Combining imaging and clinical data in manifold learning: Distance-based and graph-based extensions of Laplacian Eigenmaps

Manifold learning techniques have been widely used to produce low-dimensional representations of patient brain magnetic resonance (MR) images. Diagnosis classifiers trained on these coordinates attempt to separate healthy, mild cognitive impairment and Alzheimer´s disease patients. The performance of such classifiers can be improved by incorporating clinical data available in most large-scale clinical studies. However, the standard non-linear dimensionality reduction algorithms cannot be applied directly to imaging and clinical data. In this paper, we introduce a novel extension of Laplacian Eigenmaps that allow the computation of manifolds while combining imaging and clinical data. This method is a distance-based extension that suits better continuous clinical variables than the existing graph-based extension, which is suitable for clinical variables in finite discrete spaces. These methods were evaluated in terms of classification accuracy using 288 MR images and clinical data (ApoE genotypes, Aβ₄₂ concentrations and mini-mental state exam (MMSE) cognitive scores) of patients enrolled in the Alzheimer´s disease neuroimaging initiative (ADNI) study.