The lecture introduces applications of the linear dimensionality reduction methods such as principal component analysis (PCA), non-negative matrix factorization (NMF), Bayesian Linear Unmixing (BLU) to spectral data. Similarly, k-means clustering is illustarted. Brief history of the multivariate statistical methods including early work by Bonnet and Watanabe is presented. The special emphasis is made on the underpinning assumptions in the ML, and the conditions when the physical meaning of the data can be deduced. The accompanying notebook introduces startegies for denoising the data based on k-nearest neighbours, Sawitzy-Golay, and Gaussian Processes and Random forest. The PCA/NMF on EELS data is illustarted. As additional method, the decomposiiton into known end spectar using linear regression is illustarted.
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