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Edited by: Jean-Baptiste Poline, Commissariat à l’Energie Atomique et aux Energies Alternatives, France

Reviewed by: Francisco Pereira, Siemens Corporation, Corporate Research and Technology, USA

This article was submitted to Brain Imaging Methods, a section of the journal Frontiers in Neuroscience.

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Multivariate pattern analyses of fMRI responses have become widely used in cognitive neuroscience. A popular method introduced by Haxby et al. (

Before computing correlations between conditions, many researchers subtract each voxel’s overall mean response to all conditions from its response to each condition^{1}

Here, we discuss the effects of subtracting the mean pattern separately for two datasets^{2}

In multivariate correlation analyses, researchers typically estimate the response at each voxel to each condition, for example, by using the general linear model to estimate regression coefficients. The response patterns across voxels are then used to calculate the correlations among conditions in a certain region of interest. It is common to have some voxels that have high or low absolute responses across all or some conditions, which may even be caused by noise. This creates a “common activation pattern” that is shared by some or all conditions and that similarly influences the magnitude of correlations among conditions (Sayres and Grill-Spector,

To illustrate the consequences of subtracting the mean pattern, we simulated one example with patterns of responses to two conditions, faces and houses (Figure

Figure

This can be generalized to cases with any number of conditions. The response patterns across conditions for even runs can be represented in a _{even}, in which _{even}(_{even} contains the response pattern to a condition ^{3}_{even} using matrix

_{n} is the

_{even} is the resulting data matrix for even runs and it has the same dimensions as _{even}.

Equation 2 shows that the response to each condition after subtracting the mean pattern is given by a linear combination of the responses to all the conditions. When we look at the variance of each condition after subtracting the mean pattern, we need to consider these same linear combinations—the variance of each condition is now distributed over all other conditions. These changes in response patterns of each condition within each dataset modify, in turn, the relationships between conditions _{even} and the rows of _{odd} (_{odd} corresponds to the mean-pattern-subtracted matrix for odd runs and it is similarly derived using Equation 2).

The changes in correlations

Critically, the correlation values have

Correlation matrices are further used for other analyses, such as discrimination/classification analyses and Representational Similarity Analysis (RSA—Kriegeskorte et al.,

In case of classification analyses, researchers compare the within-condition correlations with the between-condition correlations across even and odd runs to examine whether it is possible to discriminate the response patterns to two or more conditions. In Figure

In case of RSA, researchers use correlations between conditions to examine how similar the representations of different conditions are in a certain region of interest, and thus characterize the information that is being represented. In certain cases, subtracting the mean pattern can change the relative magnitudes of correlation between conditions, which will result in changes in the rank-order of correlations of pairs of conditions, and have consequences for RSA results. This is more likely to happen if one or more conditions have large variances compared to other conditions, or if one or more pair of conditions have large covariance compared with the covariance of other pairs of conditions. In all cases, subtracting the mean pattern substantially obscures interpretation and understanding of these analyses. Conversely, correlation values before subtracting the mean pattern straightforwardly indicate which conditions share more signal than others.

Finally, some researchers have interpreted negative correlations as opposing patterns of activity for the conditions (Hanson et al.,

We suggest that a suitable approach to the various problems created by subtracting the mean pattern is to skip this step, and work instead with the original data; this approach enables most common analyses. There might be cases, nevertheless, in which it is important to accurately estimate and remove the influence of a common activation pattern. Examples of these cases are when the covariance between all conditions is extremely high, or if researchers want to compare correlation magnitudes across regions^{4}

To conclude, subtracting the mean pattern changes the relationships between conditions. Here, we described how this step, applied to two separate datasets, changes the variance of each condition, and the relative correlations between conditions

This work was supported by a grant from the National Institutes of Health 5RO1EY013602-07 to Ken Nakayama. We thank the members of the Harvard Vision Lab, Jörn Diedrichsen, and Nikolaus Kriegeskorte for helpful discussions about the ideas and simulations presented here. We thank Katie Rainey and Sam Anthony for help with the equations. We thank Jörn Diedrichsen, Nicholas Furl, Laura Germine, and Matthew Longo for thoughtful comments on an earlier version of this manuscript.

^{1}Examples of studies that subtracted the mean pattern are: Pietrini et al. (

^{2}Here, we use the term “dataset” to refer to half or part of the data to which subtraction of mean pattern is applied. For example, data from even and odd runs form two datasets. Data from different runs, sessions or experiments is also considered to be separate datasets. The correlation analyses described here are computed across datasets.

^{3}We note that subtracting the mean pattern results in having the mean of each _{even} equal to zero. Conversely, by using Pearson correlation, we are also automatically mean centering the _{even}.

^{4}Note that this is not possible with raw data, given that different levels of common activation pattern across regions influences those correlations, nor it is possible after subtracting the mean pattern.