Abstract
This paper presents a nonlinear principal component analysis (PCA) that identifies underlying sources causing the expression of spatial modes or patterns of activity in neuroimaging time-series. The critical aspect of this technique is that, in relation to conventional PCA, the sources can interact to produce (second-order) spatial modes that represent the modulation of one (first-order) spatial mode by another. This nonlinear PCA uses a simple neural network architecture that embodies a specific form for the nonlinear mixing of sources that cause observed data. This form is motivated by a second-order approximation to any general nonlinear mixing and emphasizes interactions among pairs of sources. By introducing these nonlinearities principal components obtain with a unique rotation and scaling that does not depend on the biologically implausible constraints adopted by conventional PCA. The technique is illustrated by application to functional (positron emission tomography and functional magnetic resonance imaging) imaging data where the ensuing first- and second-order modes can be interpreted in terms of distributed brain systems. The interactions among sources render the expression of any one mode context-sensitive, where that context is established by the expression of other modes. The examples considered include interactions between cognitive states and time (i.e. adaptation or plasticity in PET data) and among functionally specialized brain systems (using a fMRI study of colour and motion processing).
Full Text
The Full Text of this article is available as a PDF (431.1 KB).
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Biswal B., Yetkin F. Z., Haughton V. M., Hyde J. S. Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magn Reson Med. 1995 Oct;34(4):537–541. doi: 10.1002/mrm.1910340409. [DOI] [PubMed] [Google Scholar]
- Büchel C., Josephs O., Rees G., Turner R., Frith C. D., Friston K. J. The functional anatomy of attention to visual motion. A functional MRI study. Brain. 1998 Jul;121(Pt 7):1281–1294. doi: 10.1093/brain/121.7.1281. [DOI] [PubMed] [Google Scholar]
- Friston K. J., Frith C. D., Fletcher P., Liddle P. F., Frackowiak R. S. Functional topography: multidimensional scaling and functional connectivity in the brain. Cereb Cortex. 1996 Mar-Apr;6(2):156–164. doi: 10.1093/cercor/6.2.156. [DOI] [PubMed] [Google Scholar]
- Friston K. J., Frith C. D., Liddle P. F., Frackowiak R. S. Functional connectivity: the principal-component analysis of large (PET) data sets. J Cereb Blood Flow Metab. 1993 Jan;13(1):5–14. doi: 10.1038/jcbfm.1993.4. [DOI] [PubMed] [Google Scholar]
- Friston K. J., Holmes A. P., Poline J. B., Grasby P. J., Williams S. C., Frackowiak R. S., Turner R. Analysis of fMRI time-series revisited. Neuroimage. 1995 Mar;2(1):45–53. doi: 10.1006/nimg.1995.1007. [DOI] [PubMed] [Google Scholar]
- Friston K. J., Josephs O., Rees G., Turner R. Nonlinear event-related responses in fMRI. Magn Reson Med. 1998 Jan;39(1):41–52. doi: 10.1002/mrm.1910390109. [DOI] [PubMed] [Google Scholar]
- Földiák P. Forming sparse representations by local anti-Hebbian learning. Biol Cybern. 1990;64(2):165–170. doi: 10.1007/BF02331346. [DOI] [PubMed] [Google Scholar]
- McIntosh A. R., Bookstein F. L., Haxby J. V., Grady C. L. Spatial pattern analysis of functional brain images using partial least squares. Neuroimage. 1996 Jun;3(3 Pt 1):143–157. doi: 10.1006/nimg.1996.0016. [DOI] [PubMed] [Google Scholar]
- Treue S., Maunsell J. H. Attentional modulation of visual motion processing in cortical areas MT and MST. Nature. 1996 Aug 8;382(6591):539–541. doi: 10.1038/382539a0. [DOI] [PubMed] [Google Scholar]
- Worsley K. J., Friston K. J. Analysis of fMRI time-series revisited--again. Neuroimage. 1995 Sep;2(3):173–181. doi: 10.1006/nimg.1995.1023. [DOI] [PubMed] [Google Scholar]