As odd as it may sound, search engine users really do not care how a search engine works; they are just interested in getting the information they have requested. Once they have the answer they want, they log off - end of query. This disregarding attitude creates certain challenges for the search engine builder. For example, only the user can ultimately judge if the retrieved information meets his or her needs.
In information retrieval, this is known as relevance, or judging how well the information received matches the query. (Augmenting this problem is that oftentimes the user is not sure what he or she is looking for.) Fortunately, vector space modeling, because of its applied mathematical underpinnings, has characteristics which improve the
chances that the user will eventually receive relevant documents to his or her corresponding query. The search engine does this in two ways: by ranking the retrieved documents according to how well they match the query and relevance feedback or asking the user to identify which documents best meet his or her information needs and then, based on that answer, resubmitting the query.
Applied mathematics plays such an integral part of vector-based search engines, because there is already in place a quantifiable way to say, Document A ranks higher in meeting your criteria than Document B. This idea can then be taken one step further, when the user is asked, Do you want more documents like Document A or Document B or Document C…? After the user makes the selection, more similar documents are retrieved and ranked. Again, this process is known as relevance feedback.
Using a more mathematical perspective, we will discuss in Chapter 6 the use of vector-based similarity measures (e.g., cosines) to rank-order docu¬ments (and terms) according to their similarity with a query.