Spatiotemporal Patterns and Driving Factors on Crime Changing During Black Lives Matter Protests

: The death of George Floyd has brought a new wave of 2020 Black Lives Matter (BLM) protests into U.S. cities. Protests happened in a few cities accompanied by reports of violence over the ﬁrst few days. The protests appear to be related to rising crime. This study uses newly collected crime data in 50 U.S. cities / counties to explore the spatiotemporal crime changes under BLM protests and to estimate the driving factors of burglary induced by the BLM protest. Four spatial and statistic models were used, including the Average Nearest Neighbor (ANN), Hotspot Analysis, Least Absolute Shrinkage, and Selection Operator (LASSO), and Binary Logistic Regression. The results show that (1) crime, especially burglary, has risen sharply in a few cities / counties, yet heterogeneity exists across cities / counties; (2) the volume and spatial distribution of certain crime types changed under BLM protest, the activity of burglary clustered in certain regions during protests period; (3) education, race, demographic, and crime rate in 2019 are related with burglary changes during BLM protests. The ﬁndings from this study can provide valuable information for ensuring the capabilities of the police and governmental agencies to deal with the evolving crisis. These results make an important contribution not only to the government in dealing with emergencies and adjustment of policy instructions, but also to the prediction of crime during large-scale social events.


Introduction
Investigating spatiotemporal distribution patterns and driving factors of crime are continuing concerns within the geography of crime and criminological research [1,2]. The general hypothesis is that social disorganization theory, low economic status, ethnic heterogeneity, residential instability, and family disruption lead to community social disorganization and lack of informal social control, which, in turn, increases crime and delinquency rates [3,4]. The routine activities theory argues that (macro-level) social changes introduce adjustments in people's lifestyles and, subsequently, contribute to the supply of crime opportunities (i.e., the agglomeration in space and time of motivated offenders, suitable targets, and the absence of capable guardians) [5,6]. These two foundational, place-based criminological theories relate socioeconomic factors (i.e., demographic, ethnicity, economic, social, family disruption, marital status, and urbanization) to criminal events [7][8][9].
Black Lives Matter (BLM) is a decentralized movement advocating for non-violent civil disobedience in protest against incidents of police brutality and all racially motivated violence Figure 1 shows the workflow of the entire analytical process. First, the collection and processing of the dataset are described in Sections 2.2.1 and 2.2.2. Next, methods are introduced from two aspects in Sections 2.3.1 and 2.3.2. Then, the research contents are divided into four parts: (1) an overall temporal trend of crime during the COVID-19 pandemic (Section 3.1); (2) an overall change in different crime types (Section 3.2); (3) spatiotemporal variations of burglary during BLM protects (Section 3.3), and (4) impacts of driving factors on burglary changing (Section 3.4). Note that based on the results of Sections 3.1 and 3.2, the change in burglary accurately reflects the change in crime during the BLM protest compared to other crime types or total crimes. Therefore, Sections 3.3 and 3.4 will also focus on burglary instead of total crime. Figure 1 shows the workflow of the entire analytical process. First, the collection and processing of the dataset are described in Sections 2.2.1 and 2.2.2. Next, methods are introduced from two aspects in Sections 2.3.1 and 2.3.2. Then, the research contents are divided into four parts: (1) an overall temporal trend of crime during the COVID-19 pandemic (Section 3.1); (2) an overall change in different crime types (Section 3.2); (3) spatiotemporal variations of burglary during BLM protects (Section 3.3), and (4) impacts of driving factors on burglary changing (Section 3.4). Note that based on the results of Section 3.1 and 3.2, the change in burglary accurately reflects the change in crime during the BLM protest compared to other crime types or total crimes. Therefore, Sections 3.3 and 3.4 will also focus on burglary instead of total crime. The analysis time (from 15 May 2020 to 15 June 2020) encompasses the entirety of protests, including George Floyd's death (25 May 2020) and the outbreak of urban protests. In this paper, multiple spatial and statistical analysis methods were used in the research process. First, we created a simple descriptive graph to depict crime counts for the entirety of the data. To take account of the spatial nature of the data, Average Nearest Neighbor (ANN) [24] and hotspot analysis [25] were used to analyze the spatial distribution and its changes. Finally, to detect the impact of the influencing factors on the burglary changes during BLM protests, we made use of the Least Absolute Shrinkage and Selection Operator (LASSO) and Binary Logistic Regression model for feature selection and driving factors analysis. All the methods were accomplished through programs Python or R.

Crime Dataset
The crime events data were obtained from the SpotCrime website [26], which is a crime incident aggregator and public crime visualization service. The SpotCrime website collects crime events data from police departments, verified news reports, user-generated content submissions, and other validated sources [27]. A comprehensive crime data scheme is provided in the SpotCrime dataset, including description, referral source, and spatiotemporal attributes, e.g., date, time, location address, and coordinates by latitude and longitude. Crime types are classified into 9 categories, including assault, arson, arrest, burglary, robbery, shooting, theft, vandalism, and others. The crime events data are organized and presented by a combination of county/city name and date under web pages. In this research, crime incidents between 1 January and 15 June 2019, and 2020 were collected by a customized web crawler and geocoded geocoder library in python. In addition to this, 50 counties/cities (including 12 cities and 38 counties) were selected from the overall 3370 regions in the SpotCrime website based on the following requirements. The analysis time (from 15 May 2020 to 15 June 2020) encompasses the entirety of protests, including George Floyd's death (25 May 2020) and the outbreak of urban protests. In this paper, multiple spatial and statistical analysis methods were used in the research process. First, we created a simple descriptive graph to depict crime counts for the entirety of the data. To take account of the spatial nature of the data, Average Nearest Neighbor (ANN) [24] and hotspot analysis [25] were used to analyze the spatial distribution and its changes. Finally, to detect the impact of the influencing factors on the burglary changes during BLM protests, we made use of the Least Absolute Shrinkage and Selection Operator (LASSO) and Binary Logistic Regression model for feature selection and driving factors analysis. All the methods were accomplished through programs Python or R.

Crime Dataset
The crime events data were obtained from the SpotCrime website [26], which is a crime incident aggregator and public crime visualization service. The SpotCrime website collects crime events data from police departments, verified news reports, user-generated content submissions, and other validated sources [27]. A comprehensive crime data scheme is provided in the SpotCrime dataset, including description, referral source, and spatiotemporal attributes, e.g., date, time, location address, and coordinates by latitude and longitude. Crime types are classified into 9 categories, including assault, arson, arrest, burglary, robbery, shooting, theft, vandalism, and others. The crime events data are organized and presented by a combination of county/city name and date under web pages. In this research, crime incidents between 1 January and 15 June 2019, and 2020 were collected by a customized web crawler and geocoded geocoder library in python. In addition to this, 50 counties/cities (including ISPRS Int. J. Geo-Inf. 2020, 9, 640 4 of 19 12 cities and 38 counties) were selected from the overall 3370 regions in the SpotCrime website based on the following requirements.

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The crime events data missing days for each region should be less than 30 days in 2020 to maintain data consistency for long period time-series analysis.

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The average number of all crime events is higher than 15 each day in individual regions to avoid data noising by small samples.
The selected 50 counties/cities list and spatial distribution in the U.S. are shown in Table 1 and Figure 2, respectively. Fifty counties/cities are distributed in 20 states and cover over about 60,770 square miles. Thirteen counties/cities with a population of over one million people, and 4 counties with a population of fewer than 10,000 people. Additionally, the U.S. median household income was $63,179 in 2018. seven cities and twenty-one counties with a median household income in 2018 above average. Major, medium, and small counties/cities are all considered in this research. The research results thus will partly represent crime changes during BLM protest in the U.S.

•
The crime events data missing days for each region should be less than 30 days in 2020 to maintain data consistency for long period time-series analysis.

•
The average number of all crime events is higher than 15 each day in individual regions to avoid data noising by small samples.
The selected 50 counties/cities list and spatial distribution in the U.S. are shown in Table 1 and Figure 2, respectively. Fifty counties/cities are distributed in 20 states and cover over about 60,770 square miles. Thirteen counties/cities with a population of over one million people, and 4 counties with a population of fewer than 10,000 people. Additionally, the U.S. median household income was $63,179 in 2018. seven cities and twenty-one counties with a median household income in 2018 above average. Major, medium, and small counties/cities are all considered in this research. The research results thus will partly represent crime changes during BLM protest in the U.S.
To validate the crime dataset collected from SpotCrime, we randomly selected and downloaded the available crime events data from publicly available official datasets. A quantitative comparison with the SpotCrime data collection and data sources was conducted from a statistical and spatiotemporal perspective. We found that the data match well in consistency and accuracy. Additionally, we checked the operationalizations of crime included in SpotCrime and found that "arrest" and "other" are not Part I index crimes according to the FBI's Uniform Crime Reporting (UCR) program [28]. Therefore, "arrest" and "other" categories are excluded from this research.   To validate the crime dataset collected from SpotCrime, we randomly selected and downloaded the available crime events data from publicly available official datasets. A quantitative comparison with the SpotCrime data collection and data sources was conducted from a statistical and spatiotemporal perspective. We found that the data match well in consistency and accuracy. Additionally, we checked the operationalizations of crime included in SpotCrime and found that "arrest" and "other" are not Part I index crimes according to the FBI's Uniform Crime Reporting (UCR) program [28]. Therefore, "arrest" and "other" categories are excluded from this research.

Driving Factors Datasets
Inspired by social disorganization theory and routine activities theory, relevant factors including demographic, education, poverty, race, and economic factors are collected in our study. As an estimated value, population, age, sex, race, education, and poverty were collected from U.S. Census Bureau reports. After the preprocessing, the factors of population density, population under 18 years, population over 60 years, age dependency ratio, males per 100 females, less than 9th grade, Bachelor's degree, median household income, below poverty level, White population, and Black or African American population were obtained. The diversity index captures the racial and ethnic diversity of a geographic area in a single number, from 0 to 100 [29], and is provided by Esri [30]. Additionally, the crime rate per 10,000 people from 1 January 2019, to 15 June 2019, is considered as a driving factor in our study. This is because the counties/cities with higher crime rates have environments that are more likely to cause crime. It is necessary to detect the relationship between the crime change during BLM protests with the crime rate in the same period last year. The descriptive statistics for these variables are provided in Table 2.

Spatial Distribution Analysis
To identify the space concentration level and distribution of crime during BLM protests, we utilized the ANN model and hotspot mapping analysis. Here, the ANN method measures the distance between each crime point and its nearest neighbor's location [24]. It is used to quantify and compare the spatial distribution of crime within a county/city over time. If the ANN ratio is less than 1, the pattern exhibits clustering. If the value is greater than 1, the trend is toward dispersion. The ANN ratio of county/city c is defined as follows: where D O is the mean distance between each crime point and its nearest neighbor. D E is the expected mean distance for n points given in a random pattern. d i represents the distance between the point i and its nearest neighboring feature. n c corresponds to the total number of points in county/city c. A c represent the area of county/city c. Note that we use the great-circle distance as the calculation method of distance. Hotspot mapping is a popular analytical technique in the geography of crime. KDE model, a hotspot mapping technique, is regarded as the most suitable spatial analysis technique for visualizing crime data. It can be used for visually identifying hotspots of crime, and spatially interpreting location, size, shape, and orientation of clusters of crime incidents [31]. The Folium package in Python was used in hotspot analysis.

Logistic Regression Model
The Logistic Regression model was used to estimate the effect of driving factors on the crime changing during BLM protests. Binary Logistic Regression is a statistical technique used to predict the relationship between predictors (independent variables) and a predicted variable (the dependent variable). In this section, we built the model from three steps: dependent variable definition, independent variables selection, and modeling building.
(1) Dependent variable definition We calculated the changing rate of crime to represent the changing degree in crime during the BLM protests. The higher the growth rates, the higher the crime than the average. The changing rate is defined as follows: where, avg n a f ter is the n days' average crime rate after the start date of protests, avg n be f ore represents the n days' average crime rate before the start date of protests. n is decided based on the peak crime duration. The start dates of protests were collected from news reports.
It is not appropriate to directly use the changing rate as the dependent variable of the linear model, because we did not eliminate random fluctuations caused by seasonality and periodicity of crime. However, minor random fluctuations of crime will be ignored through classification. This is also the reason we selected the Logistic Regression model for our research. Therefore, we divided counties/cities into two categories based on the value of the changing rate, defined as follows: where, r represents the changing rate during the BLM protests. σ is the threshold value. y c = 1 means that crime in the city c has a big variation during BLM protests, y c = 0 means the opposite. y = y 1 , y 2 , · · · , y N is defined as the dependent variable, N is the number of counties and cities. The result of the classification is defined as the dependent variable.
(2) Independent variables selection Independent variable selection is one of the main techniques for selecting an important subset of features as a specific factor in model development, particularly for variables with collinearity. Variable selection methods target removing excess or insignificant variables [32]. LASSO is a regression analysis method that performs variable selection while in regression analysis, to enhance the interpretability of the statistical model it produces [33,34]. Lasso regularization is easily extended to Generalized Linear Models (GML). When the response variable is binary, the optimization objective for a Logistic regression model is defined as [35]: where Y represents the outcome, consisting of N cases. X = (x 1 , x 2 , · · · , x m ) is the covariate. λ is a prespecified free parameter in Constant that multiplies the L1 term. The larger the value of λ, the greater the amount of shrinkage. R glmnet function has been used in experiments.
(3) Modeling building Finally, the binary logistic regression model is defined as follows [36]: where p is the probability of the event occurring, p = P(y c = 1). x i := (x 1 , x 2 , · · · , x n ) is the independent variable selected by the LASSO model. β 0 , β 1 , · · · , β n are regression coefficients of variables.

Overall Trend of Crime during COVID-19 Pandemic
This subsection tends to offer overall analytics on crime trend during the COVID-19 crisis and provide a background that BLM protests took place. In Figure 3, we display the distribution of the total crime rate per 10,000 people from January 1, 2020, to June 15, 2020, based on a boxplot. Each box represents a county/city, plotted by county/city id (Table 1) on the horizontal axis and crime rate per 10,000 people on the vertical. The boxes are sorted by a median of the crime rates (shown as the orange line). The overall trend of crime rate in Figure 3 illustrates the counties/cities with lower crime rates are tighter than counties/cities with higher crime rates, and counties/cities with higher crime rates have more outliers (shown as red circles). Finally, the binary logistic regression model is defined as follows [36]: where p is the probability of the event occurring, ( ) are regression coefficients of variables.

Overall Trend of Crime during COVID-19 Pandemic
This subsection tends to offer overall analytics on crime trend during the COVID-19 crisis and provide a background that BLM protests took place. In Figure 3, we display the distribution of the total crime rate per 10,000 people from January 1, 2020, to June 15, 2020, based on a boxplot. Each box represents a county/city, plotted by county/city id (Table 1) on the horizontal axis and crime rate per 10,000 people on the vertical. The boxes are sorted by a median of the crime rates (shown as the orange line). The overall trend of crime rate in Figure 3 illustrates the counties/cities with lower crime rates are tighter than counties/cities with higher crime rates, and counties/cities with higher crime rates have more outliers (shown as red circles). We manually selected nine typical counties and cities from 50 counties/cities with different scales to visualize the current patterns. The daily time series (from 1 January 2020, to 15 June 2020) for the total crime in several counties/cities are shown in Figure 4. The results do not show the same trend of crime in different cities or counties during the COVID-19 pandemic. In Figure 4a-e, crime dropped between the date that the first confirmed case was reported and the date that the stay-at-home order was implemented, then slowly increased or remained stable when the stay-at-home order was implemented. Meanwhile, in (f)-(i), crime did not change during the COVID-19 pandemic. The overall trend of crime during the COVID-19 pandemic concur with those seen in other studies. We manually selected nine typical counties and cities from 50 counties/cities with different scales to visualize the current patterns. The daily time series (from 1 January 2020, to 15 June 2020) for the total crime in several counties/cities are shown in Figure 4. The results do not show the same trend of crime in different cities or counties during the COVID-19 pandemic. In Figure 4a-e, crime dropped between the date that the first confirmed case was reported and the date that the stay-at-home order was implemented, then slowly increased or remained stable when the stay-at-home order was implemented.
Meanwhile, in (f)-(i), crime did not change during the COVID-19 pandemic. The overall trend of crime during the COVID-19 pandemic concur with those seen in other studies. However, we only provide an analysis of the total number of crimes, noting that not all crime types have the same trend under the COVID-19 pandemic. after the BLM protests for all counties/cities. This suggested that the BLM protest took place in the backdrop of relative crime stability. For the current stage, we only provide an analysis of the total number of crimes; trends in different types of crime are needed. To summarize, Figure 4 does not show the same trend of crime in different cities or counties during the COVID-19 pandemic and BLM protests, i.e., heterogeneity exists across cities/counties. The heterogeneity between counties/cities may be related to their socioeconomic difference. We will explore the changes in different types of crime, the spatiotemporal variations of burglary, and the driving factors of burglary changes during BLM protests in the next three subsections.

Changes in Different Crime Types during Black Lives Matter Protests
From the overall time series analysis, crime changed a lot in a few counties/cities during the BLM protests, and there is heterogeneity across counties/cities in the context of the COVID-19 pandemic. However, the overall trend of crime cannot reflect all types of crime. The daily time series for the various crime types are shown in Figure 5. Lines with different colors represent seven different crime types.
Figure 5a-f show that there are sharp changes in burglary in both cities. Minor increases exist in vandalism and assault in several cities, such as vandalism increasing slightly in San Francisco and Chicago, along with assault in Los Angeles County and Minneapolis. The trends of other crime types changed less, and they exhibited a consistent fluctuation in relation to other periods. That means other crime types except burglary were not seriously affected by BLM protests. This is likely because the Covid-19 epidemic shifted routine activities by moving owners and customers away from business locations, leaving them highly vulnerable to burglary and trespassing [19]. In addition, As shown in Figure 4a-f, crime rose sharply in a few cities/counties during the BLM protests. The trend of crime in Figure 4g-i performs a consistent fluctuation with other periods. Additionally, there were no outliers (greater than or less than three standard deviations) in the days before and after the BLM protests for all counties/cities. This suggested that the BLM protest took place in the backdrop of relative crime stability. For the current stage, we only provide an analysis of the total number of crimes; trends in different types of crime are needed.
To summarize, Figure 4 does not show the same trend of crime in different cities or counties during the COVID-19 pandemic and BLM protests, i.e., heterogeneity exists across cities/counties. The heterogeneity between counties/cities may be related to their socioeconomic difference. We will explore the changes in different types of crime, the spatiotemporal variations of burglary, and the driving factors of burglary changes during BLM protests in the next three subsections.

Changes in Different Crime Types during Black Lives Matter Protests
From the overall time series analysis, crime changed a lot in a few counties/cities during the BLM protests, and there is heterogeneity across counties/cities in the context of the COVID-19 pandemic. However, the overall trend of crime cannot reflect all types of crime. The daily time series for the various crime types are shown in Figure 5. Lines with different colors represent seven different crime types.
value. Hence, the effects of the protests on burglary appear to be somewhat transitory and fade over the short-run period, as the violence and scope of the protests abate. Thus, the protests in these cities that were accompanied by crime became peaceful after three to five days. Figure 5g-i shows that crime has no obvious changes in these counties in late May or early June 2020 when it would be expected to increase. Compared with bigger counties/cities with higher populations (i.e., Los Angeles County, New York City), Shelby County, Olmsted County, and Newberry County had smaller protests and were not seriously affected by the BLM Protests.
In summary, Figure 5 does not show the same trend in different crime types and cities/counties during the BLM protests. The change in burglary accurately reflects the change in crime during the BLM protest compared to other crime types or total crimes. The heterogeneity of burglary between counties/cities may be related to their socioeconomic difference. We will analyze the spatiotemporal patterns and driving factors of burglary changes (instead of total crime changes) during BLM protests in the next two subsections.   That means other crime types except burglary were not seriously affected by BLM protests. This is likely because the Covid-19 epidemic shifted routine activities by moving owners and customers away from business locations, leaving them highly vulnerable to burglary and trespassing [19]. In addition, protests happened in a few cities accompanied by reports of burglary, and dozens of shops and stores have been stolen from and damaged during protests periods. Although there are reports that the numbers of homicides and victims shot increased during BLM protests [37,38], the increase was less obvious compared with burglary.
Additionally, burglary peaked between 27 May 2020, and 3 Jun 3 2020, and continued three to five days since the start of the early protests. Then, the number of burglaries decreased to their regular value. Hence, the effects of the protests on burglary appear to be somewhat transitory and fade over the short-run period, as the violence and scope of the protests abate. Thus, the protests in these cities that were accompanied by crime became peaceful after three to five days. Figure 5g-i shows that crime has no obvious changes in these counties in late May or early June 2020 when it would be expected to increase. Compared with bigger counties/cities with higher populations (i.e., Los Angeles County, New York City), Shelby County, Olmsted County, and Newberry County had smaller protests and were not seriously affected by the BLM Protests.
In summary, Figure 5 does not show the same trend in different crime types and cities/counties during the BLM protests. The change in burglary accurately reflects the change in crime during the BLM protest compared to other crime types or total crimes. The heterogeneity of burglary between counties/cities may be related to their socioeconomic difference. We will analyze the spatiotemporal patterns and driving factors of burglary changes (instead of total crime changes) during BLM protests in the next two subsections.

Spatiotemporal Variations of Burglary during Black Lives Matter Protests
We analyzed the spatial distribution changes in burglary instead of total crime. It should be noted that geocoding the locations of these crimes introduces error. We made topologic analysis and deleted points outside the boundary of cities/counties. This may slightly affect the results of the average nearest neighbor analysis. The resulting ANN shows that counties/cities with higher changes in burglary showed spatial aggregation during protests. This is probably because burglaries centered around the protests. The spatial distribution of counties/cities with lower changing rates is not obvious. Figure 6 illustrates the average nearest neighbor values in burglary for six sample counties/cities. Bars with brown color mean that the P values are greater than or equal to 0.05, and ANN values are statistically significant. The red line represents the start day of protests in each city/county. ANN values decrease after the start of the protest, compared to before in both cities. The trend of ANN values illustrates that the activity of burglary clustered in several certain regions during the protests period. Additionally, different from Los Angeles County and San Francisco, burglaries in Chicago, Washington DC, and Minneapolis are considered more clustered than ever before.

Spatiotemporal Variations of Burglary during Black Lives Matter Protests
We analyzed the spatial distribution changes in burglary instead of total crime. It should be noted that geocoding the locations of these crimes introduces error. We made topologic analysis and deleted points outside the boundary of cities/counties. This may slightly affect the results of the average nearest neighbor analysis. The resulting ANN shows that counties/cities with higher changes in burglary showed spatial aggregation during protests. This is probably because burglaries centered around the protests. The spatial distribution of counties/cities with lower changing rates is not obvious. Figure 6 illustrates the average nearest neighbor values in burglary for six sample counties/cities. Bars with brown color mean that the P values are greater than or equal to 0.05, and ANN values are statistically significant. The red line represents the start day of protests in each city/county. ANN values decrease after the start of the protest, compared to before in both cities. The trend of ANN values illustrates that the activity of burglary clustered in several certain regions during the protests period. Additionally, different from Los Angeles County and San Francisco, burglaries in Chicago, Washington D.C., and Minneapolis are considered more clustered than ever before. We selected the day with the peak value of burglary, the 7th day before, and the 7th day after the peak day for each county/city. The second figure (i.e., (b)) in Figures 7-12 shows the hotspots maps of the peak day. Hot spots can be found in both counties/cities during BLM protests. Figures 7-12 shows that burglaries are spread throughout the city in the usual time and mainly occur in the downtown areas during BLM protests. This means burglaries gathered in space on the peak day, We selected the day with the peak value of burglary, the 7th day before, and the 7th day after the peak day for each county/city. The second figure (i.e., (b)) in Figures 7-12 shows the hotspots maps of the peak day. Hot spots can be found in both counties/cities during BLM protests. Figures 7-12 shows that burglaries are spread throughout the city in the usual time and mainly occur in the downtown areas during BLM protests. This means burglaries gathered in space on the peak day, coinciding with the ANN analysis. Furthermore, the spatial distribution of burglary in Chicago, San Francisco, and Minneapolis exhibits a clear spatial concentration pattern along the street. This is because burglaries occurred in non-residential areas where protests gathered, where there are many commercial buildings and shops along the street. Therefore, both the volume and distribution of burglaries were altered during BLM protests. The spike in burglaries is characterized by its abruptness, size, brevity, and clustering. coinciding with the ANN analysis. Furthermore, the spatial distribution of burglary in Chicago, San Francisco, and Minneapolis exhibits a clear spatial concentration pattern along the street. This is because burglaries occurred in non-residential areas where protests gathered, where there are many commercial buildings and shops along the street. Therefore, both the volume and distribution of burglaries were altered during BLM protests. The spike in burglaries is characterized by its abruptness, size, brevity, and clustering.   coinciding with the ANN analysis. Furthermore, the spatial distribution of burglary in Chicago, San Francisco, and Minneapolis exhibits a clear spatial concentration pattern along the street. This is because burglaries occurred in non-residential areas where protests gathered, where there are many commercial buildings and shops along the street. Therefore, both the volume and distribution of burglaries were altered during BLM protests. The spike in burglaries is characterized by its abruptness, size, brevity, and clustering.

Changing Rate of Burglary
The results of Sections 3.1 and 3.2 lead us to explore which counties/cities have changed obviously with burglary during the BLM protest. To explain the degree of effect of protests on burglary, we calculated the changing rate using Equation (2). In addition, the parameter n is 5, because burglary usually peaked and continued three to five days from the start of the early protests.

Changing Rate of Burglary
The results of Sections 3.1 and 3.2 lead us to explore which counties/cities have changed obviously with burglary during the BLM protest. To explain the degree of effect of protests on burglary, we calculated the changing rate using Equation (2). In addition, the parameter n is 5, because burglary usually peaked and continued three to five days from the start of the early protests. It is worth noting that when the number of burglaries is less than two per day, the rate will have a large fluctuation when adding or subtracting a small number. Therefore, we removed the cities/counties with fewer than two burglaries per day.
The changing rates of burglary in the remaining 36 cities/counties are provided in Table 3. The higher the growth rates, the higher the burglary than the average. The changing rate reflects the severity of burglaries and the effect of protests on crime. Table 3 shows that the changing rates of cities/counties differ greatly. All the cities listed in Table 3 were accompanied by mainstream media reports of burglaries on protests. Specifically, Minneapolis, Fairfax County, Boston, St. Paul, Chicago, and Washington DC had more burglaries than ever before. The result of the classification is shown in the fifth and tenth columns in Table 3. Additionally, Figure 13 shows the distribution of research regions with and without a 50% increase in burglary. The changing rates in 12 areas exceed 50%, and there are 10 areas (except Minneapolis and St. Paul) with a population of more than 50,000 people. This means big changes in burglary exist in large counties/cities. However, not all major counties/cities have experienced a sudden increase in burglaries during BLM protests, such as Orange County, CA, and Miami-Dade County, FL.  Figure 13. Distribution of burglary changing rate. Red circles denote the research regions where the burglary has increased by more than 50%. Figure 13. Distribution of burglary changing rate. Red circles denote the research regions where the burglary has increased by more than 50%.

Independent Variables Selection
The Person Correlation Coefficient (PCC) [39,40] for these variables are provided in Table 4. The correlations shown in Table 4 exhibit a surprising relationship, with the highest of these correlations involving the 60 years and overpopulation and age dependency ratio (r = 0.86, p-value < 0.01). Owning a Bachelor's degree has a strong positive relationship with the median household income (r = 0.79, p-value < 0.01). Strong positive relationships are present between the less than 9th grade and diversity index (r = 0.69, p-value < 0.01), and population under 18 years with males per 100 females (r = 0.66, p-value < 0.01). With regard to the statistical modeling below, some correlations do cause some concerns for collinearity. The effect of collinearity makes the regression coefficients unreliable. Therefore, feature selection is needed in choosing a subset of important features to be specific factors for model development. LASSO was used in our experiments. Figure 14 demonstrates the variable importance with their probabilities. During the feature selection process, the variables that still have a non-zero coefficient are selected to be part of the model. For the value of λ lse (λ lse gives a model such that error is within one standard error of the minimum), the following five variables were selected: Bachelor's degree, diversity index, age dependency ratio, population density, and 2019 crime rate per 10,000 people. This means education, race, demographic, and crime rate in 2019 are related to burglary changes during BLM protests. Specifically, the crime rate in 2019 has a significant relationship with burglary changes compared with other variables. over 60 years; X4: age dependency ratio; X5: males per 100 females; X6: less than 9th grade; X7: Bachelor's degree; X8: median household income; X9: below the poverty level; X10: White population; X11: Black or African American population; X12: diversity index; X13: 2019 crime per 10,000 people.
The effect of collinearity makes the regression coefficients unreliable. Therefore, feature selection is needed in choosing a subset of important features to be specific factors for model development. LASSO was used in our experiments. Figure 14 demonstrates the variable importance with their probabilities. During the feature selection process, the variables that still have a non-zero coefficient are selected to be part of the model. For the value of lse λ ( lse λ gives a model such that error is within one standard error of the minimum), the following five variables were selected: Bachelor's degree, diversity index, age dependency ratio, population density, and 2019 crime rate per 10,000 people. This means education, race, demographic, and crime rate in 2019 are related to burglary changes during BLM protests. Specifically, the crime rate in 2019 has a significant relationship with burglary changes compared with other variables.

Driving Factors Analysis
The result of Binary Logistic Regression is shown in Table 5. The Pseudo R square is 0.6479, and the p-value of this model is less than 0.01. Somewhat surprisingly, except for a Bachelor's degree, the P values of other independent variables are all greater than 0.1. There is no significant statistical evidence that x 1 , x 4 , x 12 , x 13 are related to the changing rate of burglary in this logistic regression model. To check the reliability of the results, we also performed experiments with a linear regression model, and the results were consistent. We observed that a Bachelor's degree had a strong and significant positive effect on the changing rate of burglary. Current research suggests that education is shown to reduce crime [41,42]. Different from the effect of education on crime, counties/cities with higher educated rates have a positive effect on the burglary changing rate. During the protests, burglaries are more likely to occur in counties/cities with a higher percentage of Bachelor's degrees.
Additionally, the odds ratios of crime rate per 10,000 people in 2019 are greater than the other four variables. For every one-unit increase in crime rate per 10,000 people in 2019, there is an increase of 4.485 for burglary changing rate during protests. That means the crime rate per 10,000 people in 2019 has a positive effect on the changing rate of burglary. This is consistent with the result of LASSO.
It is worth noting that the percent of white or black people are not selected as determinant factors in LASSO, although BLM is a movement in protest against incidents of all racially motivated violence against Black people. This is probably because the majority of Americans, across all racial and ethnic groups, have expressed support for the Black Lives Matter movement [43].

Discussion
Although society and social media have widely reported the protests and responded to the George Floyd incident, the incident was not a sentinel incident in changing the direction of the overall decline in crime. Our analysis was well-positioned to identify the variables of crime and driving factors during BLM protests among the 50 samples of U.S. cities examined to date. We observed sharp increases in burglaries for a particular time period in some locations, but no widespread changes were detected in overall crime trends among the counties/cities in our study. We also found that the burglary case number went back to a normal level that did not change substantially 5 days later. Therefore, our analysis confirms the long-standing understanding that the cause of crime reflects a slow process and is not affected by emergencies [22,44]. The change of crime number, no matter increase or decrease, in a short time would go back to a normal stage soon after the end of the emergency event. Additionally, there are several limitations to the present study.
This study is not the final word on the crime variations. We did not consider the persistent changes of burglary after15 June 2020 due to a lack of data, which is a missing of seasonal analysis during the BLM period. Similarly, since we only calculated the change rate for 2020 (instead of a difference in difference, e.g., comparing the change rate with 2019 data), we essentially could not account for potential trending in the data.
Secondly, the spatiotemporal variations reflect the locations of protests. While the six cities in Figures 7-12 account for both a large-scale hotspot in the peak day of burglaries, it omits more precise area analysis such as residential and nonresidential areas. There may be apparent differences based on the land use type that our analysis does not capture. In addition, the distribution of burglaries may also have a connection with the distributions of commercial districts such as shops and stores. Police and business owners could take steps to prevent these events from happening again in the future. This is a typical data mining method used to test the effect of driving factors on crime by identifying the importance of the features. Different from the statistical models, the significance could not be easily interpreted.
Additionally, tragic events such as the death of Trayvon Martin, Michael Brown, George Floyd, have sparked widespread attention and discussion over such as police accountability and police legitimacy. Such discussion, however, should be informed by solid data and detailed analysis. Policy decisions that are not based on evidence can have a negative impact on public safety and reduce government credibility. We sought to bring empirical evidence to the effect of protests on crime. We hope that our results will help provide evidence-based discussions about the crime variations and its reasons during BLM protests, especially a broader discussion of changes in crime trends.

Conclusions
This research offers one of the first empirical analyses of the spatiotemporal patterns and influencing factors on crime rates during the 2020 BLM protests, which has been a point of concern among public safety and health officials and the media. Specifically, we use multiple spatial (ANN and KDE) and statistical analysis (LASSO and Logistic Regression) methods to model the spatiotemporal trend and driving factors of burglary during BLM protests in 50 counties and cities, U.S. The results reflect the overall crime changes during BLM protests in the United States to a certain extent.
From the results of the experiments and statistics, we show that (1) crime in the U.S. appears to be going down overall during the COVID-19 pandemic, but the BLM protest took place in the backdrop of relative crime stability; (2) different temporal patterns of crime rates emerge during the 2020 BLM protests in the U.S.; (3) only certain types of crime, i.e., burglary, have a sharp change in numbers and spatial distribution; and (4) education, race, demographic, and crime rate in 2019 are related with burglary changes during BLM protests. Specifically, counties/cities with higher education rates have a positive effect on the burglary changing rate. The results offer suggestions and a basis for the police and governmental agencies to take steps in preventing the diffusion of violent protests and the increase in crimes.
Finally, as a future augmentation of our work, detailed spatiotemporal analysis [42,45] at a blocklevel or community-level will better reflect crime changes in the county/city. Additionally, violent assault and gun violence are important areas of research in criminology, and more attention will be paid to these two crime types in metropolitan cities. The spatial distribution character inspired us to conduct further study on the impact of point-of-interests on crime using various methods such as the Poisson regression model and ARIMA [14]. More detailed data, e.g., the crime incident attributes, including the suspect anonymized background, would help explain the changes. For example, does the influx of people with lower education flooding to an area with a well-educated population drive up the crime rates?