Parcellation of fMRI datasets with ICA and PLS: a data driven approach

Inter-subject parcellation of functional Magnetic Resonance Imaging (fMRI) data based on a standard General Linear Model (GLM) and spectral clustering was recently proposed as a means to alleviate the issues associated with spatial normalization in fMRI. However, for all its appeal, a GLM-based parcellation approach introduces its own biases, in the form of a priori knowledge about the shape of Hemodynamic Response Function (HRF) and task-related signal changes, or about the subject behaviour during the task. In this paper, we introduce a data-driven version of the spectral clustering parcellation, based on Independent Component Analysis (ICA) and Partial Least Squares (PLS) instead of the GLM. First, a number of independent components are automatically selected. Seed voxels are then obtained from the associated ICA maps and we compute the PLS latent variables between the fMRI signal of the seed voxels (which covers regional variations of the HRF) and the principal components of the signal across all voxels. Finally, we parcellate all subjects data with a spectral clustering of the PLS latent variables. We present results of the application of the proposed method on both single-subject and multi-subject fMRI datasets. Preliminary experimental results, evaluated with intra-parcel variance of GLM t-values and PLS derived t-values, indicate that this data-driven approach offers improvement in terms of parcellation accuracy over GLM based techniques.

Towards the systematic simplification of mechanistic models

Mechanistic models used for prediction should be parsimonious, as models which are over-parameterised may have poor predictive performance. Determining whether a model is parsimonious requires comparisons with alternative model formulations with differing levels of complexity. However, creating alternative formulations for large mechanistic models is often problematic, and usually time-consuming. Consequently, few are ever investigated. In this paper, we present an approach which rapidly generates reduced model formulations by replacing a model’s variables with constants. These reduced alternatives can be compared to the original model, using data based model selection criteria, to assist in the identification of potentially unnecessary model complexity, and thereby inform reformulation of the model. To illustrate the approach, we present its application to a published radiocaesium plant-uptake model, which predicts uptake on the basis of soil characteristics (e.g. pH, organic matter content, clay content). A total of 1024 reduced model formulations were generated, and ranked according to five model selection criteria: Residual Sum of Squares (RSS), AICc, BIC, MDL and ICOMP. The lowest scores for RSS and AICc occurred for the same reduced model in which pH dependent model components were replaced. The lowest scores for BIC, MDL and ICOMP occurred for a further reduced model in which model components related to the distinction between adsorption on clay and organic surfaces were replaced. Both these reduced models had a lower RSS for the parameterisation dataset than the original model. As a test of their predictive performance, the original model and the two reduced models outlined above were used to predict an independent dataset. The reduced models have lower prediction sums of squares than the original model, suggesting that the latter may be overfitted. The approach presented has the potential to inform model development by rapidly creating a class of alternative model formulations, which can be compared.