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Erin Taylor
Ian Frankenburg
Eric Peshkin
Mentor: Joe Marion
Client: Dr. John Harer,
Geometric Data Analytics
Geometry and Topology for Data
Problem:
● Detect abnormal behaviour in
communications networks
using principles of statistics,
topological data analysis, and
machine learning.
● Capture both local and global
anomalies using a
comprehensive combination of
mathematical methods.
Computer Network
Data
Features
Anomaly Detection
Algorithms
Leveraging topological and statistical tools to uncover structure in data
Methods
We built a network with nodes representing
different IP addresses and edges representing
communications between them. Topological tools
allowed us to study how the connectivity within the
network changed as edges were added between
nodes.
We automated the process of fitting a probability
distribution to our data. Our utility fit many potential
probability distributions and used AIC to determine
the best one. This gave us a probabilistic basis for
separating improbable (potentially anomalous)
events from typical events.
Results
When compared with the
training network, communication
within the testing network
appears more sparse, and some
nodes exhibit unusual
communication.
Conclusion:
We identified many
potentially
anomalous
communications
using both the
topological and
statistical
methods. Our
analysis indicates
that further
exploration on
more
comprehensive
data sets could
result in interesting
findings, especially
on the network
level.
Using a moving
average of the
frequency of
communication
between two
nodes, we found
many anomalous
communications.
Training Testing

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Geom_ExecSummSlides

  • 1. Erin Taylor Ian Frankenburg Eric Peshkin Mentor: Joe Marion Client: Dr. John Harer, Geometric Data Analytics Geometry and Topology for Data Problem: ● Detect abnormal behaviour in communications networks using principles of statistics, topological data analysis, and machine learning. ● Capture both local and global anomalies using a comprehensive combination of mathematical methods. Computer Network Data Features Anomaly Detection Algorithms Leveraging topological and statistical tools to uncover structure in data
  • 2. Methods We built a network with nodes representing different IP addresses and edges representing communications between them. Topological tools allowed us to study how the connectivity within the network changed as edges were added between nodes. We automated the process of fitting a probability distribution to our data. Our utility fit many potential probability distributions and used AIC to determine the best one. This gave us a probabilistic basis for separating improbable (potentially anomalous) events from typical events.
  • 3. Results When compared with the training network, communication within the testing network appears more sparse, and some nodes exhibit unusual communication. Conclusion: We identified many potentially anomalous communications using both the topological and statistical methods. Our analysis indicates that further exploration on more comprehensive data sets could result in interesting findings, especially on the network level. Using a moving average of the frequency of communication between two nodes, we found many anomalous communications. Training Testing