A wide range of  phenomena in the physical, engineering, biological, and social sciences feature rich dynamics that give rise to multiscale structures in both space and time, including fluid dynamics, atmospheric-ocean interactions, climate modeling, epidemiology, and neuroscience. Constrained matrix factorizations are powerful techniques for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating between distinct time scales. However, the emergence of large-scale datasets has severely challenged our ability to analyze data using such techniques. We discuss randomized methods as a computational strategy to accelerate techniques such as sparse principal component analysis (SPCA) and nonnegative matrix factorization (NMF). The proposed algorithms are demonstrated using both synthetic and real world data, showing great computational efficiency and diagnostic performance.