Matrix factorization
Matrix factorization is the decomposition or approximation of a matrix as a product of simpler, often lower-dimensional or structured matrices.
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Matrix factorization is a mathematical technique that decomposes a user-item interaction matrix into lower-dimensional factors representing users, latent attributes, and items.
- How it is used
- Improves personalized recommendations and search relevance when sparse interactions limit direct collaborative-filtering lookup.
- How deep it goes
- Defines matrix decomposition, latent factors, dot-product prediction, and reconstruction, but does not detail model-training procedures.
- Examples
- Uses movie purchases, appliance colors, entertainment systems, smartphones, and reconstructed preference matrices.
- What you can do after
- Apply it to infer unseen user-item preferences and discover item similarities from sparse interaction signals.
Grokking Machine Learning
An algorithmic technique that represents a matrix through products of lower-dimensional matrices to reduce its row and column dimensions.
- How it is used
- Simplifies data by reducing both the rows and columns of a matrix, and can support predictions from user–movie ratings.
- How deep it goes
- Defines the smaller-matrix product idea and illustrates recommendation use, but gives no factorization procedure or equations.
- Examples
- Uses a user–movie rating table to illustrate extracting movie features and predicting ratings.
- What you can do after
- Understand how a smaller-matrix product can simplify data and help predict ratings from user–movie features.
Read how Grokking Machine Learning explains matrix factorization →
Related concepts
- alternating least squaresincludes · Alternating least squares is an iterative optimization algorithm that alternately estimates each factor matrix while holding the others fixed.
- user-item interaction matrixuses · A user-item interaction matrix is a matrix whose rows represent users, columns represent items, and entries encode their interactions, preferences, or ratings.
- collaborative filteringused by · Collaborative filtering is a recommendation technique that infers preferences or associations from interaction patterns among users, items, or other entities.
- latent semantic analysisused by · Latent semantic analysis is a dimensionality-reduction technique that factorizes term-document statistics to represent words and documents in a lower-dimensional semantic space.
- scalar multiplicationuses · Scalar multiplication applies a scalar to a mathematical object according to the rules of its algebraic structure, such as scaling a vector or repeated addition of a group element.
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