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Each factorization run produces matrix factors: G1 related to gene set, and G2 related to GO terms.
The problem with a direct factorization in first order factors is that complex matrix factors appear.
Two non‐negative tensor models have been more particularly studied in the literature, the so‐called non‐negative tensor factorization (NTF), i.e., PARAFAC models with non‐negativity constraints on the matrix factors, and non‐negative Tucker decomposition (NTD), i.e., Tucker models with non‐negativity constraints on the core tensor and/or the matrix factors.
which corresponds to a PARAFAC model with matrix factors ( Φ ( 1 ), Φ ( 2 ), I I 3 ).
Other matrix slices can be deduced from (40) by simple permutations of the matrix factors.
Incorporation of constraints in tensor models may facilitate physical interpretability of matrix factors.
Note that uniqueness of the matrix factors of the contracted PARAFAC model (83) implies uniqueness of the matrix factors A(1) and A(2) of the original PARATUCK‐(2,4) model.
Convergence to the global minimum can sometimes be slow if all the matrix factors H ̄, S, and C are unknown.
The ALS algorithm rapidly converges when one of the three matrix factors of the model is known.
After convergence of the ALS algorithm, the estimated matrix factors S ̂, C ̂, and H ̄ ̂ are affected by unknown scaling factors.
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In addition, non-matrix factors can influence the organization of the actin cytoskeleton and can have profound effects on differentiation of chondrocytes.
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