lda2vec
lda2vec builds representations over both words and documents by mixing word2vec’s skipgram architecture with Dirichlet-optimized sparse topic mixtures. The Skipgram Negative-Sampling (SGNS) objective of word2vec is modified to utilize document-wide feature vectors while simultaneously learning continuous document weights loading onto topic vectors. The total loss term $L$ is the sum of the Skipgram Negative Sampling Loss (SGNS) $L^{neg}\_{ij}$ with the addition of a Dirichlet-likelihood term over document weights, $L\_{d}$. The loss is conducted using a context vector, $\overrightarrow{c\_{j}}$ , pivot word vector $\overrightarrow{w\_{j}}$, target word vector $\overrightarrow{w\_{i}}$, and negatively-sampled word vector $\overrightarrow{w\_{l}}$: $$ L = L^{d} + \Sigma\_{ij}L^{neg}\_{ij} $$ $$L^{neg}\_{ij} = \log\sigma\left(c\_{j}\cdot\overrightarrow{w\_{i}}\right) + \sum^{n}\_{l=0}\sigma\left(-\overrightarrow{c\_{j}}\cdot\overrightarrow{w\_{l}}\right)$$
Mixing Dirichlet Topic Models and Word Embeddings to Make lda2vec