Elsevier

NeuroImage

Volume 23, Supplement 1, 2004, Pages S250-S263
NeuroImage

Partial least squares analysis of neuroimaging data: applications and advances

https://doi.org/10.1016/j.neuroimage.2004.07.020Get rights and content

Partial least squares (PLS) analysis has been used to characterize distributed signals measured by neuroimaging methods like positron emission tomography (PET), functional magnetic resonance imaging (fMRI), event-related potentials (ERP) and magnetoencephalography (MEG). In the application to PET, it has been used to extract activity patterns differentiating cognitive tasks, patterns relating distributed activity to behavior, and to describe large-scale interregional interactions or functional connections. This paper reviews the more recent extension of PLS to the analysis of spatiotemporal patterns present in fMRI, ERP, and MEG data. We present a basic mathematical description of PLS and discuss the statistical assessment using permutation testing and bootstrap resampling. These two resampling methods provide complementary information of the statistical strength of the extracted activity patterns (permutation test) and the reliability of regional contributions to the patterns (bootstrap resampling). Simulated ERP data are used to guide the basic interpretation of spatiotemporal PLS results, and examples from empirical ERP and fMRI data sets are used for further illustration. We conclude with a discussion of some caveats in the use of PLS, including nonlinearities, nonorthogonality, and interpretation difficulties. We further discuss its role as an important tool in a pluralistic analytic approach to neuroimaging.

Section snippets

Partial least squares

The term “partial least squares” refers to the computation of the optimal least-squares fit to part of a correlation or covariance matrix (Wold, 1982). The part is the “cross-block” correlation between some set of exogenous and dependent measures. PLS is similar to principal components analysis (PCA), but one important feature of PLS is that the solutions are constrained to the part of the covariance structure that is attributable to experimental manipulations or that relates to behavior.

Computation

Computational overhead may be a concern when conducting PLS analysis, especially in the case of fMRI or ERP/MEG data when high density spatial or temporal sampling is used. For an average-sized event-related fMRI study, an analysis including 500 permutations and 100 bootstraps takes 30 to 60 min when running on a Linux-based Intel workstation with 4GB of RAM, depending on the workstation load. In systems with parallel architectures, it is possible to distribute the resampling operations across

Conclusions

Starting from the basic emphasis on explaining the relation between two or more blocks of data, PLS can address questions ranging from identifying task-specific patterns of activity to extracting neural activity patterns that predict behavior. The flexibility of PLS, especially when used in concert with other analytic methods, enables more thorough testing of specific hypotheses and development of neurocognitive theory.

As noted in the introduction, PLS is part of a family of multivariate data

Acknowledgments

This work was supported by Canadian Institutes for Health Research grants to ARM and NJL, and a JS McDonnell Foundation grant to ARM.

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