Machine Learning on Gun Protests Diffusion: Cluster-Tree-MLE Analysis
in Space-time Metric Space




Lanston Hau Man Chu
University of Wisconsin-Madison

Machine Learning on Gun Protests Diffusion: Cluster-Tree-MLE Analysis in Space-time Metric Space

Protests for stricter gun control have gained momentum since 2017

How have these gun control protests spread within the United States?

Studies the diffusion pattern of gun-control protests

Using a space-time metric space which combines temporal and spatial information

Spanning trees are constructed for statistical modeling

Image Source: Hammill Post (Left); POPSUGAR (Right)

Existing Models for Diffusion of Social Movements

Existing mathematical models for diffusion of social movements mostly focus on either time or locations

The temporal mathematical model focuses on time versus the number of participants (e.g. Time series or differential equations of growth)

The spatial one evaluates outbreaks statistically

Image Source: Reising, U., 1999  (Left); Andrews, K. and Biggs, M., 2006 (Right)

Diffusion of Protest

Diffusion refers to the spread of something within a social system.

Different practices would spread in a region inside the society (Strang and Soule, 1998).

Enlightenment and encouragement effect to subsequent events, and that geographical factor plays a key role in the spread of movements (Andrews and Biggs, 2006; Reising, 1999).

Geographical factors matter (e.g. Jasmine revolutions in 2012)

Image Source: Elcom (Left)

Cluster Analysis - 3D Scatter Plot

Put latitude, longitude and time together to form a space-time metric space.

3D nebula: A “vessel-shaped” U.S. obtained by Plot3D

More than 2,600 gun related protests from March 2017 to June 2018

Cluster Analysis - Clustering

Cluster analysis is a machine learning technique to group data

Use FindClusters to apply the technique. DistanceFunction -> EuclideanDistance would be specified.

cts=FindClusters[data[[All,{1,-2,-1}]]->data[[All]],DistanceFunction->EuclideanDistance]

plot3=Table[{HighlightMesh[ConvexHullMesh[ctsSel[[i]]],Style[2,colCts[[i]],Opacity[0.5]]]},{i,n}]

Mass Shooting Cases

Relationship between protest and mass shooting in the sense of the cluster analysis

Most severe cases would draw the attention of the public much more than the smaller one

BubbleChart3D would be used for data visualization

Tree of Diffusion

To construct network between the data points inside each cluster

Spanning tree (Graph Theory): A tree which includes all the vertices of the graph, with the minimum possible number of edges

We would use the functions DelaunayMesh and FindSpanningTree as below, where ctsSelJ is the j-th cluster:

graph = IGMeshGraph@DelaunayMesh[ctsSelJ];
plot5=FindSpanningTree[graph,VertexCoordinates->GraphEmbedding@graph,EdgeShapeFunction->"Line",
EdgeStyle->{Thick,Black},VertexSize->Tiny,VertexStyle->Black,PlotTheme->"Default"];

Jump Modeling by Maximum Likelihood Estimation (MLE)

Each edge of the tree refers to a “jump” from one protest to another protest.

Focus on the spatial factor as a whole, and thus would combine latitude and longitude jump on Euclidean sense

Assume that the spatial jumps of each cluster follow the Exponential Distribution

λ of Exp(λ) are obtained by maximum likelihood estimation (MLE)

distml=Table[EstimatedDistribution[edgeVectorsAllJ[[j,All,i]],ExponentialDistribution[λ]],{i,1,2}];
{λ1,λ2}=1/Mean/@distml;

Geographical Visualization - Geographical Diffusion

See how the protest spread inside the cluster at the county level.

GeoListPlot would be applied to each of the nine clusters.

listTimeCountyI={#[[1]],Entity["AdministrativeDivision",{#[[-4]],#[[-3]],"UnitedStates"}]}&/@ctsI
GeoListPlot[Select[listTimeCountyI,#[[1]]≤date&][[All,2]],GeoRange->gr,GeoProjection->"CylindricalEqualArea"]

Cluster spanning October 2017 to March 2, 2018 in the US West coast (geographical diffusion observed):

Geographical Visualization - Burst

Another cluster which is located at the “time of waves” from March 3 to March 31, 2018, in the western US.

When the waves (i.e. March 14 and 24, 2018) arrived, there are bursts of protests

Geographical factors are much less significant

Happens within a very short timeframe

The Two Drivers

The factors of protest diffusion can be separated into two types of main drivers

Geographical Diffusion: Acting in the long timeframe

Burst: Acting in the short timeframe

Future Work

Figure out how to separate the two factors (i.e. Geographical Diffusion and Burst) from the data

Geographical Diffusion can be processed by the similar tree-MLE approach

Burst can be processed further by time series

Apply cluster-tree-MLE techniques to other areas regarding contagion

Contagious diseases; or

Other social practices

Image Source : University of Oxford (Left); WIRED (Right)

Conclusion

Cluster analysis with Euclidean distance on the time-space metric space of the gun protests events.

Significant relationship between the bottom boundary of the clusters and the severe mass shooting cases.

Spanning trees are constructed as the network between protest events.

The tree’s edge (i.e. the jump) can be modeled by Maximum Likelihood Estimation (MLE)

Factors of protest diffusion can be separated into two types of main drivers:  geographical diffusion and burst, respectively acting in the long and short timeframe.

References and Source Code

Source Code and Data: https://github.com/lanstonchu/GunProtestDiffusion

Andrews, K. and Biggs, M. (2006). The Dynamics of Protest Diffusion: Movement Organizations, Social Networks, and News Media in the 1960 Sit-Ins. American Sociological Review, 71(5), pp.752-777.

Cohen, J. and Tita, G. (1999). Diffusion in Homicide: Exploring a General Method for Detecting Spatial Diffusion Processes. Journal of Quantitative Criminology, 15(4), pp.451-493.

Lohmann, S. (1994). The Dynamics of Informational Cascades: The Monday Demonstrations in Leipzig, East Germany, 1989–91. World Politics, 47(01), pp.42-101.

Reising, U. (1999). United in Opposition A Cross-National Time-Series Analysis of European Protest in Three Selected Countries. Journal of Conflict Resolution, 43(3), pp.317-342.

Strang, D. and Soule, S. (1998). Diffusion in Organizations and Social Movements: From Hybrid Corn to Poison Pills. Annual Review of Sociology, 24(1), pp.265-290.

End of Presentation

Thank you!