# Neural Word Embedding as Implicit Matrix Factorization

@inproceedings{Levy2014NeuralWE, title={Neural Word Embedding as Implicit Matrix Factorization}, author={Omer Levy and Yoav Goldberg}, booktitle={NIPS}, year={2014} }

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…

## 1,661 Citations

### Word Embedding Revisited: A New Representation Learning and Explicit Matrix Factorization Perspective

- Computer ScienceIJCAI
- 2015

It is pointed out that SGNS is essentially a representation learning method, which learns to represent the co-occurrence vector for a word, and that extended supervised word embedding can be established based on the proposed representation learning view.

### Fast PMI-Based Word Embedding with Efficient Use of Unobserved Patterns

- Computer ScienceAAAI
- 2019

A new word embedding algorithm that works on a smoothed Positive Pointwise Mutual Information (PPMI) matrix which is obtained from the word-word co-occurrence counts and a kernel similarity measure for the latent space that can effectively calculate the similarities in high dimensions is proposed.

### Word Embeddings via Tensor Factorization

- Computer ScienceArXiv
- 2017

It is shown that embeddings based on tensor factorization can be used to discern the various meanings of polysemous words without being explicitly trained to do so, and motivate the intuition behind why this works in a way that doesn't with existing methods.

### WordRank: Learning Word Embeddings via Robust Ranking

- Computer ScienceEMNLP
- 2016

This paper argues that word embedding can be naturally viewed as a ranking problem due to the ranking nature of the evaluation metrics, and proposes a novel framework WordRank that efficiently estimates word representations via robust ranking, in which the attention mechanism and robustness to noise are readily achieved via the DCG-like ranking losses.

### Exponential Family Word Embeddings: An Iterative Approach for Learning Word Vectors

- Computer Science
- 2018

This work proposes an iterative algorithm for computing word vectors based on modeling word co-occurrence matrices with Generalized Low Rank Models and demonstrates that multiple iterations of the algorithm improves results over the GloVe method on the Google word analogy similarity task.

### PMIVec: a word embedding model guided by point-wise mutual information criterion

- Computer ScienceMultimedia Systems
- 2022

This paper proposes a novel word embedding method based on point-wise mutual information criterion (PMIVec), which explicitly learns the context vector as the final word representation for each word, while discarding the word vector.

### A Generative Word Embedding Model and its Low Rank Positive Semidefinite Solution

- Computer ScienceEMNLP
- 2015

This work proposes a generative word embedding model, which is easy to interpret, and can serve as a basis of more sophisticated latent factor models, and is competitive to word2vec, and better than other MF-based methods.

### Continuous Word Embedding Fusion via Spectral Decomposition

- Computer ScienceCoNLL
- 2018

This paper builds on the established view of word embeddings as matrix factorizations to present a spectral algorithm for this task, and demonstrates that the method is able to embed the new words efficiently into the original embedding space.

### Spectral Word Embedding with Negative Sampling

- Computer ScienceAAAI
- 2018

This work examines the notion of ``negative examples'', the unobserved or insignificant word-context co-occurrences, in spectral methods and proposes a new formulation for the word embedding problem by proposing a new intuitive objective function that perfectly justifies the use of negative examples.

### Word Embedding With Zipf’s Context

- Computer ScienceIEEE Access
- 2019

A simpler but efficient word embedding method based on cooccurrence matrix factorization according to Zipf’s word frequency law, which shows a comparable performance though it is much simpler than the neural language models.

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