UBC Theses and Dissertations

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UBC Theses and Dissertations

Dimensionality reduction techniques with applications in Raman spectroscopy Shreeves, Phillip


Raman spectroscopy (RS) is an optical interrogation method used to identify molecules through inelastic light scattering. This process often results in the acquired data having high dimensionality, as each observation has multiple intensities over hundreds of wave numbers. As a result, a common progression in the analysis of the spectra is to first reduce the dimensionality of the data before further examination. This thesis details the use of different dimensionality reduction techniques, including an extension of nonnegative matrix factorization (NMF). NMF is the process of decomposing the data matrix of interest into two lower rank matrices, with the constraint that all matrices must be nonnegative. This algorithm is extended in order to impose constraints on the model by decomposing the one of the specified matrices into two further nonnegative matrices, creating three in total. The application of this technique handles the previously discussed issues while also having added interpretability in comparison to principal component analysis (PCA), which is currently used in RS.

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