Neural Information Processing Systems http://nips.cc/

We analyze skip-gram with negative-sampling (SGNS), a word embedding method introduced by Mikolov et al., and show that it is implicitly factorizing a word-context matrix, whose cells are the pointwise mutual information (PMI) of the respective word and context pairs, shifted by a global constant. We find that another embedding method, NCE, is implicitly factorizing a similar matrix, where each cell is the (shifted) log conditional probability of a word given its context. We show that using a sparse Shifted Positive PMI word-context matrix to represent words improves results on two word similarity tasks and one of two analogy tasks. When dense low-dimensional vectors are preferred, exact factorization with SVD can achieve solutions that are at least as good as SGNS's solutions for word similarity tasks. On analogy questions SGNS remains superior to SVD. We conjecture that this stems from the weighted nature of SGNS's factorization.

Data sparsity has been one of the long-standing problems for recommender systems. One of the solutions to mitigate this issue is to exploit knowledge available in other source domains. However, many cross-domain recommender systems introduce a complex architecture that makes them less scalable in practice. On the other hand, matrix factorization methods are still considered to be strong baselines for single-domain recommendations. In this paper, we introduce the CDIMF, a model that extends the standard implicit matrix factorization with ALS to cross-domain scenarios. We apply the Alternating Direction Method of Multipliers to learn shared latent factors for overlapped users while factorizing the interaction matrix. In a dual-domain setting, experiments on industrial datasets demonstrate a competing performance of CDIMF for both cold-start and warm-start. The proposed model can outperform most other recent cross-domain and single-domain models. We also provide the code to reproduce experiments on GitHub.

We analyze skip-gram with negative-sampling (SGNS), a word embedding method introduced by Mikolov et al., and show that it is implicitly factorizing a word-context matrix, whose cells are the pointwise mutual information (PMI) of the respective word and context pairs, shifted by a global constant. We find that another embedding method, NCE, is implicitly factorizing a similar matrix, where each cell is the (shifted) log conditional probability of a word given its context. We show that using a sparse Shifted Positive PMI word-context matrix to represent words improves results on two word similarity tasks and one of two analogy tasks. When dense low-dimensional vectors are preferred, exact factorization with SVD can achieve solutions that are at least as good as SGNS's solutions for word similarity tasks. On analogy questions SGNS remains superior to SVD.