The **Topic-based Vector Space Model (TVSM)**^{ [1] } (literature: ) extends the vector space model of information retrieval by removing the constraint that the term-vectors be orthogonal. The assumption of orthogonal terms is incorrect regarding natural languages which causes problems with synonyms and strong related terms. This facilitates the use of stopword lists, stemming and thesaurus in TVSM. In contrast to the generalized vector space model the TVSM does not depend on concurrence-based similarities between terms.

The basic premise of TVSM is the existence of a *d* dimensional space *R* with only positive axis intercepts, i.e. *R in R ^{+}* and

The enhancement of the Enhanced Topic-based Vector Space Model (eTVSM)^{ [2] } (literature: ) is a proposal on how to derive term vectors from an Ontology. Using a synonym Ontology created from WordNet Kuropka shows good results for document similarity. If a trivial Ontology is used the results are similar to Vector Space model.

**Information retrieval** (**IR**) is the activity of obtaining information system resources that are relevant to an information need from a collection of those resources. Searches can be based on full-text or other content-based indexing. Information retrieval is the science of searching for information in a document, searching for documents themselves, and also searching for the metadata that describes data, and for databases of texts, images or sounds.

The **principal components** of a collection of points in a real *p*-space are a sequence of direction vectors, where the vector is the direction of a line that best fits the data while being orthogonal to the first vectors. Here, a best-fitting line is defined as one that minimizes the average squared distance from the points to the line. These directions constitute an orthonormal basis in which different individual dimensions of the data are linearly uncorrelated. **Principal component analysis** (**PCA**) is the process of computing the principal components and using them to perform a change of basis on the data, sometimes using only the first few principal components and ignoring the rest.

In mathematics, **orthogonality** is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms. Two elements *u* and *v* of a vector space with bilinear form *B* are **orthogonal** when *B*(*u*, *v*) = 0. Depending on the bilinear form, the vector space may contain nonzero self-orthogonal vectors. In the case of function spaces, families of orthogonal functions are used to form a basis.

**Latent semantic analysis** (**LSA**) is a technique in natural language processing, in particular distributional semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms. LSA assumes that words that are close in meaning will occur in similar pieces of text. A matrix containing word counts per document is constructed from a large piece of text and a mathematical technique called singular value decomposition (SVD) is used to reduce the number of rows while preserving the similarity structure among columns. Documents are then compared by taking the cosine of the angle between the two vectors formed by any two columns. Values close to 1 represent very similar documents while values close to 0 represent very dissimilar documents.

A **document-term matrix** or **term-document matrix** is a mathematical matrix that describes the frequency of terms that occur in a collection of documents. In a document-term matrix, rows correspond to documents in the collection and columns correspond to terms. There are various schemes for determining the value that each entry in the matrix should take. One such scheme is tf-idf. They are useful in the field of natural language processing.

**Semantic similarity** is a metric defined over a set of documents or terms, where the idea of distance between items is based on the likeness of their meaning or semantic content as opposed to lexicographical similarity. These are mathematical tools used to estimate the strength of the semantic relationship between units of language, concepts or instances, through a numerical description obtained according to the comparison of information supporting their meaning or describing their nature. The term semantic similarity is often confused with semantic relatedness. **Semantic relatedness** includes any relation between two terms, while semantic similarity only includes "is a" relations. For example, "car" is similar to "bus", but is also related to "road" and "driving".

In information retrieval, **tf–idf** or **TFIDF**, short for **term frequency–inverse document frequency**, is a numerical statistic that is intended to reflect how important a word is to a document in a collection or corpus. It is often used as a weighting factor in searches of information retrieval, text mining, and user modeling. The tf–idf value increases proportionally to the number of times a word appears in the document and is offset by the number of documents in the corpus that contain the word, which helps to adjust for the fact that some words appear more frequently in general. tf–idf is one of the most popular term-weighting schemes today. A survey conducted in 2015 showed that 83% of text-based recommender systems in digital libraries use tf–idf.

**Distributional semantics** is a research area that develops and studies theories and methods for quantifying and categorizing semantic similarities between linguistic items based on their distributional properties in large samples of language data. The basic idea of distributional semantics can be summed up in the so-called Distributional hypothesis: *linguistic items with similar distributions have similar meanings.*

**Cosine similarity** is a measure of similarity between two non-zero vectors of an inner product space. It is defined to equal the cosine of the angle between them, which is also the same as the inner product of the same vectors normalized to both have length 1. The cosine of 0° is 1, and it is less than 1 for any angle in the interval (0, π] radians. It is thus a judgment of orientation and not magnitude: two vectors with the same orientation have a cosine similarity of 1, two vectors oriented at 90° relative to each other have a similarity of 0, and two vectors diametrically opposed have a similarity of -1, independent of their magnitude. The cosine similarity is particularly used in positive space, where the outcome is neatly bounded in . The name derives from the term "direction cosine": in this case, unit vectors are maximally "similar" if they're parallel and maximally "dissimilar" if they're orthogonal. This is analogous to the cosine, which is unity when the segments subtend a zero angle and zero when the segments are perpendicular.

In signal processing, **signal subspace** methods are empirical linear methods for dimensionality reduction and noise reduction. These approaches have attracted significant interest and investigation recently in the context of speech enhancement, speech modeling, and speech classification research. The signal subspace is also used in radio direction finding using the MUSIC (algorithm).

In machine learning, **semantic analysis** of a corpus is the task of building structures that approximate concepts from a large set of documents. It generally does not involve prior semantic understanding of the documents. A metalanguage based on predicate logic can analyze the speech of humans. Another strategy to understand the semantics of a text is symbol grounding. If language is grounded, it is equal to recognizing a machine readable meaning. For the restricted domain of spatial analysis, a computer based language understanding system was demonstrated.

**Ranking** of query is one of the fundamental problems in information retrieval (IR), the scientific/engineering discipline behind search engines. Given a query q and a collection D of documents that match the query, the problem is to rank, that is, sort, the documents in D according to some criterion so that the "best" results appear early in the result list displayed to the user. Ranking in terms of information retrieval is an important concept in computer science and is used in many different applications such as search engine queries and recommender systems. A majority of search engines use ranking algorithms to provide users with accurate and relevant results.

**Vector space model** or **term vector model** is an algebraic model for representing text documents as vectors of identifiers. It is used in information filtering, information retrieval, indexing and relevancy rankings. Its first use was in the SMART Information Retrieval System.

In natural language processing and information retrieval, **cluster labeling** is the problem of picking descriptive, human-readable labels for the clusters produced by a document clustering algorithm; standard clustering algorithms do not typically produce any such labels. Cluster labeling algorithms examine the contents of the documents per cluster to find a labeling that summarize the topic of each cluster and distinguish the clusters from each other.

The **Extended Boolean model** was described in a Communications of the ACM article appearing in 1983, by Gerard Salton, Edward A. Fox, and Harry Wu. The goal of the Extended Boolean model is to overcome the drawbacks of the Boolean model that has been used in information retrieval. The Boolean model doesn't consider term weights in queries, and the result set of a Boolean query is often either too small or too big. The idea of the extended model is to make use of partial matching and term weights as in the vector space model. It combines the characteristics of the Vector Space Model with the properties of Boolean algebra and ranks the similarity between queries and documents. This way a document may be somewhat relevant if it matches some of the queried terms and will be returned as a result, whereas in the Standard Boolean model it wasn't.

The **Generalized vector space model** is a generalization of the vector space model used in information retrieval. Wong *et al.* presented an analysis of the problems that the pairwise orthogonality assumption of the vector space model (VSM) creates. From here they extended the VSM to the generalized vector space model (GVSM).

The **Binary Independence Model** (BIM) is a probabilistic information retrieval technique that makes some simple assumptions to make the estimation of document/query similarity probability feasible.

In natural language processing and information retrieval, **explicit semantic analysis** (**ESA**) is a vectoral representation of text that uses a document corpus as a knowledge base. Specifically, in ESA, a word is represented as a column vector in the tf–idf matrix of the text corpus and a document is represented as the centroid of the vectors representing its words. Typically, the text corpus is English Wikipedia, though other corpora including the Open Directory Project have been used.

**Word2vec** is a technique for natural language processing. The word2vec algorithm uses a neural network model to learn word associations from a large corpus of text. Once trained, such a model can detect synonymous words or suggest additional words for a partial sentence. As the name implies, word2vec represents each distinct word with a particular list of numbers called a vector. The vectors are chosen carefully such that a simple mathematical function (the cosine similarity between the vectors) indicates the level of semantic similarity between the words represented by those vectors.

**Semantic folding** theory describes a procedure for encoding the semantics of natural language text in a semantically grounded binary representation. This approach provides a framework for modelling how language data is processed by the neocortex.

- ↑ Dominik Kuropka; Jörg Becker (2003),
*Topic-based Vector Space Model*(PDF) - ↑ Dominik Kuropka; Artem Polyvyanyy (2007),
*A Quantitative Evaluation of the Enhanced Topic-Based Vector Space Model*(PDF)

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