Lattice independent component analysis for functional magnetic resonance imaging

We introduce a lattice independent component analysis (LICA) unsupervised scheme to functional magnetic resonance imaging (fMRI) data analysis. LICA is a non-linear alternative to independent component analysis (ICA), such that ICA’s statistical independent sources correspond to LICA’s lattice independent sources. In this paper, LICA uses an incremental lattice source induction algorithm (ILSIA) to induce the lattice independent sources from the input dataset. The ILSIA computes a set of Strongly Lattice Independent vectors using properties of lattice associative memories regarding Lattice Independence and Chebyshev best approximation. The lattice independent sources constitute a set of Affine Independent vectors that define a simplex covering the input data. LICA carries out data linear unmixing based on the lattice independent sources basis. Therefore, LICA is a hybrid combination of a non-linear lattice based component and a linear unmixing component. The principal advantage over ICA is that LICA does not impose any probabilistic model assumptions on the data sources. We compare LICA with ICA in two case studies. Firstly, including simulated fMRI data, LICA discovers the spatial location of meaningful sources with less ambiguity than ICA. Secondly, including real data from an auditory stimulation experiment, LICA improves over some state of the art ICA variants discovering the activation patterns detected by Statistical Parametric Mapping (SPM) on the same data.