"# <center>Applying Topological Data Analysis to Agent Based</center>\n",
"\n",
"<center>by Shawk Masboob</center>"
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"Topological Data Analysis (TDA) tools can be applied to Agent Based Modeling (ABM). TDA can be used for models that reside within complicated spaces. TDA can also be applied to ABM when the outputs are high-dimensional. This report will provide two examples of how TDA can be used with ABM. \n",
"\n",
"#### Example 1 - Biological Aggregation Models\n",
"\n",
"This project applied TDA tools to biological aggregation models such as bird flocks, fish schools, and insect swarms. In these models, the agents interact with each other based on alignment, attraction, and/or repulsion, with each time simulation frame being a point cloud in position-velocity space. [2]. The data used within this research are the numerical simulation outputs from the models. Biological aggregation data is complicated in that there is a large quantity of data. Because of this, powerful tools need to be used that respond best to the complexity of the data. \n",
"\tThe researchers analyzed the topological structure of the point clouds by calculating the Betti numbers and then interpreting the persistent homology. [2]. The Betti numbers capture interesting features by counting the connected components, topological circles, and trapped volumes contained in the data. [2]. \n",
"\tBy applying TDA to the simulation, the researchers found some interesting features: “the homological measures distinguish simulations that the usual alignment oder parameter cannot, …, there is topological similarity between different order parameter time series, the topological calculations recognize the presence of a double mill state.” [2]. These results may have gone unseen if the researcher relied on other methods. \n",
"\n",
"#### Example 2 - Agent Taxonomy\n",
"\n",
"This report analyzed agent trajectories from disaster simulation. The simulation is known as the National Planning Scenario 1: a nuclear device is detonated in Washington DC. The model includes “agent demographics, household structures, daily activity patterns, road networks, and various kinds of locations such as workplaces, schools, government buildings, etc.” [1]. The simulation also includes multiple infrastructures such as power, communication, transportation, and health. The researchers also modeled interactions between human behaviors and the infrastructures. [1]. The researchers sampled 10,000 agents of the total 730,833 that were modeled in the simulation. The aim of this research is to generate a taxonomy of agents based on the results of the simulation. A taxonomy is rich because it not only identifies meaningful types from the data set, but also establishes relationships among those types.” [1]. \n",
"\tThe researchers applied TDA to this simulation in order to gather insight about the structure of the data. TDA is used to find create a topological space where the data set naturally exists. [1]. This space is represented by a proximity graph which can be enhanced into higher dimensions. Higher dimensions reveal more interesting features about the space. For instance, TDA is capable of capturing the shape of the data as a graph regardless of the data points not being in the same clusters. \n",
"\tUsing TDA, the researchers were able to create a taxonomy based on the agents movements: “agents who are (1) close to ground zero from the beginning, but have low exposure, (2) far from ground zero to begin with but move closer had have slightly more exposure, and (3) close to ground zero and have high exposure.” [1]. What is interesting about this taxonomy is that it emerged naturally from the agents movements, behavior, and communication. TDA was able to capture the complicated structure of the data set by allowing the researchers to see the natural connections. "
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"---\n",
"# References\n",
"\n",
"[1] Rezazadegan, Reza, and Samarth Swarup. “Generating an Agent Taxonomy Using Topological Data Analysis.” AAMAS: International Conference on Autonomous Agents and Multiagent Systems, 13 May 2017.\n",
"\n",
"[2] Topaz CM, Ziegelmeier L, Halverson T (2015) Topological Data Analysis of Biological Aggregation Models. PLoS ONE 10(5): e0126383. https://doi.org/10.1371/journal.pone.0126383"
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%% Cell type:markdown id: tags:
# <center>Applying Topological Data Analysis to Agent Based</center>
<center>by Shawk Masboob</center>
%% Cell type:markdown id: tags:
Topological Data Analysis (TDA) tools can be applied to Agent Based Modeling (ABM). TDA can be used for models that reside within complicated spaces. TDA can also be applied to ABM when the outputs are high-dimensional. This report will provide two examples of how TDA can be used with ABM.
#### Example 1 - Biological Aggregation Models
This project applied TDA tools to biological aggregation models such as bird flocks, fish schools, and insect swarms. In these models, the agents interact with each other based on alignment, attraction, and/or repulsion, with each time simulation frame being a point cloud in position-velocity space. [2]. The data used within this research are the numerical simulation outputs from the models. Biological aggregation data is complicated in that there is a large quantity of data. Because of this, powerful tools need to be used that respond best to the complexity of the data.
The researchers analyzed the topological structure of the point clouds by calculating the Betti numbers and then interpreting the persistent homology. [2]. The Betti numbers capture interesting features by counting the connected components, topological circles, and trapped volumes contained in the data. [2].
By applying TDA to the simulation, the researchers found some interesting features: “the homological measures distinguish simulations that the usual alignment oder parameter cannot, …, there is topological similarity between different order parameter time series, the topological calculations recognize the presence of a double mill state.” [2]. These results may have gone unseen if the researcher relied on other methods.
#### Example 2 - Agent Taxonomy
This report analyzed agent trajectories from disaster simulation. The simulation is known as the National Planning Scenario 1: a nuclear device is detonated in Washington DC. The model includes “agent demographics, household structures, daily activity patterns, road networks, and various kinds of locations such as workplaces, schools, government buildings, etc.” [1]. The simulation also includes multiple infrastructures such as power, communication, transportation, and health. The researchers also modeled interactions between human behaviors and the infrastructures. [1]. The researchers sampled 10,000 agents of the total 730,833 that were modeled in the simulation. The aim of this research is to generate a taxonomy of agents based on the results of the simulation. A taxonomy is rich because it not only identifies meaningful types from the data set, but also establishes relationships among those types.” [1].
The researchers applied TDA to this simulation in order to gather insight about the structure of the data. TDA is used to find create a topological space where the data set naturally exists. [1]. This space is represented by a proximity graph which can be enhanced into higher dimensions. Higher dimensions reveal more interesting features about the space. For instance, TDA is capable of capturing the shape of the data as a graph regardless of the data points not being in the same clusters.
Using TDA, the researchers were able to create a taxonomy based on the agents movements: “agents who are (1) close to ground zero from the beginning, but have low exposure, (2) far from ground zero to begin with but move closer had have slightly more exposure, and (3) close to ground zero and have high exposure.” [1]. What is interesting about this taxonomy is that it emerged naturally from the agents movements, behavior, and communication. TDA was able to capture the complicated structure of the data set by allowing the researchers to see the natural connections.
%% Cell type:markdown id: tags:
---
# References
[1] Rezazadegan, Reza, and Samarth Swarup. “Generating an Agent Taxonomy Using Topological Data Analysis.” AAMAS: International Conference on Autonomous Agents and Multiagent Systems, 13 May 2017.
[2] Topaz CM, Ziegelmeier L, Halverson T (2015) Topological Data Analysis of Biological Aggregation Models. PLoS ONE 10(5): e0126383. https://doi.org/10.1371/journal.pone.0126383
