Cluster Analysis of fMRI Data Using Dendrogram Sharpening L. Stanberry, R. Nandy, and D. Cordes Presenter: Abdullah-Al Mahmood

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

The Task Identify areas of activation in the brain in response to certain stimuli

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)

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

Basic Algorithm Hierarchical clustering

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

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

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

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

Dendrogram Example - I

Dendrogram Example - II

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)

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).

Sharpening Example - I

Sharpening Example - II

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)

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

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

Once Sharpened Data (P – I)

Twice Sharpened Data (P – I)

Final classification (P – I)

Map from SPM analysis

A cluster from Paradigm II

Numerical Comparison

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

Reference L. Stanberry, R. Nandy and D. Cordes Cluster Analysis of fMRI Data Using Dendrogram Sharpening. Human Brain Mapping, 20: , N.B. All figures and tables are taken from the original work

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