Skip to main content

Table 4 Some scientific applications and potential constraints to matrix factorization approaches

From: Deep data analysis via physically constrained linear unmixing: universal framework, domain examples, and a community-wide platform

Scientific applications Data dimension Input vector Constraints
ToF-SIMS 3D 2D (spatial × mass spectrum) Non-negativity
STEM (phase analysis by sliding FFT) 4D 2D (spatial × FFT spectrum) Non-negativity
STM 3D 2D (spatial × tunneling spectrum) Non-negativity, sum to 1
X-ray microscopy 3D or 4D 2D (spatial × Q spectrum) Non-negativity, sum to 1, orthogonality
Raman spectra (AFM) None 2D (spatial × Raman spectrum) Non-negativity
  1. Note that sparseness and spatial smoothness constraints discussed in the text are generally applicable to each of the listed methods