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Table 3 Modeling of different dimensionality reduction techniques on MFF

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

Matrix factorization Transformation Constraints Regularization Weights Similarity
SVD [63] None Orthogonal
UTU = I
VTV = I
None Uniform Frobenius
PCA [64] None Orthogonal
UTU = I
VTV = I
None Uniform Frobenius
NMF [65] None Non-negativity
\(U \ge 0, V \ge 0\)
None Uniform Frobenius
pLSI None Sum to 1 None Uniform KL-divergence
Sparse NMF [25, 66] None Non-negativity
\(U \ge 0, V \ge 0\)
ℓ1 on V
||V||1
Uniform Frobenius
Bounded [26, 27] None Bounded entries in the low-rank approximation
\(\alpha < UV < \beta\)
None Uniform Frobenius