What is the difference between Latent and Explicit Semantic Analysis
The difference is that with ESA, the concepts are already known and labeled (hence, "manifest concepts"), whereas in LSA the concepts are latent (they are undefined and need to be discovered).

Note the following statement from the ESA Wikipedia page:


The name "explicit semantic analysis" contrasts with latent semantic analysis (LSA), because the use of a knowledge base makes it possible to assign human-readable labels to the concepts that make up the vector space.[3][1]


In short, ESA uses prior knowledge of relationships between words and concepts (as well as labels for those concepts), whereas LSA does not.

References cited by Wikipedia for the quote above:

[1] Ofer Egozi, Shaul Markovitch and Evgeniy Gabrilovich (2011). "Concept-Based Information Retrieval using Explicit Semantic Analysis" (PDF). ACM Transactions on Information Systems 29 (2). Retrieved January 3, 2015.


[3] Gabrilovich, Evgeniy; Markovitch, Shaul (2007). Computing semantic relatedness using Wikipedia-based Explicit Semantic Analysis (PDF). Proc. 20th Int'l Joint Conf. on Artificial Intelligence (IJCAI). pp. 1606–1611.