This blog below tells the story of LSI and LSA: these two algorithms are based on SVD (singular value decomposition). According the article below, LSA may work differently to overcome the problem of synonymy and polysemy...
LSA and LSI are mostly used synonymously, with the information retrieval community usually referring to it as LSI. LSA/LSI uses to decompose the term-document matrix A into a term-concept matrix U, a singular value matrix S, and a concept-document matrix V in the form: A = USV'.