The nearest-neighbor principle is a foundational approach for document retrieval in text mining. It relies on the idea that documents similar to a given query document, as measured by a chosen similarity score, are likely to be relevant. In practical terms, you represent all documents — including the query — as vectors in a high-dimensional space, typically using methods such as TF-IDF. The similarity between the query vector and each document vector is then computed, often using cosine similarity or another distance metric. Documents are retrieved by selecting those with the highest similarity scores to the query, implementing the nearest-neighbor principle in the context of document spaces.

Ranking a collection of documents by their similarity to a query allows you to order search results by relevance. Suppose you have a small set of movie descriptions, and you want to find which ones are most similar to the query "A detective investigates a mysterious disappearance". After vectorizing both the query and the documents using TF-IDF, you calculate the cosine similarity between the query vector and each document vector. The documents are then sorted in descending order of their similarity scores, so the most relevant ones appear first in the ranking.

High dimensionality and sparsity are inherent in document-term matrices, especially as the vocabulary grows. Each document vector may have thousands of dimensions, most of which are zero for any single document. This sparsity can make similarity calculations less stable, as small changes in term frequency or the presence of rare terms may disproportionately affect similarity scores. High dimensionality can also lead to the curse of dimensionality, where the distinction between nearest and farthest neighbors becomes less pronounced, potentially reducing retrieval accuracy and making rankings less reliable.

The nearest-neighbor retrieval method assumes that similarity in the chosen vector space corresponds to semantic relevance, which may not always hold true. It also presumes that the vector representation captures all relevant aspects of document meaning, an assumption that can break down when documents use synonyms or have complex structures. Additionally, nearest-neighbor methods are sensitive to the choice of similarity measure and the effects of high-dimensional noise. These limitations highlight the importance of understanding the assumptions behind nearest-neighbor retrieval and the potential need for more advanced modeling in complex retrieval tasks.