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It works by decomposing a matrix into two or more lower-dimensional matrices. The original matrix can then be reconstructed by multiplying the two lower-dimensional matrices together.
The process of matrix factorization involves minimizing the error between the reconstructed matrix and the original matrix by adjusting the values in the factor matrices. This can be achieved through various optimization algorithms, such as gradient descent or alternating least squares.
It can be performed using different methods, including , NMF, and PMF. Each method has its own characteristics and is suitable for different scenarios.
In collaborative filtering, a matrix is constructed with users as rows, items as columns, and the entries representing user-item interactions (such as ratings or purchase history). Matrix factorization aims to approximate this original matrix by finding two (or more) lower-rank matrices whose product closely matches the original matrix.
Matrix factorization has proven to be effective in recommender systems because it can handle sparse data, capture latent factors, and provide personalized recommendations even for new or unrated items.