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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
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