Cluster Analysis of fMRI Data Using Dendrogram Sharpening

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Cluster Analysis of fMRI Data Using Dendrogram
Sharpening

• L. Stanberry, R. Nandy, and D. Cordes
• Presenter Abdullah-Al Mahmood

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Outline

• Problem Definition
• The Solution
• Choice of methods, parameters etc.
• Algorithm Dendrogram Sharpening
• Experiments and Results
• Discussion

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The Task

• Identify areas of activation in the brain in
  response to certain stimuli

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The Task

• Identify areas of activation in the brain in
  response to certain stimuli
• Simple case Single Stimulus
• Paced motor paradigm (finger tapping)
• Region of Interest Motor cortex (Motion
  controlling area)

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The Task

• Identify areas of activation in the brain in
  response to certain stimuli
• Simple case Single Stimulus
• Paced motor paradigm (finger tapping)
• Region of Interest Motor cortex (Motion
  controlling area)
• Challenges Noise Data Volume

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Basic Algorithm

• Hierarchical clustering

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Basic Algorithm

• Hierarchical clustering
• Factors to consider
• The (dis)similarity measure
• The linkage method
• Threshold for cutting tree vs. number of nodes

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Distance Measure

• Two voxels are similar if the activation patterns
  are similar
• Correlation coefficient of the time courses
  measures similarity
• Distance between voxels i and j
• d(i, j ) 1 corr. coeff.(T (i ), T ( j ))
• Not a metric

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Linkage Methods

• Single distance between closest pair of points
  of two clusters
• Average average distance of all pairs of
  points, one from each cluster
• Complete largest distance between two points in
  two clusters
• Single linkage is used in this work

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Single Linkage Dendrogram (SLD)

• Pros
• Correctly identifies structure when clusters
  overlap
• Invariant under reordering of objects
• Computationally simple
• Cons
• Chaining effect highly dissimilar size of
  children nodes

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Dendrogram Example - I
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Dendrogram Example - II
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Dendrogram Sharpening

• Removes chaining effect and reveals interesting
  structure
• Discards some points in the process that are
  attached to clusters later
• Two parameters
• ncore for a node/cluster (large value)
• nfluff for its children (small value)

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Dendrogram Sharpening

• The Basic Algorithm
• Form a queue of nodes (initially containing root
  cluster only)
• While not empty(queue) dequeue node
• If size(node) lt ncore discard all points under
  it.
• Else discard child(ren) with size lt nfluff and
  queue the remaining child(ren).

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Sharpening Example - I
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Sharpening Example - II
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Cluster Identification

• Method of inconsistent edges
• Measure of inconsistency
• Threshold Median 2(Upper-hinge value
  Lower-hinge value)
• Upper and lower values correspond to first and
  third quartile values (ascending order sort for
  distance)

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Experimental Parameters

• Paradigm I
• 4 slices, each of 64?64 resolution, 750 time
  points
• Paradigm 2
• 20 slices, each of 64?64 resolution, 165 time
  points
• Activity and rest period alternated

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Data reduction

• Discard voxels with SNR value ( mean signal
  intensity ? standard deviation) in the first
  decile
• Discard voxels with correlation value below 0.5
  (normalized series with mean 0 and std. dev. 1)
  or having less than 5 significant correlations

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Once Sharpened Data (P I)
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Twice Sharpened Data (P I)
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Final classification (P I)
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Map from SPM analysis
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A cluster from Paradigm II
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Numerical Comparison
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Discussion

• Dendrogram sharpening can help in identifying
  clusters quite well
• Can be applied to raw data as well as
  preprocessed data
• Not tested for weak/multiple stimuli
• Needs parameter tuning for sharpening algorithm

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Reference

• L. Stanberry, R. Nandy and D. Cordes Cluster
  Analysis of fMRI Data Using Dendrogram
  Sharpening. Human Brain Mapping, 20201-219,
  2003.
• N.B. All figures and tables are taken from the
  original work

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Questions?