Matrices, Vector Spaces, and Information Retrieval

Abstract

Abstract. The evolution of digital libraries and the Internet has dramatically transformed the processing, storage, and retrieval of information. Efforts to digitize text, images, video, and audio now consume a substantial portion of both academic and industrial activity. Even when there is no shortage of textual materials on a particular topic, procedures for indexing or extracting the knowledge or conceptual information contained in them can be lacking. Recently developed information retrieval technologies are based on the concept of a vector space. Data are modeled as a matrix, and a user's query of the database is represented as a vector. Relevant documents in the database are then identified via simple vector operations. Orthogonal factorizations of the matrix provide mechanisms for handling uncertainty in the database itself. The purpose of this paper is to show how such fundamental mathematical concepts from linear algebra can be used to manage and index large text collections.

The Impact of Modes of Mediation on the Web Retrieval Process

“…The Vector Space Model (VSM) is an algebraic model used for information filtering, information retrieval, indexing and relevance ranking (Berry, Drmac andElizabeth 1999, Polyvyanyy andKuropka 2007 …”

Cross - Language Information Retrieval Using Two Methods: LSI via SDD and LSI via SVD

“…Latent semantic indexing (LSI) [3][4][5], also called latent semantic analysis (LSA) is an automatic indexing method based on the semantics of documents, which attempts to overcome the two main problems that have the traditional indexing schemes of lexical coincidences: polysemy and synonymy. The first has to do with a word that can have multiple meanings, and therefore, the words of a query may not coincide in meaning with those of the documents; the second means that several terms can have the same meaning and hence the words used in queries can match nonrelevant documents.…”

Seurat: A Pointillist Approach to Anomaly Detection

“…For each vector The correlation is based on the distances among vectors. Seurat uses a cosine distance metric, which is a common similarity measure between binary vectors [9,10]. We define the distance …”