Recommender System -- singular value decomposition (SVD) & truncated SVD

When it comes to dimensionality reduction, the Singular Value Decomposition (SVD) is a popular method in linear algebra for matrix factorization in machine learning. Such a method shrinks the space dimension from N-dimension to K-dimension (where K N) and reduces the number of features. SVD constructs a matrix with the row of users and columns of items and the elements are given by the users' ratings.