Randomized Nonnegative Matrix Factorization for Imaging Mass Spectrometry

Abstract

Imaging Mass Spectrometry (IMS) data calls for computational methods to perform factorizations efficiently that facilitate interpretable components. Despite the widespread use of Nonnegative Matrix Factorization (NMF) for IMS-related dimensionality reduction, conventional NMF algorithms are not up to par to scale for extremely large datasets. To remedy this problem, this thesis explores Randomized Nonnegative Matrix Factorization as an efficient alternative to compute IMS data on whole-body mouse pup tissue data.

In this thesis, the author demonstrates how Randomized NMF inherits its two-stage framework for computation from Randomized SVD. The main bottleneck between Randomized NMF replicating the success of its predecessor is the lower-dimensional basis used to compress the data matrix. Although the basis has been conventionally effective for Randomized SVD with provable guarantees, the lack of entry-wise nonnegativity constraint requires existing methods to compromise the projection quality and interpretability and rely on the relaxation of nonnegativity constraints within the update rules. Therefore, this work motivates and explores the use of alternative bases that directly satisfy entry-wise nonnegativity.