Using Linear Algebra for Intelligent Information Retrieval

Abstract

Currently, most approaches to retrieving textual materials from scienti c databases depend on a lexical match b e t ween words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity i n t h e w ords people use to describe the same document, lexical methods are necessarily incomplete and imprecise. Using the singular value decomposition (SVD), one can take a d v antage of the implicit higher-order structure in the association of terms with documents by determining the SVD of large sparse term by document matrices. Terms and documents represented by 200-300 of the largest singular vectors are then matched against user queries. We call this retrieval method Latent Semantic Indexing (LSI) because the subspace represents important associative relationships between terms and documents that are not evident in individual documents. LSI is a completely automatic yet intelligent indexing method, widely applicable, and a promising way to improve users' access to many kinds of textual materials, or to documents and services for which textual descriptions are available. A survey of the computational requirements for managing LSI-encoded databases as well as current and future applications of LSI is presented.

Formalization of Technological Knowledge in the Field of Metallurgy using Document Classification Tools Supported with Semantic Techniques

“…The root is part of the word, which in a unique way is identified with the lexeme. This operation contributes to a decrease in the data to be analyzed [21].…”

Semantic, Hierarchical, Online Clustering of Web Search Results

“…Assuming the cluster-quality threshold *80% q = , the appropriate cluster number is 2 , because There are some efficient algorithms which can do SVD for large sparse matrix very quickly [15]. To save time further, we can run SVD on the top-n items in the search results returned by search engines, then "fold-in" the rest documents incrementally [1]. Because search engines usually place high quality documents at the top of the result list, this approximation would not seriously hurt the clustering quality.…”

Untitled

“…One way is to simply specify the first k or last n − k singular triplets (σ i , u i , v i ) needed to capture the most relevant information in the data matrix A for the particular application. This approach is used, for example, in information retrieval [4]. A difficult aspect of this approach is that ad hoc procedures are often used to choose k.…”

“…Certain applications give rise to low-rank matrices A in which k n. For instance, low-rank matrices arise in information retrieval using latent semantic indexing (LSI) [4], where the elements of the m×n matrix A provide an incomplete connection between n documents which define the database, and m key words pertaining to the database. The parameter k is typically 0.1% of min(m, n), thus relatively few factors are adequate for the LSI approach.…”

“…The SVD detects near-rank deficiency in a matrix very reliably and yields all the necessary subspace information. Because the SVD algorithm is so reliable and numerically stable, it is used in a wide variety of applications, such as frequency estimation via least squares and total least squares [48,49,58], principal component analysis [60], noise reduction in speech processing [33], computer-aided geometric design [40], and information retrieval [4]. Additional applications of the SVD can be found in the International Workshop on SVD and Signal Processing proceedings [17,42,59].…”