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Non-negativity constraint
Restriction requiring all elements of the factorized matrices to be positive or zero, ensuring physical interpretability and additive representations.
Additive representations
Modeling where data are reconstructed by addition of elementary components, as opposed to subtractions possible in other factorization methods.
Alternating Least Squares (ALS)
Optimization method alternating the resolution of least squares problems on each factorized matrix while keeping the other fixed.
Basis matrix (W matrix)
First factorized matrix containing the basis vectors or dictionary representing the fundamental characteristics of the data.
Coefficient matrix (H matrix)
Second factorized matrix containing the activation coefficients indicating how each sample is composed from the basis vectors.
Lee-Seung algorithm
Pioneering algorithm for NMF using multiplicative update rules based on minimization of quadratic error or KL divergence.
NMF cost function
Optimization criterion measuring reconstruction quality, typically mean squared error or Kullback-Leibler divergence.
Sparsity in NMF
Desirable property where factorized matrices contain many zeros, improving interpretability and parsimony of representations.
NMF Convergence
Property of the algorithm reaching a stable point where successive iterations no longer significantly modify the factorized matrices.
NMF Regularization
Addition of penalty terms in the cost function to control sparsity, smoothness, or other desired properties of the factors.
Supervised NMF
Extension of NMF incorporating label information to guide factorization towards discriminative representations for classification.
NMF Correlation Coefficient
Evaluation measure quantifying the similarity between obtained factors and expected structures or reference factors.
NMF Computational Complexity
Analysis of time and memory resources required for executing NMF algorithms, typically O(mnr) per iteration.