The big data trend has inspired feature-driven learning tasks, which cannot be handled by conventional machine learning models. Unstructured data produces very large binary matrices with millions of columns when converted to vector form. However, such data is often sparse, and hence can be manageable through the use of sparse random projections. This work studies efficient non-iterative and iterative methods suitable for such data, evaluating the results on two representative machine learning tasks with millions of samples and features. An efficient Jaccard kernel is introduced as an alternative to the sparse random projection. Findings indicate that non-iterative methods can find larger, more accurate models than iterative methods in different application scenarios.