an IO-HMM structure instead of a standard HMM
structure improves accuracy.
(a) 100 hours before landfall, home location
under voluntary evacuation order
(b) 100 hours before landfall, home location
under mandatory evacuation order
(c) 100 hours after landfall, home location
under voluntary evacuation order
(d) 100 hours after landfall, home location
under mandatory evacuation order
FIGURE 5 Activity Transition Matrices under different scenarios
20
(a) for activity types
(b) for activity types
(c) for identifying evacuation decisions
(d) for identifying evacuation decisions
FIGURE 6 Classification Performance of IO-HMM. (a) and (b) represent the activity
(home, office, other and evacuation) classification performance in terms of confusion matrix
and ROC curve. (c) and (d) represent the evacuee (evacuated or not) identification
performance in terms of confusion matrix and ROC curve.
We observe that the model has relatively low accuracy in identifying ‘other’ activity types
than ‘home’, ‘office’, and ‘evacuation’ activities. This happens because of the similarity between
office activity and other activity and the overlap between the learned probability distributions of
these two activity types. The result indicates that the model predicts a significant number of ‘other’
activities as ‘office’ activities (see Figure 6a). Although the model has a low performance in
identifying ‘other’ activity, it is unlikely to have any consequence in predicting evacuated users
(see Figure 6c).
21
Figure 6(b) shows the ROC curves which plot true positive rates vs. false positives rates
under every possible classification threshold. For example, for home activity recognition, a true
positive rate answers the question when an actual activity is at home how often the model predicts
it as a home activity (true home activity/all home activity). On the other hand, false positive rate
for home activity recognition answers the question when actual activity is not at home how often
the model predicts it as a home activity (false home activity/ all not home activity). In Figure 6(b)
classes 0, 1, 2, and 3 represent home, office, other, and evacuation activities, respectively. Area
under the curve or AUC represents the classification performance where AUC is percentage of the
whole box which is under the ROC curve (range 0 to 1). If any ROC curve is close the diagonal
line or AUC =0.5, the model is not any better than random guessing. We can see that the model
has the AUC values of 0.98, 0.87, 0.94, 0.99 for home, office, other, and evacuation activities,
respectively.
We also report the performance of the IO-HMM model in identifying evacuation decision
(if a user has evacuated or not) at an individual level. Using the test set, for each user, we convert
the predicted activity sequence as a binary output by checking if any evacuation state is present in
the predicted activity sequence or not. Then we compare the converted evacuation identification
result against our labeled data to estimate the model performance using confusion matrix and ROC
curve. Figure 6(c) and 6(d) show the confusion matrix, ROC curve, respectively, for individual-
level prediction. For identifying individual evacuation decision, the model has 92% and 94%
accuracy for non-evacuated and evacuated users, respectively (see Figure 6(c)). The model has the
same AUC value of 0.98 for both evacuated and non-evacuated users.
Figure 7 shows evacuation participation rates over time. From the labeled data, we divide
evacuations in two categories: evacuations generated from zones under a mandatory evacuation
order and evacuations generated from zones under a voluntary or no evacuation order. The
evacuations from later zones are also known as shadow evacuation (Sorensen and Vogt, 2006;
Zeigler et al., 1981). We find that from our collected samples, around 65% evacuations are
generated from the mandatory evacuation order zone and the remaining 35% are from a zone with
either a voluntary or no evacuation order. Shadow evacuation causes additional traffic congestion
and often hampers the evacuation of the actually threatened population (Murray-Tuite and
Wolshon, 2013). Using the trained IO-HMM model, we predict the activity sequences of all the
users (including both training and test data). We compare the predicted timing of evacuation state
and the number of evacuated users with the labeled data. From Figure 7, we see that on aggregate
the model identifies around 62% of total evacuation as mandatory evacuation and around 38% as
shadow evacuation. The model captures the overall trend of the evacuation timing and
participation numbers.
22
FIGURE 7 Cumulative evacuation frequencies and predicted evacuation frequencies
across time.
8. CONCLUSIONS
To better capture the dynamics of individual-level evacuation behavior, longitudinal spatio-
temporal data are needed covering both pre- and post-disaster periods. Traditional data collection
approaches such as household surveys are static and conducted in a post-disaster period. This limits
our ability to capture the dynamics of evacuation decision-making process such as determining the
probability of evacuation given the states of the variables (e.g., evacuation order, projected landfall
time) changing over time. With longitudinal data collected, we can determine the effects of the
changes in variables over time on evacuation decisions. In addition, since the data are collected in
real time, we are able to capture the dynamics when the situation is evolving, instead of at a post-
disaster period.
In this study, we use Twitter data from Hurricane Irma to develop a model for inferring
individual hurricane evacuation dynamics. We have collected evacuation data from Twitter
covering all counties of Florida. Based on the tweets of active users during an evacuation period,
we develop an input output hidden Markov model to infer what type of activities individuals
participate, the locations and timing of those activities, when they evacuate, and where they
evacuate to. We model individual participation in four activity types (home activity, office activity,
other activity, and evacuation) during a hurricane.
23
The modeling approach provides rich insights on evacuation and other activity types during
a hurricane both spatially and temporally. For instance, we have learned from real-time Twitter
data to what extent individual social communication and evacuation distance depend on evacuation
order type and time to landfall.
The results associated with the spatial variables (e.g., home location under a mandatory
evacuation order, home location under voluntary evacuation order) indicate that if a user’s home
location is under a mandatory or voluntary evacuation order, he/she is likely to evacuate longer
distance compared to the users under no evacuation order. We also find that users from a
mandatory evacuation zone are likely to post more about evacuation during home activity and the
users from a voluntary evacuation zone are more likely to post about evacuation during an office
activity compared to the users from no evacuation order zone. From the activity transition
dynamics, we find that given the current activity is a home activity, the probability to evacuate
increases for both mandatory and voluntary evacuation order; given the current activity is an office
activity, the probability to evacuate increases for mandatory evacuation order and decreases for
voluntary evacuation order; and given the current activity is other activity, the probability to
evacuate increases for mandatory evacuation order and decreases for voluntary evacuation order.
The results associated with the variables related to temporal dynamics show that evacuation
distance is likely to decrease with a decrease in time difference from landfall in a pre-disaster
period. The number of evacuation related tweets (representing evacuation context) are likely to
increase with decrease in time difference from landfall in a pre-disaster period. We also find that,
before the landfall, as the time difference from landfall increases (reaching closer to the landfall),
the likelihood of evacuation decreases. And after the landfall, as the time difference from landfall
increases, the probability of returning to home increases. Thus, this study can capture the dynamics
of evacuation behavior both spatially and temporally within a single modeling framework. Such
insights for hurricane evacuation are critical for emergency management. For instance, identifying
the evacuated and not evacuated population during a hurricane can make its preparation more
effective and dynamic. Another benefit of our modeling framework is that, with the parameters
estimated in this study, we can generate the behavior of a synthetic population by simulating their
activity dynamics. Such simulated data from the model based on the total population of a region
will allow us to determine evacuation demand in real-time.
This study has some limitations such as Twitter may have different penetration in different
areas. Twitter users are not equally distributed across different age groups. Consequently,
geotagged tweets may not represent the behavior of all population segments. We have assumed
200 km as a threshold distance to identify an evacuation and 20 km to detect a return from an
evacuation. Thus, our approach cannot detect shorter distance evacuation such as relocating to
higher ground or a better-protected place or a shelter within one’s locality. This is due to the lack
of granularity in our data since some tweets have a city/county level location instead of a precise
GPS location. Other variants of HMM can be applied to get better accuracy. Also, to verify our
results data from other sources are not used as they are not currently available.
In spite of the above limitations, this study adds to the growing literature on modeling the
dynamics of evacuation behavior. In particular, it investigates the potential of using social media
24
data for understanding evacuation dynamics. However, future research should focus on how to
account for potential biases present in Twitter data. As social media data can be gathered in real
time at large scale during a hurricane, our model can make evacuation traffic predictions and
provide behavioral insights in real time. Since traditional survey data are costly and often
conducted at a post-hurricane period, our method of using social media data can complement the
traditional approaches of modeling evacuation behavior.
ACKNOWLEDGEMENTS
This study was supported by the U.S. Department of Transportation University Transportation
Centers Program under the project “Disaster Analytics: Disaster Preparedness and Management
through Online Social Media” and the U.S. National Science Foundation through the grant CMMI-
1917019. However, the authors are solely responsible for the facts and accuracy of the information
presented in the paper.
SUPPORTING INFORMATION
Manual Checking of the Labeled Dataset
We created an interactive map to manually check whether a user evacuated or not. For each user,
we visualized the home, office, evacuation destination (if any), the visited locations, and the
tweets. We checked the tweets if there was any mention that the user was evacuating or leaving
home during the evacuation period. As an example, Figure S1 shows the snapshot of our manual
checking process for a user. The locations are plotted with a 5-km precision to protect user privacy.
The user, shown in Figure S1, had home and office in Lee County, FL and evacuated to
Birmingham city, Alabama. While evacuating, the user tweeted from Tampa, FL indicating that
he/she was aware of hurricane Irma’s changing path. We checked each user’s home location,
evacuation destination (if any), traveled distance, and tweet text to infer whether the user evacuated
or not. Using this process, we checked 252 evacuated users and 2,319 non-evacuated users. The
manual checking was performed by two individuals.
25
Figure S1: Demonstration of the Manual Checking Process. It shows a snapshot of the
interactive visualization a user’s home, evacuation destination, and visited places—containing
tweet time, tweet text and distance from home.
Word2Vec Model
Word2vec is a predictive model developed by Mikolov et al.(Mikolov et al., 2013b, 2013a). It
contains two distinct algorithms: Continuous Bag-of-Words (CBOW) and Skip-Gram. Skip-Gram
predicts context word given a target word and CBOW predicts the target word given the context
word. Details of word2vec model can be found in refs (Meyer, 2016; Mikolov et al., 2013a, 2013b).
It is a very simple, scalable, fast to train model that can learned over billions of words of text that
will produce exceedingly good word representations. Word2vec uses the theory of meaning to
predict between each word and the context word. Word2Vec contains two distinct algorithms,
Continuous Bag-of-Words (CBOW) and Skip-Gram, where Skip-Gram predict context word given
the target word and CBOW predict the target word given the context word. Figure S2 shows the
CBOW architecture.
26
In CBOW, for a window size C, the inputs are one-hot (size equal to vocabulary size, V)
encoded context words . The hidden layer is N-dimensional. The output/target word
for the context input words is also one hot encoded of size . The input layer and hidden layer
are connected by weights matrix of dimension and the hidden layer and output layer are
connected by another weight matrix of dimension . The workflow of CBOW can be
described in three steps described below.
Forward Propagation
This section describes how the output is computed from the input given that the input and output
weight matrixes are known. Hidden layer output is computed first from the input layer and weight
matrix . This is computed as shown in equation (7)
(7)
Figure S2: The CBOW architecture predicting the current word based on the context
27
which is the weighted average of the input vectors and weight matrix . Next, the input to each
node of output layer is computed by the following
(8)
Where
is the column of the output weight matrix . Finally, the outputs of the output
layer are computed by applying a soft-max function as shown in equation (9).
(8)
As the output is computed, the weight matrix and can be learned from by back-propagating
the errors. The process is discussed in the next section.
Learning the Weight Matrices
To learn the weight matrices, at first the and are randomly initialized. By feeding the training
examples sequentially and observing the predicted output, we get the error which is a function of
difference between the actual and predicted output. It is also known as loss function. The objective
is to maximize the conditional probability of the output word given the input context, therefore our
loss function will be the following:
(9)
Here is the index of the actual output word. The next step is to update the weight matrices based
on the gradient. The gradient of this error is computed with respect to both weight matrices and
correct them in the direction of this gradient. This optimization procedure is known as stochastic
gradient descent. Details of the optimization procedure can be found here (Bottou, 2010).
Word2Vec Sample Results
We train the model with the corpus of hurricane related tweets collected from 4 hurricanes (Irma,
Matthew, Harvey and Sandy). We use minimum word count=3 for preparing the vocabulary. We
tran the model using a window size, C=32 for context words. Once the model is trained each word
in the vocabulary will have a vector representation with its context words. The cosine similarity
between two word vectors is computed using the equation 6. Figure S3 shows the top 15 similar
words for ‘Evacuation’, ‘Evacuating’ and ‘Sheltering’. For example, similar words to evacuation
28
Evacuation
Evacuating
Sheltering
FIGURE S3 Top 15 Word2Vec Cosine Similarity Score of Evacuation, Evacuating, and
Sheltering
contains evac, evacuations, evacs, evacuations…, evacuate etc. which may have been used as a
short form of evacuation and also evac is emergency service provider name in Volusia county.
Other similar words are mandatory, curfews, patrols and a cell number (4092832172) etc.
Evacuation is very related with mandatory order for evacuation. And patrol, curfew is also
related to evacuation because during state of emergency, state issue curfew and police patrol
monitor the situation during hurricane evacuation. This cell number (409-283-2172) is the
contact number of Tyler County - Sheriffs' Association of Texas which was very active during
Harvey evacuation period. Thus, the result shows very good consistency in finding out the
related/similar word
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