Most of these techniques involve randomness, which can be undesirable in certain situations (e.g., when experiments need to be exactly reproducible).
one solution is to approximate the matrix with some Y ∈ R l×d where l n. Many matrix approximation techniques have been proposed, such as random projection (Papadimitriou et al., 1998;Vempala, 2005), sampling (Drineas and Kannan, 2003;Rudelson and Vershynin, 2007;Kim and Snyder, 2013;Kim et al., 2015b), and hashing (Weinberger et al., 2009).