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Matrix Rank
Dimension of the vector subspace generated by the columns (or rows) of a matrix, crucial for determining the complexity of factorization.
User and Item Bias
Additional terms in factorization models that capture systematic trends of users and intrinsic characteristics of items.
Latent Factor Learning
Process of identifying unobserved characteristics (latent factors) that explain patterns in the matrix data.
Low-Rank Matrix
Approximation of an original matrix by a lower-rank matrix, capturing essential information while reducing dimensionality.
Alternating Least Squares (ALS)
Optimization algorithm that solves the factorization problem by alternating the fixation of one factor matrix to optimize the other.
Parallel Factorization
Factorization approach that simultaneously processes multiple aspects of data (e.g., temporal context, social information) to improve prediction.
Interaction Matrix
Matrix representing interactions between two types of entities (e.g., users-items), often the object of factorization in recommendation systems.
Frobenius Problem
Optimization formulation aiming to minimize the Frobenius norm of the difference between the original matrix and its low-rank approximation.
Initialization of Factors
Crucial step defining the starting values of factor matrices, influencing the convergence speed and the quality of the final solution.