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Hi Hans, Under the null assumption these two approaches are identical, the only difference being that in the case of the more complicated variance normalisation the variance is based on an estimate from a truncated Gaussian (i.e. you normalise to e.g. 0.95 globally rather than 1 globally but this is irrelavant given the later Z-transform). Under the alternative hypothesis of there being signal somewhere, the PCA based variance normalisation is basically a robust estimate for the the noise standard deviation. Given the parameterisation we can flexibly move between both extremes (no variance normalisation to full variance normalisation). The details are not in the paper, the overall concept of having to do such a normalising step is. Given typical sparseness and low SNR of BOLD signals of interest the difference between the two cases is largely negligible - where it really matters is wrt non-BOLD signal variations, e.g. slice dropouts or spiking, which can induce changes in variance _much_ above the level you get from signals due to activation. The reason why it matters is that in such extreme cases the noise standard deviation does not correspond to an isotropic case which then messes with the mixture model fit used for inference in that voxels which do not contain any signal (the background noise class) cannot simply be modelled using a single Gaussian (as the corresponding PDF for the background noise will be a mixture of Gaussians just as in the case where no variance normalisation is carried out) - it is for this reason that we now use a robust estimator of the voxel-wise variances in the software. The thresholding simply is used temporarily to get a robust estimate of the noise which is then applied to the non-thresholded data. Practically, apart from the extreme cases of scanner-indiced variation, this normalisation deals with the very simple problem of tissue-dependent noise variance. Below is a plot of this (on log- scale!) highlighting that if no variance normalisation is carried out then the a single CSF voxel can easily weigh as much as 10 GM voxels in the calculation of the data covariance - one reason for not doing what you suggest (i.e. only use this normalisation in the dim- estimation step) hth Christian On 20 Aug 2009, at 17:02, Hans Tissot wrote: > Hi Christian, > > Sorry for jumping into this thread but I am very confused. I have 2 > questions: > > (1) I found your description in the previous e-mail different from > that described in your paper. Here's the text from your IEEE paper: > > "An immediate consequence of the fact that we are operating > under an isotropic noise model is that as an initial preprocessing > step we will modify the original data time courses to be normalized > to zero mean and unit variance. This appears to be a sensible > step in that on the one hand we know that the voxel-wise standard > deviation of resting state data varies significantly over the > brain but on the other hand, all voxels’ time courses are assumed > to be generated from the same noise process. This variance- > normalization > preconditions the data under the “null hypotheses” of > purely Gaussian noise, i.e., in the absence of any signal: the data > matrix X is identical up to second-order statistics to a simple set > of realizations from a N(0,1) noise process. Any signal component > contained in X will have to reveal itself via its deviation > from Gaussianity. This will turn out to be of prime importance > both for the estimation of the number of sources and the final > inferential steps. > > After a voxel-wise normalization of variance, two voxels with > comparable noise level that are modulated by the same signal > time course, aj, say, but by different amounts will have the same > regression coefficient upon regression against aj. The difference > in the original amount of modulation is, therefore, contained > in the standard deviation of the residual noise. Forming > voxel-wise statistics, i.e., dividing the PICA maps by the estimated > standard deviation of eta, thus, is invariant under the initial > variance-normalization." > > Based on this description it seems that each time course is indeed > normalized to unit variance (and this is a critical step as per the > description above). Could you please clarify. > > (2) > A different approach that you described in the previous e-mail seems > to divide each time course x_i by hat_sigma_i to equalize noise > variance across voxels as assumed in the model. I could not find > anything in the paper about thresholding the loadings at p .05 and > doing the division by hat_sigma_i only on those voxels which pass > the threshold. If I missed it, could you please direct me to the > correct section? Why is this thresholding required anyways, why not > just divide all voxels by their sigma_hat_i, once the latent > dimensionality is estimated? > > > Thanks, > Hans Tissot. > > On Wed, Aug 19, 2009 at 4:37 PM, Christian F. Beckmann <[log in to unmask] > > wrote: > Hi > > Neither - Melodic variance normalisation attempts to normalise the > residual _noise_ and therefore scales by the inverse of a robust > estimate of the noise, rather than normalise by signal + noise > (which, as you say, would remove important amplitude information). > More specifically, melodic runs a full PCA on the data, thresholds > loadings at a p .05 level (uncorrected) in order to indentify > signals which potentially will later on pass thresholding. Melodic > then regresses this out of the data and uses the residuals from this > regression to identify voxel-wise standard deviations. Each voxel > then gets normalised by the inverse of this estimate. This then > renders the data closer to the model assumptions of the > probabilistic ICA model (which assumes isotropic noise) and improves > signal detection and gives a much improved mixture model fit for > inference - see Beckmann and Smith (2004) IEEE TMI for details. > hth > Christian > > > > On 19 Aug 2009, at 21:17, MCLAREN, Donald wrote: > >> I've been trying to figure out how the variance normalization works >> in FSL. >> >> Is the variance of each voxel set to 1 or is the overall variance >> of all voxels set to 1? >> >> In the context of resting fMRI, if the former is true, isn't >> information about the amplitude of the flucuations being removed? >> This would seem to be important if your comparing data from >> different scans were done in two different states (e.g. eyes open >> versus eyes closed) since the amplitude of the flucuations how been >> shown to be different in these states. >> >> Any thoughts would be appreciated. >> >> -- >> Best Regards, Donald McLaren >> ===================== >> Support the Alzheimer's Association Memory Walk 2009 ~~~ >> Join the Wisconsin Alzheimer's Disease Research Center team or make >> a donation. >> http://madison.kintera.org/2009/donaldmclaren >> >> >> ================= >> D.G. McLaren >> University of Wisconsin - Madison >> Neuroscience Training Program >> Office: (608) 265-9672 >> Lab: (608) 256-1901 ext 12914 >> ===================== >> This e-mail contains CONFIDENTIAL INFORMATION which may contain >> PROTECTED HEALTHCARE INFORMATION and may also be LEGALLY PRIVILEGED >> and which is intended only for the use of the individual or entity >> named above. If the reader of the e-mail is not the intended >> recipient or the employee or agent responsible for delivering it to >> the intended recipient, you are hereby notified that you are in >> possession of confidential and privileged information. Any >> unauthorized use, disclosure, copying or the taking of any action >> in reliance on the contents of this information is strictly >> prohibited and may be unlawful. If you have received this e-mail >> unintentionally, please immediately notify the sender via telephone >> at (608) 265-9672 or email. > > _______________________________________________ > Christian F. Beckmann, DPhil > Senior Lecturer, Clinical Neuroscience Department > Division of Neuroscience and Mental Health > Imperial College London, Hammersmith Campus > Rm 419, Burlington Danes Bldg, Du Cane Road, London W12 0NN, UK > Tel.: +44 (0)20 7594 6685 --- Fax: +44 (0)20 7594 6548 > Email: [log in to unmask] > http://www.imperial.ac.uk/medicine/people/c.beckmann/ > > Senior Research Fellow, FMRIB Centre > University of Oxford > JR Hospital - Oxford OX3 9DU > Tel.: +44 (0)1865 222551 --- Fax: +44 (0)1865 222717 > Email: [log in to unmask] > http://www.fmrib.ox.ac.uk/~beckmann > > > > _______________________________________________ Christian F. Beckmann, DPhil Senior Lecturer, Clinical Neuroscience Department Division of Neuroscience and Mental Health Imperial College London, Hammersmith Campus Rm 419, Burlington Danes Bldg, Du Cane Road, London W12 0NN, UK Tel.: +44 (0)20 7594 6685 --- Fax: +44 (0)20 7594 6548 Email: [log in to unmask] http://www.imperial.ac.uk/medicine/people/c.beckmann/ Senior Research Fellow, FMRIB Centre University of Oxford JR Hospital - Oxford OX3 9DU Tel.: +44 (0)1865 222551 --- Fax: +44 (0)1865 222717 Email: [log in to unmask] http://www.fmrib.ox.ac.uk/~beckmann