Generalized Correspondence-LDA Models (GC-LDA) for Identifying Functional Regions in the Brain
This paper presents Generalized Correspondence-LDA (GC-LDA), a generalization of the Correspondence-LDA model that allows for variable spatial representations to be associated with topics, and increased flexibility in terms of the strength of the correspondence between data types induced by the model. We present three variants of GC-LDA, each of which associates topics with a different spatial representation, and apply them to a corpus of neuroimaging data. In the context of this dataset, each topic corresponds to a functional brain region, where the region's spatial extent is captured by a probability distribution over neural activity, and the region's cognitive function is captured by a probability distribution over linguistic terms. We illustrate the qualitative improvements offered by GC-LDA in terms of the types of topics extracted with alternative spatial representations, as well as the model's ability to incorporate a-priori knowledge from the neuroimaging literature. We furthermore demonstrate that the novel features of GC-LDA improve predictions for missing data.
The submission #635, entitled " Generalized Correspondence-LDA Models (GC-LDA) for Identifying Functional Regions in the Brain" presents a topic model that accounts for both word occurrence and associated locations to build a cognitive atlas from the brain imaging literature. The main contribution of the paper is a novel "generalized correspondence model" that is derived into three versions, e.g. including (or not) symmetry constraints on the spatial distributions involved. The model is handled in a Bayesian framework, and the results display an improved predictive accuracy in cross-validation when the full power of the correspondence model is used. 
This paper addresses an important topic, and presents a clear, well-detailed and well-presented framework. I find the results and their illustration compelling. In enjoyed reading the paper.  my only major concern regards the cross-validation scheme adopted in the paper (see below).   More in detail --------------  8: 'probability distribution over neural activity' is a bit vague and potentially misleading to describe the kind of statistics made in coordinate-based meta-analysis.  99-111: I find this paragraph a bit awkward. To me the message boils down to: although gamma does not enjoy a very clear interpretation in the generative model, it plays the role of a regularizer. Presenting it in such a way would clarify the presentation.  125 why not 'semantic' instead of 'linguistic' ? Would sound better to me.  130-132: Again, a rather awkward way to introduce symmetry about the x=0 plane.  Fig. 2: I did not get the meaning of the colors. Usually, red/blue refer to positive/negative values, but it cannot be the case here.  192 the authors probably mean A2.  238-241: I would _really_ prefer a cross-validation across documents, as it would probably fit with the properties that you expect from a cognitive atlas. The authors should --at least-- explain why they did not do it that way, and if possible, describe the performance of cross-document generalization.  The paper did not address model selection (how many classes ?). While I understand that this is ill-posed and potentially impossible in their unsupervised setting, I think that the question should be discussed.  Using GMMs with two classes is fairly limited. Why not using more general spatial distributions, such as kernel density estimators ?  Gibbs sampling has a strong drawback wrt variational schemes: its computational cost. I have no idea of the computation time for the model (this should be stated at least in SM) , but I think that it would be great to perform a comparison: either confirm the weakness of the variational approach or propose  it as an efficient alternative.