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A Novel Thresholding Method For The
Analysis Of Functional Connectivity
Networks Of The Brain
A Novel Thresholding Method For The
Analysis Of Functional Connectivity
Networks Of The Brain
Athanasios Anastasiou, Emmanuel Ifeachor
Signal Processing and Multimedia
Communications Research Group
University of Plymouth - UK
TopicsTopics
• Functional Connectivity & Brain Networks
• Proposed Thresholding Method
• Performance Evaluation
• Results
Functional Connectivity & Brain
Networks
Functional Connectivity & Brain
Networks
ThresholdingThresholding
Currently Used Methods
•Set A Limit On The Maximum Number Of Neighbours
•Arbitrary
•Order The Values Of The Correlation Matrix And Select A Point Heuristically
•Does This Correspond To The Underlying Effects?
•Pick The Threshold Value That Generates Maximum Separation Between Groups
•Advance Knowledge Of Subject Groups
Correlation Matrix  Adjacency Matrix (Affects Network Structure)
Proposed Thresholding MethodProposed Thresholding Method
• Based Only On A Subject’s Correlation Matrix
• Single Threshold Implies Two Correlation Groups
– Pairs Of Channels
• Strongly Correlated
• Weakly Correlated
• Bimodal Distribution.
– Five Parameters
• μstrong, σstrong
• μweak, σweak
• α:Mixing Parameter
Proposed Thresholding MethodProposed Thresholding Method
Correlation Matrix
M(i,j)
Obtain Histogram
H(M(i,j))
Select A Threshold
Value
Estimate True &
False Positive
Rates
Fit A Bimodal
(μS, σS, μW, σW,
a)
Performance Evaluation
Simulation Framework
Performance Evaluation
Simulation Framework
Performance Evaluation
Simulation Framework
Performance Evaluation
Simulation Framework
• Simulation
– Adjacency Matrix  Correlation Matrix
• Contributing Factors
– Underlying System Dynamics
– Coupling
– Correlation Function
Performance Evaluation
Mapping The Correlation Function
Performance Evaluation
Mapping The Correlation Function
ResultsResults
Percentage Of Recovered Edges As A Function Of Noise
(Lower Is Better By The Definition Of The Edge Recovery Error)
Simulated EEG
N=28, k=6, C=0.4, L=4.10
Simulated MEG
N=126, k=16, C=0.50,L=5.00
Concluding RemarksConcluding Remarks
• An Iterative, Subject Specific Process To Determine
The Threshold Value
• Recovers More Edges Than Currently Employed
Techniques
– Simulated Conditions
• Thresholding Is Extremely Difficult Without Prior
Information
– Especially At Low SNRs
• Is A Threshold Really Necessary?

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ITAB2010-Thresholding Correlation Matrices

  • 1. A Novel Thresholding Method For The Analysis Of Functional Connectivity Networks Of The Brain A Novel Thresholding Method For The Analysis Of Functional Connectivity Networks Of The Brain Athanasios Anastasiou, Emmanuel Ifeachor Signal Processing and Multimedia Communications Research Group University of Plymouth - UK
  • 2. TopicsTopics • Functional Connectivity & Brain Networks • Proposed Thresholding Method • Performance Evaluation • Results
  • 3. Functional Connectivity & Brain Networks Functional Connectivity & Brain Networks
  • 4. ThresholdingThresholding Currently Used Methods •Set A Limit On The Maximum Number Of Neighbours •Arbitrary •Order The Values Of The Correlation Matrix And Select A Point Heuristically •Does This Correspond To The Underlying Effects? •Pick The Threshold Value That Generates Maximum Separation Between Groups •Advance Knowledge Of Subject Groups Correlation Matrix  Adjacency Matrix (Affects Network Structure)
  • 5. Proposed Thresholding MethodProposed Thresholding Method • Based Only On A Subject’s Correlation Matrix • Single Threshold Implies Two Correlation Groups – Pairs Of Channels • Strongly Correlated • Weakly Correlated • Bimodal Distribution. – Five Parameters • μstrong, σstrong • μweak, σweak • α:Mixing Parameter
  • 6. Proposed Thresholding MethodProposed Thresholding Method Correlation Matrix M(i,j) Obtain Histogram H(M(i,j)) Select A Threshold Value Estimate True & False Positive Rates Fit A Bimodal (μS, σS, μW, σW, a)
  • 8. Performance Evaluation Simulation Framework Performance Evaluation Simulation Framework • Simulation – Adjacency Matrix  Correlation Matrix • Contributing Factors – Underlying System Dynamics – Coupling – Correlation Function
  • 9. Performance Evaluation Mapping The Correlation Function Performance Evaluation Mapping The Correlation Function
  • 10. ResultsResults Percentage Of Recovered Edges As A Function Of Noise (Lower Is Better By The Definition Of The Edge Recovery Error) Simulated EEG N=28, k=6, C=0.4, L=4.10 Simulated MEG N=126, k=16, C=0.50,L=5.00
  • 11. Concluding RemarksConcluding Remarks • An Iterative, Subject Specific Process To Determine The Threshold Value • Recovers More Edges Than Currently Employed Techniques – Simulated Conditions • Thresholding Is Extremely Difficult Without Prior Information – Especially At Low SNRs • Is A Threshold Really Necessary?

Editor's Notes

  1. The bigger picture of correlation analysis for functional connectivity Data are obtained from a patient with a degree of noise. They are preprocessed (and “distorted” because of the processing). The functional connectivity metric, returns information about the correlation between channels but again, there is the potential for some information to be lost. Consider for example the mismatches that are introduced when examining signals from non-linear systems with linear techniques.)
  2. How is thresholding applied? How has it being carried out so far by others and what problems are associated with it?