Exploring Spatial Relationships in Functional Neuroimaging Data

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Exploring Spatial Relationships in Functional
Neuroimaging Data

• Rajan Patel
• F. DuBois Bowman
• Emory University
• Rollins School of Public Health
• Department of Biostatistics

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Overview

• Gain insight into the organization of human brain
  function by classifying localized brain regions
  that exhibit similar patterns of activity
• Examine data structure from a PET study
• Present new and existing clustering methods,
  stopping rules, and a performance evaluation a
  criterion
• Conduct empirical analysis
• Identify clustering methods that perform well for
  PET functional neuroimaging data

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PET Data Ethanol Study

• K10 Subjects, each with S4 scans
• LOW dose ethanol Scan 2
• HIGH dose ethanol Scan 3
• Subjects complete continuous performance tasks
  during each scan
• We apply clustering methods to
• Identify collections of voxels that exhibit
  similar ethanol-induced changes in neural
  processing
• Characterize brain activity patterns within each
  cluster

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PET data (2)

• Represents serial rCBF for subject k at voxel v.
• We calculate a summary measure across individuals
  by implementing a general linear model.
• Let X denote a matrix of design variables with
  columns corresponding to the scan numbers a final
  column containing a covariate adjustment for
  gCBF.
• We will cluster brain voxels based on this
  vector.

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Functional Distance

• Define the functional distance between two voxels
  as
• where BVi,Vj is a positive semi-definite matrix
  (inverse of the covariance matrix).
• We create a partition of the V voxels into G
  clusters, attempt to group voxels with small
  distances.

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Visual Distance Matrix
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Clustering Methods

• Hierarchical Methods
• Form a hierarchy of nested cluster solutions
• We compare several existing methods
• We introduce a new method
• Variable Linkage
• Generalization of kth nearest neighbor clustering
• k is a function of the size of the two clusters

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Clustering Methods (2)

• Stopping rules for hierarchical methods
• Determine the optimal number of clusters
• (where to stop on the hierarchical clustering
  tree)
• 3 methods we compare are
• Pseudo-F (Calinski and Habarasz, 1974)
• Pseudo-t2 (Duda and Hart, 1973)
• Cubic Clustering Criterion (CCC) (Sarle, 1983)
• Provided by SAS

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Clustering Methods (3)

• Partitioning Methods
• Separates observations into predefined number of
  subgroups based on functional distance
• Examples
• K-Means, Fuzzy K-Means
• Most commonly used in clustering of functional
  neuroimaging data.
• Less computationally and memory intensive
• Must pre-specify number of clusters

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Clustering Methods (4)

• Evaluating cluster performance
• F-Score Algorithm
• Requires knowledge of true clustering
• Range from 0 to 1 where 1 represents a perfect
  clustering and 0 indicates that no voxels are
  correctly classified
• Let ?g represent a true cluster, ?g represent a
  computed cluster, and Vgg be the number of
  voxels in both ?g and ?g

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Simulation Study

• Empirical analysis of 100 simulated data sets
  with 11 actual clusters with properties based on
  ethanol data set
• Also considered 100 simulated data sets with
  additional noise
• Analyze clustering results of hierarchical and
  partitioning clustering algorithms
• Compare F-Score values at 11 clusters
• Analyze accuracy of stopping rules for each
  clustering algorithm

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Results (1)
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Results (2)
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Results (3)
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Results (4)
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Results (5)
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Results (6)
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Results (7)
The figure shows the two clusters that exhibit
the largest ethanol-related decrease in rCBF
(Scan 1 Scan 4), based on Wards method. The
two clusters are located in the cerebellum, which
controls coordinated movement of the body.
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Summary

• Wards Method, Beta-Flexible recommended
• F-Score values consistently high
• Stopping rules work the best
• K-Means, Fuzzy K-Means
• F-Scores relatively high for noisy data
• Stopping rules do not work as well
• Pseudo-F, CCC, and Pseudo-t2 worked well for many
  of the hierarchical algorithms with the standard
  simulated data
• Pseudo-F produced more accurate results than CCC
  and Pseudo-t2 for noisy data
• For PET data, we recommend Wards Method or
  Beta-Flexible in conjunction with a simultaneous
  inspection of Pseudo-F, CCC, and Pseudo-t2
• For noisy data, we recommend Wards Method or
  Beta-Flexible in conjunction with Pseudo-F

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K-Means Explanation
K Means Clustering (11 clusters)
Actual Clustering Simulated
Data Noisy Data
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K-Means Explanation (2)