Let's not bury the lede because I know that's why you're reading this—latent semantic indexing (LSI) doesn't matter for search engine optimization (SEO).
I know, I know... You've read about it on a site somewhere, or a developer or marketer told you about it that one time. Maybe you've used it for a while, and you swear by the results.
But the truth of the matter is that it's an old technology, and the algorithms used by modern search engines are far more advanced than LSI.
Let's see what LSI is and why you shouldn't care about it.
LSI is a natural language processing (NLP) technique
Latent semantic indexing is a method for finding words related to other words contextually. It was developed in the 1980s to index or rank the strength of the relationships of words when used in the context of a written document.
This way of examining words and their connections to each other in a document is powerful in its specific applications. However, the type of data it can be used on isn't the type of data search engines care about today—it must be used on much smaller amounts of data than the entire internet.
It worked great for smaller libraries of content, but the methods used in its algorithms wouldn't scale appropriately for the sheer size of text found online. Search engines are already inundated with data to parse. The internet holds well over one trillion unique pages, and LSI isn't up to dealing with that number of words, paragraphs, and documents.
Google uses more advanced and proprietary algorithms now
These algorithms take many factors of your page into account when determining where to place it in the list of results for an individual search query. Much of the confusion around LSI is that these algorithms often rank content highly that similarly appears to rank highly on LSI indexes when looking for specific keywords.
The funny thing about LSI's misunderstood role in SEO is that this is all due to the nature of written content. A page that ranks as highly contextually related to a keyword is just what good content looks like. If you're writing about cars in any depth, you're probably writing about driving, motors, engines, gasoline (or electric power), windshields, passengers, seat belts, etc.
Repeating keywords isn't good content, so search engines learned to modify algorithms by adding much more complex analysis.
On the other hand, a well-written explanation of a topic—the type of page that many people will find helpful, click on, and return to again and again—will have a wide variety of related words that fit into the context of the topic. There will be several keywords that match many similar search queries, and there will be questions followed by answers, like... "What is latent semantic indexing? It's a natural language processing method that ranks the strength of contextual relationships between words in a document and is mistakenly assumed to be used by Google."
But that's a topic for another day, especially regarding Google's interest in questions and answers. That should be its own in-depth piece. For now, understand that latent semantic indexing isn't a part of the algorithms used for ranking search results, and you shouldn't worry about it when working on your site's SEO.