The Latent Dirichlet allocation (LDA) is a generative statistical model that allows sets of observations to be explained by unobserved groups that explain why some parts of the data are similar. It's actually a three level Bayesian model from words to themes to documents. Generally speaking, we consider a word in a document is selected by selecting a theme for this position first and selecting a word for the theme after that.

Latent Dirichlet allocation(LDA)

Probabilistic latent semantic analysis (PLSA), also known as probabilistic latent semantic indexing (PLSI, especially in information retrieval circles) is a statistical technique for the analysis of two-mode and co-occurrence data. Compared to standard latent semantic analysis which stems from linear algebra and downsizes the occurrence tables (usually via a singular value decomposition), probabilistic latent semantic analysis is based on a mixture decomposition derived from a latent class model.

Probabilistic Latent Semantic Analysis(pLSA)

lda2vec is an impressive and intuitional work combining LDA and word2vec together. The goal of lda2vec is to make volumes of text useful to humans (not machines!) while still keeping the model simple to modify. 
1.Their blog is https://multithreaded.stitchfix.com/blog/2016/05/27/lda2vec/#topic=38&lambda=1&term=
2.Their github link is 
https://github.com/cemoody/lda2vec

lda2vec Reference

University of Michigan - Ann Arbor

LSA is a well-known and widely used language model in natural language processing area.
LSA assumes that words that are close in meaning will occur in similar pieces of text (the distributional hypothesis). A matrix containing word counts per document (rows represent unique words and columns represent each document) is constructed from a large piece of text and a mathematical technique called singular value decomposition (SVD) is used to reduce the number of rows while preserving the similarity structure among columns. Documents are then compared by taking the cosine of the angle between the two vectors (or the dot product between the normalizations of the two vectors) formed by any two columns. Values close to 1 represent very similar documents while values close to 0 represent very dissimilar documents.
It's the basic method of Glove and many other modern methods of word embedding.

Latent Semantic Analysis

https://en.wikipedia.org/wiki/Latent_semantic_analysis

Latent Semantic Analysis(LSA)-Reference

1.Advantages: LSA is easy to understand and with high efficiency.
2.Disadvantages: LSA is lack of explainable embedding. LSA needs a lot of documents and words to train a reasonable model. LSA is not such friendly for generalization as local context based model and LDA.

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