Cluster Analysis of fMRI Data Using Dendrogram

Sharpening

L. Stanberry, R. Nandy, and D. Cordes

Presenter: Abdullah-Al Mahmood

Outline

Problem DefinitionThe Solution

Choice of methods, parameters etc.Algorithm – Dendrogram Sharpening

Experiments and ResultsDiscussion

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 StimulusPaced 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 StimulusPaced motor paradigm (finger

tapping)Region of Interest: Motor cortex

(Motion controlling area)Challenges: Noise & Data Volume

Basic Algorithm

Hierarchical clustering

Basic Algorithm

Hierarchical clusteringFactors to consider

The (dis)similarity measureThe linkage methodThreshold for cutting tree vs. number of nodes

Distance Measure

Two voxels are similar if the activation patterns are similarCorrelation coefficient of the time courses measures similarityDistance 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 clustersAverage – average distance of all pairs of points, one from each clusterComplete – largest distance between two points in two clustersSingle linkage is used in this work

Single Linkage Dendrogram (SLD)

ProsCorrectly identifies structure when clusters overlapInvariant under reordering of objectsComputationally simple

Cons“Chaining effect” – highly dissimilar size of children nodes

Dendrogram Example - I

Dendrogram Example - II

Dendrogram Sharpening

Removes chaining effect and reveals “interesting” structureDiscards some points in the process that are attached to clusters laterTwo parameters

ncore for a node/cluster (large value)

nfluff for its children (small value)

Dendrogram Sharpening

The Basic AlgorithmForm a queue of nodes (initially containing root cluster only)While not empty(queue) dequeue node

If size(node) < ncore discard all points under it.Else discard child(ren) with size < nfluff and queue the remaining child(ren).

Sharpening Example - I

Sharpening Example - II

Cluster Identification

Method of inconsistent edgesMeasure of inconsistencyThreshold = 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 I4 slices, each of 6464 resolution, 750 time points

Paradigm 220 slices, each of 6464 resolution, 165 time points

Activity and rest period alternated

Data reduction

Discard voxels with SNR value (= mean signal intensity standard deviation) in the first decileDiscard 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 wellCan be applied to raw data as well as preprocessed dataNot tested for weak/multiple stimuliNeeds parameter tuning for sharpening algorithm

Reference

L. Stanberry, R. Nandy and D. Cordes Cluster Analysis of fMRI Data Using Dendrogram Sharpening. Human Brain Mapping, 20:201-219, 2003.

N.B. All figures and tables are taken from the original work

Questions?