Nonlinear PCA: characterizing interactions between modes of brain activity

This paper presents a nonlinear principal component analysis (PCA) that ide ntifies underlying sources causing the expression of spatial modes or patte rns of activity in neuroimaging time-series. The critical aspect of this te chnique is that, in relation to conventional PCA, the sources can interact to produce (second-order) spatial modes that represent the modulation of on e (first-order) spatial mode by another. This nonlinear PCA uses a simple n eural network architecture that embodies a specific form for the nonlinear mixing of sources that cause observed data. This form is motivated by a sec ond-order approximation to any general nonlinear mixing and emphasizes inte ractions among pairs of sources. By introducing these nonlinearities princi pal components obtain with a unique rotation and scaling that does not depe nd on the biologically implausible constraints adopted by conventional PCA. The technique is illustrated by application to functional (positron emissio n tomography and functional magnetic resonance imaging) imaging data where the ensuing first- and second-order modes can be interpreted in terms of di stributed brain systems. The interactions among sources render the expressi on 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 da ta) and among functionally specialized brain systems (using a fMRI study of colour and motion processing).