Skip to main content

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

\(U \ge 0, V \ge 0\)

â„“1 on V

||V||1

Uniform

Frobenius

Bounded [26, 27]

None

Bounded entries in the low-rank approximation

\(\alpha < UV < \beta\)

None

Uniform

Frobenius