High-dimensional biological datasets with molecular, spatial, and temporal dimensions are increasingly common. However, their analysis requires approaches that can integrate multiple data axes, accommodate noisy and missing measurements, and capture both dynamic interactions and localization changes. To address this, we provide an end-to-end tensor analysis pipeline that handles sparsity by employing tensor decomposition methods (HOSVD and CP) that are augmented with a binary mask for missing data and a framework for measurement error. We showcase this on a three-dimensional mammalian lipid transport dataset depending on lipid identities, organelle localizations, and time-series abundances. Our approach successfully identifies specific lipid-organelle pairs undergoing rapid temporal evolution, uncovers modules of lipids that co-vary across organelles and time, and extracts latent factors representing global redistribution trajectories. Direct comparison with a previous kinetic ODE model confirms that the tensor decompositions faithfully reproduce key lipid flux features.
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