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Knowledge Graph Embedding
In representation learning, knowledge graph embedding (KGE), also referred to as knowledge representation learning (KRL), or multi-relation learning, is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their semantic meaning. Leveraging their embedded representation, knowledge graphs (KGs) can be used for various applications such as link prediction, triple classification, entity recognition, clustering, and relation extraction. Definition A knowledge graph \mathcal = \ is a collection of entities E , relations R, and facts F. A ''fact'' is a triple (h, r, t) \in F that denotes a link r \in R between the head h \in E and the tail t \in E of the triple. Another notation that is often used in the literature to represent a triple (or fact) is . This notation is called resource description framework (RDF). A knowledge graph represents the knowledge related to a specific domain; leveraging this s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymmetric Relation
In mathematics, an asymmetric relation is a binary relation R on a set X where for all a, b \in X, if a is related to b then b is ''not'' related to a. Formal definition A binary relation on X is any subset R of X \times X. Given a, b \in X, write a R b if and only if (a, b) \in R, which means that a R b is shorthand for (a, b) \in R. The expression a R b is read as "a is related to b by R." The binary relation R is called if for all a, b \in X, if a R b is true then b R a is false; that is, if (a, b) \in R then (b, a) \not\in R. This can be written in the notation of first-order logic as \forall a, b \in X: a R b \implies \lnot(b R a). A logically equivalent definition is: :for all a, b \in X, at least one of a R b and b R a is , which in first-order logic can be written as: \forall a, b \in X: \lnot(a R b \wedge b R a). An example of an asymmetric relation is the " less than" relation \,<\, between |
Many-to-one Relation
In mathematics, a binary relation associates elements of one set, called the ''domain'', with elements of another set, called the ''codomain''. A binary relation over sets and is a new set of ordered pairs consisting of elements in and in . It is a generalization of the more widely understood idea of a unary function. It encodes the common concept of relation: an element is ''related'' to an element , if and only if the pair belongs to the set of ordered pairs that defines the ''binary relation''. A binary relation is the most studied special case of an -ary relation over sets , which is a subset of the Cartesian product X_1 \times \cdots \times X_n. An example of a binary relation is the "divides" relation over the set of prime numbers \mathbb and the set of integers \mathbb, in which each prime is related to each integer that is a multiple of , but not to an integer that is not a multiple of . In this relation, for instance, the prime number 2 is related to number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
One-to-many (data Model)
In systems analysis, a one-to-many relationship is a type of cardinality that refers to the relationship between two entities (see also entity–relationship model) A and B in which an element of A may be linked to many elements of B, but a member of B is linked to only one element of A. For instance, think of A as books, and B as pages. A book can have many pages, but a page can only be in one book. In a relational database, a one-to-many relationship exists when one row in table A may be linked with many rows in table B, but one row in table B is linked to only one row in table A. It is important to note that a one-to-many relationship is not a property of the data, but rather of the relationship itself. A list of authors and their books may happen to describe books with only one author, in which case one row of the books table will refer to only one row of the authors table, but the relationship itself is not one-to-many, because books ''may'' have more than one author, forming ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Sum
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a '' directed line segment'', or graphically as an arrow connecting an ''initial point'' ''A'' with a ''terminal point'' ''B'', and denoted by \overrightarrow . A vector is what is needed to "carry" the point ''A'' to the point ''B''; the Latin word ''vector'' means "carrier". It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from ''A'' to ''B''. Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TransE
''Transe'' is a 2006 Portuguese film directed by Teresa Villaverde. It won a Special Jury Award at the 2007 Lecce Festival of European Cinema. Plot Sonia is a young woman born and raised in St. Peters burg Russia. Her life in Russia falls apart after her family and work life crumbles. Sonia leaves Russia for Germany in search of a better life with a group of other immigrants. Sonia Eventually arrives in Germany and is employed at a car dealership. One day, an individual comes to the dealership informing Sonia that all the immigrants and her passport have been taken by immigration authorities. Having no choice, Sonia gets into the car with the individual who promises her escape from immigration custody. Sonia falls asleep while traveling and eventually another man who identifies as Russian enters the car and begins driving. Sonia eventually realizes something is wrong and manages to get out of the car after protesting, but is left in the wilderness. Sonia is eventually picked bac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word2vec
Word2vec is a technique for natural language processing (NLP) published in 2013. 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 they capture the semantic and syntactic qualities of words; as such, a simple mathematical function (cosine similarity) can indicate the level of semantic similarity between the words represented by those vectors. Approach Word2vec is a group of related models that are used to produce word embeddings. These models are shallow, two-layer neural networks that are trained to reconstruct linguistic contexts of words. Word2vec takes as its input a large corpus of text and produces a vector space, typically of several hundred dimensions, with e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tucker Decomposition
In mathematics, Tucker decomposition decomposes a tensor into a set of matrices and one small core tensor. It is named after Ledyard R. Tucker although it goes back to Hitchcock in 1927. Initially described as a three-mode extension of factor analysis and principal component analysis it may actually be generalized to higher mode analysis, which is also called higher-order singular value decomposition (HOSVD). It may be regarded as a more flexible PARAFAC (parallel factor analysis) model. In PARAFAC the core tensor is restricted to be "diagonal". In practice, Tucker decomposition is used as a modelling tool. For instance, it is used to model three-way (or higher way) data by means of relatively small numbers of components for each of the three or more modes, and the components are linked to each other by a three- (or higher-) way core array. The model parameters are estimated in such a way that, given fixed numbers of components, the modelled data optimally resemble the actual da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Polyadic Decomposition
In multilinear algebra, the tensor rank decomposition or the rank-R decomposition of a tensor is the decomposition of a tensor in terms of a sum of minimum R rank-1 tensors. This is an open problem. Canonical polyadic decomposition (CPD) is a variant of the rank decomposition which computes the best fitting K rank-1 terms for a user specified K. The CP decomposition has found some applications in linguistics and chemometrics. The CP rank was introduced by Frank Lauren Hitchcock in 1927 and later rediscovered several times, notably in psychometrics. The CP decomposition is referred to as CANDECOMP, PARAFAC, or CANDECOMP/PARAFAC (CP). Another popular generalization of the matrix SVD known as the higher-order singular value decomposition computes orthonormal mode matrices and has found applications in econometrics, signal processing, computer vision, computer graphics, psychometrics. Notation A scalar variable is denoted by lower case italic letters, a and an upper bound scalar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analogical
Analogy (from Greek ''analogia'', "proportion", from ''ana-'' "upon, according to" lso "against", "anew"+ ''logos'' "ratio" lso "word, speech, reckoning" is a cognitive process of transferring information or meaning from a particular subject (the analog, or source) to another (the target), or a linguistic expression corresponding to such a process. In a narrower sense, analogy is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction, in which at least one of the premises, or the conclusion, is general rather than particular in nature. The term analogy can also refer to the relation between the source and the target themselves, which is often (though not always) a similarity, as in the biological notion of analogy. Analogy plays a significant role in problem solving, as well as decision making, argumentation, perception, generalization, memory, creativity, invention, prediction, emotion, explanation, conceptu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
