Multivariate Effect Ranking via Adaptive Sparse PLS

Unsupervised learning approaches, such as Sparse Partial Least Squares (SPLS), may provide useful insights into the brain mechanisms by finding relationships between two sets of variables (i.e. Views) from the same subjects. The algorithm outputs two sets of paired weight vectors, where each pair expresses an "effect" between both views. However, each effect can be described by a different number of variables. In this paper, we propose a novel approach to find multivariate associations between combinations of clinical/behavioural variables and brain voxels/regions which provides an unique solution with different levels of sparsity per weight vector pair. The effects described by the weight vector pairs are ranked by how much data covariance they explain. The proposed method was able to find statistically significant effects or relationships in a dementia dataset between clinical/demographic information and brain scans. Its adaptive nature allowed not only to determine an optimal sparse solution, but also provided the flexibility to select the adequate number of clinical/demographic variables and voxels to describe each effect, which enabled it to distinguish the effects associated with age from the ones associated with dementia.