What are LSI and LSA and its Relevance to SEO?

LSA is an acronym for latent semantic analysis and LSI for latent semantic indexing. LSA is a system and hypothesis used to extract and represent the contextual meaning of a number of words based on a larger quantity of words. This determines the relevance of a paragraph or sentence to the rest of the content. The reasoning behind this is that it enables people create a link between one word and another based on a given topic and try to prove that each word is somehow linked to the other. LSA is accurate in that it has proven to ensure content is more coherent than most human conversations and also ensures that readers learn more from the content. Because it ensures that content is related and every word is somehow relevant to the topic, it consequently ensures that the amount of information packed in a page is sufficient and the quality of that information is reliable.
LSI system categorizes all words with similarities into groups and ensures that the ones placed together actually have some form of common ground. It takes into account the keyword and looks for content that contains that keyword and categorizes them in terms of relevance based on the number of times that keyword appears. However, all documents are examined individually then ranked in order of which contains the most keywordsand therefore most likely more relevant to the topic. LSI also puts together documents that contain a specific word to make searching for them easier. This systems ranks documents with similar keywords as related because they share the same keyword and the consistency is related. This method relates to how humans classify content as well based on the keyword and how many times it has appeared. However, the LSI algorithm does not distinguish the meanings of words and can therefore not take synonyms as related words. It takes words as they are and categorizes them based on usage.
Relevance to SEO
When internet users enter a search query on search engines, the results displayed are normally all geared towards the keyword searched. Search engines make use of LSI and LSA technologies to ensure that the search results produced are as closely related to the searched term as possible. The simple fact that humans would categorize based on theme or context distinguishes these algorithms as more accurate because they matchkeywords to the exact word in other web pages. LSI therefore does more than examine the keywords but also looks at how the keyword has been used and gets a feel of the context between one document and many others.
Before using these algorithms, documents were crammed with a specific word and that would automatically rank a page higher. LSA and LSI ensure that it is not just keyword density that counts towards ranking. LSI results are said to give more accurate search results because pages that ranked very high simply because they had optimized the keyword now rank low based on content and relevance. It ensures that internet users get what they are looking for and a much broader base of the keyword they are looking for.
source: Thanks to  Amitabh Shukla for providing this info.

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