Diversification and Generalization for Metric Learning with Applications in Neuroimaging

Many machine learning algorithms rely on "good" metrics to quantify the distances or similarities between data instances.Context dependent metrics learned from the training data are often effective in improving the performance of metric-based algorithms under different circumstances, or for different tasks at hand.At present, most of existing metric learning algorithms learn metrics only from a binary similarity perspective, overlooking the fact that similarities tend to have different levels and binary configurations cannot fully account for many situations occurring in practice.In addition, many state-of-the-art metric learning solutions only estimate Mahalanobis metrics, which are linear transformation models with limited expressive power.More complicated nonlinear structures embeded in the data often cannot be well handled, thus failing to improve or even deteriorating the performance of the metric-based algorithm that follows.In this dissertation, we address the aforementioned drawbacks along two directions: diversify and generalize the forms of metric learning.For diversification, a novel Prior Distance Informed Metric Learning (PDIML) model is developed.Both global and local PDIML implementations have been successfully applied to diversify the similarities between data points through integrating prior distance knowledge into pairwise distance matrices.For generalization, we tackle metric learning from the perspective of feature transformation, and propose a set of novel nonlinear solutions through the utilization of deformable geometric models to learn spatially varying metrics.Thin-plate splines (TPS) are chosen as the geometric model due to their remarkable versatility and representation power in accounting for high-order deformations.TPS based metric learning algorithms