Latent Semantic Indexing ( LSI ) is a technique used by search engines to understand WebPages and assess their theme by taking into effect the keywords, synonyms & semantically related keywords.
The search engines index the web and assess the pages by the theme of content. The words used in the content are related to other words used around it. The frequency of usage of these related words around the web on other pages is effectively taken into account to form a semantic relation.
On any given keyword the Search Engine can form a keyword Universe (A set of related words) with each word having a degree of relationship & degree of deviation from the given keyword.
For example keyword phone has close association with words like mobile, Nokia, Cell phone, Telephone, Motorola, etc. Similarly Tiger woods is synonymous to Golf, Paris Hilton, to fashion & not Paris City.
The related words semantically associated can be synonyms, brands, phonetic words or any words closely used in relation through the web.
The Semantic Study is done by various experts in various universities which can be found in below resources:
1) Case Study 1
2) Case Study 2
3) Case Study 3
Try a Google Search of Keyword latent semantic analysis study.
The Semantic relation is taken into effect especially when ranking of generic keywords such as phone, jobs, insurance etc..
On Google Semantic relation of the keywords can be obtained by operator ~ , used in prefix to keywords searched.
~phone on Google displays semantically related pages ranked in relevancy.