We propose a novel approach for processing diffusion MRI tractography datasets using the sparse closest point transform (SCPT). Tractography enables the 3D geometry of white matter pathways to be reconstructed; however, algorithms for processing them are often highly customized, and thus, do not leverage the existing wealth of machine learning (ML) algorithms. We investigated a vector-space tractography representation that aims to bridge this gap by using the SCPT, which consists of two steps: first, extracting sparse and representative landmarks from a tractography dataset, and second transforming curves relative to these landmarks with a closest point transform. We explore its use in three typical tasks: fiber bundle clustering, simplification, and selection across a population. The clustering algorithm groups fibers from single whole-brain datasets using a non-parametric k-means clustering algorithm, with performance compared with three alternative methods and across four datasets. The simplification algorithm removes redundant curves to improve interactive visualization, with performance gauged relative to random subsampling. The selection algorithm extracts bundles across a population using a one-class Gaussian classifier derived from an atlas prototype, with performance gauged by scan- rescan reliability and sensitivity to normal aging, as compared to manual mask-based selection. Our results demonstrate how the SCPT enables the novel application of existing vector-space ML algorithms to create effective and efficient tools for tractography processing. Our experimental data is available online, and our software implementation is available in the Quantitative Imaging Toolkit.