Final answer:
The vector space model is a key concept in text mining where texts are represented as vectors in a multi-dimensional space. It uses the frequency of words as vector components and allows the comparison of documents through angular distances between vectors. This model leverages linear algebra to process and compare complex documents.
Step-by-step explanation:
The vector space model is a mathematical approach used in text mining and information retrieval. It represents text documents as vectors of identifiers, such as, for example, the frequency of each word in the document. The concept of proximity in reading, as illustrated by the tendency to group letters to form words, can be related to the vector space model in that words or terms within documents are treated as distinct dimensions in a multi-dimensional space.
In the vector space model, text is transformed into a numerical format by mapping each unique word to a dimension in a space where each document is represented as a vector. The components of these vectors correspond to the term frequencies. The angular distance between any two document vectors can then be used to determine the similarity between the documents. This model allows complex documents to be compared and processed using the principles of linear algebra.
Vectors are used in many fields to represent quantities with both magnitude and direction. Following this concept, in text mining, vectors do not just signify the presence of terms but also convey the relative importance of those terms within each document based on their frequency or other weighting schemes.