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Technical NoteResampling as a Cluster Validation Techniquein fMRIR. Baumgartner, PhD, R. Somorjai, PhD,* R. Summers, MSc, W. Richter, PhD,L. Ryner, PhD, and M. Jarmasz, PhDExploratory, data-driven analysis approaches such as clus-ter analysis, principal component analysis, independentcomponent analysis, or neural network-based techniquesare complementary to hypothesis-led methods. They maybe considered as hypothesis generating methods. The rep-resentative time courses they produce may be viewed asalternative hypotheses to the null hypothesis, ie, “no ac-tivation.” We present here a resampling technique to val-idate the results of exploratory fuzzy clustering analysis.In this case an alternative hypothesis is represented by acluster centroid. For both simulated and in vivo functionalmagnetic resonance imaging data, we show that by permu-tation-based resampling, statistical significance may becomputed for each voxel belonging to a cluster of interestwithout parametric distributional assumptions.Reson. Imaging 2000;11:228–231. © 2000 Wiley-Liss, Inc.Index terms: exploratory fuzzy clustering; resampling; fMRIJ. Magn.HARD AND FUZZY clustering analysis (HCA and FCA)(1–6), principal component analysis (PCA) (7), indepen-dent component analysis (ICA) (8), and Kohonen maps(KM) (9,10) are data driven (exploratory) methods thatwere found useful in analyzing functional (f)MR imagesof the human brain. These techniques partition thefMRI data and yield representative time courses (TCs)with corresponding activation maps. Exploratory ap-proaches may be viewed as hypothesis-generating pro-cedures (11), in which the representative TC of a groupof pixels may be considered as an alternative hypothe-sis to the null hypothesis, ie, no activation. Given suchan alternative model, the question of statistical valida-tion of the results arises. Such validation may be per-formed by resampling-based techniques (as also notedin refs. 8 and 5).Resampling techniques have been used in humanbrain mapping in positron emission tomography (PET;12) and fMRI (13) in the context of hypothesis-led anal-ysis. Recently, Griswold et al (14) used resampling forvalidation of the results from PCA. Here we investigatea permutation-based resampling technique to validatethe results of data-driven FCA in fMRI. The importanceof using such a technique is that no parametric as-sumptions need to be made about the TCs’ distribu-tional properties. The permutation based techniquesare performed in several steps (15): a) a null hypothesisand an alternative are defined; b) a test statistic ischosen; c) the test statistic for the original labelling ofthe observations is computed; d) the labels are per-muted (resampled), the test statistic is recomputed forthe resampled labels—this process is repeated a pre-scribed number of times, and thus a distribution of thetest statistic is generated; e) the statistical significanceof the observed value of the test statistic is calculated,and the null hypothesis is accepted or rejected. In thetechnique presented here, the null vs. alternative cor-responds to “no activation” vs. “activation.” The alter-native hypothesis is represented by the relevant clustercentroid obtained from FCA. Pearson’s correlation co-efficient between the cluster centroid and each TC be-longing to the “activation” cluster was chosen as thetest statistic. The distribution of the correlation coeffi-cient was calculated by permuting the time point labelsof the cluster centroid. The statistical significance de-termined from the generated distribution permits ac-ceptance or refusal of the null hypothesis at a specifiedlevel of significance.MATERIALS AND METHODSSimulated fMRI DataThe resampling method was first tested on simulatedfMRI time series (16,17), for which in vivo data acquiredunder the null condition were combined with simulatedactivation. In vivo data were acquired on a GE 1.5 TSigna scanner with a variety of scanner and noise con-tributions (16) and with three different TRs (of 3500,2500, and 1250 msec). The focal activated region wasselected in the motor cortex, and a hemodynamic re-sponse was simulated as the combination of twogamma functions (18), with varying contrast-to-noiseratios (CNR ? ? S/?noise, CNR ? 1–10).In Vivo fMRI Data With Real Activation ParadigmFive fMRI data sets, from a time-resolved mental rota-tion study (D1) and from visual (M3, T1, T2) and motorInstitute for Biodiagnostics, National Research Council Canada, Win-nipeg, Manitoba, Canada, R3B 1Y6.*Address reprint requests to: R.S., Institute for Biodiagnostics, NationalResearch Council of Canada, 435 Ellice Avenue, Winnipeg, Manitoba,R3B 1Y6 Canada. E-mail: somorjai@ilod.nrc.caReceived July 15, 1999; Accepted October 13, 1999.JOURNAL OF MAGNETIC RESONANCE IMAGING 11:228–231 (2000)© 2000 Wiley-Liss, Inc.228