Paper:
A Reduced-Dimension fMRI Shared Response Model
Multi-subject fMRI data is critical for evaluating the generality and validity of findings across subjects, and its effective utilization helps improve analysis sensitivity. We develop a shared response model for aggregating multi-subject fMRI data that accounts for different functional topographies among anatomically aligned datasets. Our model demonstrates improved sensitivity in identifying a shared response for a variety of datasets and anatomical brain regions of interest. Furthermore, by removing the identified shared response, it allows improved detection of group differences. The ability to identify what is shared and what is not shared opens the model to a wide range of multi-subject fMRI studies.

Review:
The manuscript "A Reduced-Dimension fMRI Shared Response Model" provides a model for correspondence across multi-subject fMRI datasets, related to the popular hyper-alignment model.I appreciate the fact that the paper does a good effort to build a sound mathematical model behind hyper-alignment related algorithms and provide good validation. Given the popularity and promises of such techniques, this work in important. The manuscript is in general clear and well written, although some details about the validation could be added. The work is original: it does not claim to be a radical departure from the prior art, which often reflects a lack of knowledge of the literature, but explains well how it relates to previous work, and how it improves significantly upon it. Below I give specific comments that I believe that authors can use to improve their paper. To me, an important aspect of the paper is that it reframes the popular hyper alignement technique and improves upon. I think that the formulation of paper does not make it appear enough. The term "hyper alignment", that is well known to the fMRI world, should be used more, in particular in the abstract, introduction, and conclusion. I understand that the authors may fear that it could make their work look incremental, however, nothing is built from a void, and stressing the relationship to previous work is a strength, given that this contribution improves upon it. I believe that experiment 1 does not show what the authors claim that it shows, in particular the sentence 'This supports the claim of a shared response with distinct functional topographies across subjects.'. Indeed, smoothing reduces the degrees of freedom of the noise. Thus is makes the variance of a comparison across subjects decrease. If there is common information across subjects, the correlation increases mechanically as long as the amplitude of the common information decreases less than the amplitude of the noise (as in the matched filter theorem). This can be shown with very simple simulations using random signals. Thus the increase of correlation across subjects is actually quite trivial. The problem is that smoothing and SRM are both transformations that shrink the volume of the accessible space. The smaller this volume, the more likely correlations are to be strong. In this regard, I do not think that experiment 1 is telling us much. I think that the limitation of correlation as a validation metric appears in the fact that the authors fully explore the logic of maximizing correlation. Indeed, it would be interesting to increase smoothing, and decrease k, until a peak in correlation is reached. Both of these cases would lead to exploring a very restricted signal space, and our intuition tells us that we would probably be throwing out the baby with the bath water. I think that the paragraphs on experiment 1 need to be significantly reworked and downplayed, as they do not provide much evidence that SRM is specific to common signal across subjects. One interesting variant of the experiment would however be to show that when varying SRM parameters, the peak of correlation is higher than when varying smoothing. This would show that SRM is a better filter than smoothing to extract common information.In experiment 2, what was the smoothing used by for the spatial correspondence methods (Talairach and MNI)? Is an optimal in classification reached through varying this parameter?In experiment 2 and 3, more details should be given on how PCA and ICA are used. Right now, it is not possible to reproduce the experiments. In particular, I don't understand the difference between the performances of ICA and PCA, given that 1) the learner used (SVM) is rotationally-invariant and 2) ICA and PCA only differ by a rotation.As a side note, in experiment 3, the sub-space spanned by ICA and PCA are the same, thus it makes sense that they perform the same.The authors have shown that the dimensionality reduction of their SRM method what a strong benefit to prediction accuracy. I am curious to know what dimensionality they used for the ICA and PCA approaches, and if the results of the ICA and the PCA could be improved by varying this dimensionality.