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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 n core for a node/cluster (large value) n fluff 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) < n core discard all points under it. Else discard child(ren) with size < n fluff 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, 20:201-219, 2003. N.B. All figures and tables are taken from the original work

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