## Wednesday, October 31, 2012

### needles and haystacks: information mapping quirks

I really like this image and analogy for describing some of the distortions that can arise from searchlight analysis: a very small informative area ("the needle") can turn into a large informative area in the information map ("the haystack"), but the reverse is also possible: a large informative area can turn into a small area in the information map ("haystack in the needle").

I copied this image from the poster Matthew  Cieslak,  Shivakumar  Viswanathan,  and  Scott  T.  Grafton  presented last year at SfN (poster 626.16, Fitting and Overfitting in Searchlights, SfN2011). The current article covers some of the same issues as the poster, providing a mathematical foundation and detailed explanation.

They step through several proofs of information map properties, using reasonable assumptions. One result I'll highlight here is that the information map's representation of a fixed-size informative area will grow as searchlight radius increases (my phrasing, not theirs). Note that this (and the entire paper) is describing the  single-subject, not group level of analysis.

This fundamental 'growing' property is responsible for many of the strange things that can appear in searchlight maps, such as the edge effects I posted about here. As Viswanathan et al. point out in the paper, it also means that interpreting the number of voxels found significant in a searchlight analysis is fraught with danger: it is affected by many factors other than the amount and location of informative voxels. They also show that it is possible to have just 430 properly-spaced informative voxels create the entire brain to be marked as informative in the information map, using just 8 mm radius searchlights (that's not particularly large in the literature).

I recommend taking a look at this paper if you generate or interpret information maps via searchlight analysis, particularly if you have a mathematical bent. It nicely complements diagram- and description-based explanations of searchlight analysis (including, hopefully soon, my own). It certainly does not include all the aspects of information mapping, but provides a solid foundation for those it does include.

Shivakumar Viswanathan, Matthew Cieslak, & Scott T. Grafton (2012). On the geometric structure of fMRI searchlight-based information maps. arXiv: 1210.6317v1