Component analysis

The number of significant components in the nano-XANES data was estimated using the singular value decomposition (SVD).²⁷ After identifying the number of significant components (k), the 3D stack is decomposed into individual 2D component maps using principal component analysis (PCA), NMF, or other decomposition methods available in the scikit-learn library.²⁸ In particular, NMF²⁹ is suitable for nano-XANES data because of the positivity constraint during the factorization. The component maps are then used to generate the component spectrum that resembles a XANES spectrum. For decomposition analysis, the 3D nano-XANES matrix ( was restructured to a 2D matrix V ) and factorized into two new matrices (W and H) using Equation 1 for NMF.

The component spectra and images were computed from the W and H matrices. For example, the model sample stack with 73 energy points and 160 × 160 points was converted to a 73 × 25 600 matrix before factorization. The factorized matrix with five significant components then has a shape of a 5 × 160 × 160 matrix. In other words, a 73 × 160 × 160 matrix was reduced to a 5 × 160 × 160 matrix. The component spectra were normalized and compared with the reference library to generate a Pearson's correlation matrix.