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Knowledge Graph Embedding
In representation learning, knowledge graph embedding (KGE), also called 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 Semantics, semantic meaning. Leveraging their Embedding (machine learning), embedded representation, knowledge graphs (KGs) can be used for various applications such as link prediction, triple classification, entity recognition, Cluster analysis, 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 re ... [...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 Preliminaries 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." Definition 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). A relation is asymmetric if and only if it is both antisymmetric and irreflexive, so this may also be taken as a definit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Many-to-one Relation
In mathematics, a binary relation associates some elements of one set called the ''domain'' with some elements of another set called the ''codomain''. Precisely, a binary relation over sets X and Y is a set of ordered pairs (x, y), where x is an element of X and y is an element of Y. It encodes the common concept of relation: an element x is ''related'' to an element y, if and only if the pair (x, y) belongs to the set of ordered pairs that defines the binary relation. 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 p is related to each integer z that is a multiple of p, but not to an integer that is not a multiple of p. In this relation, for instance, the prime number 2 is related to numbers such as -4, 0, 6, 10, but not to 1 or 9, just as the prime number 3 is related to 0, 6, and 9, but not to 4 or 13. Binary relations, and especially homogeneous relations, are used in man ... [...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). For example, take a car and an owner of the car. The car can only be owned by one owner at a time or not owned at all, and an owner could own zero, one, or multiple cars. One owner could have many cars, one-to-many. In a relational database, a one-to-many relationship exists when one record is related to many records of another table. A one-to-many relationship is not a property of the data, but rather of the relationship itself. One-to-many often refer to a primary key to foreign key relationship between two tables, where the record in the first table can relate to multiple records in the second table. A foreign key is one side of the relationship that shows a row or multiple rows, with one of those rows being the primary key already listed on the first table. This is also called a foreign key constraint, which is i ... [...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. Euclidean vectors can be added and scaled to form a vector space. A '' vector quantity'' is a vector-valued physical quantity, including units of measurement and possibly a support, formulated as a '' directed line segment''. A vector is frequently depicted graphically as an arrow connecting an ''initial point'' ''A'' with a ''terminal point'' ''B'', and denoted by \stackrel \longrightarrow. A vector is what is needed to "carry" the point ''A'' to the point ''B''; the Latin word 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 numb ... [...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 European Film Festival. Plot Sonia is a young woman from St. Petersburg. After her personal and work life fall apart, she leaves Russia in search of a better life. She eventually arrives in Germany and finds an undeclared job at a car dealership. One day, an individual comes to her work, telling that the other immigrants have been taken by the authorities. Promising to help her get her passport, Sonia gets into the car with him. After falling asleep, another man enters the car and begins driving. With the situation still unclear, he lets her out, but she is left in the wilderness. Still in the forest and unconscious, she is picked up by the same person, who locks her naked in a bathroom until she pleads for help. When he finally lets her out, he proceeds to rape her as she tries to warm herself under a bed's covers. He then tells her that he has no other choice but t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word2vec
Word2vec is a technique in natural language processing (NLP) for obtaining vector representations of words. These vectors capture information about the meaning of the word based on the surrounding words. The word2vec algorithm estimates these representations by modeling text in a large corpus. Once trained, such a model can detect synonymous words or suggest additional words for a partial sentence. Word2vec was developed by Tomáš Mikolov, Kai Chen, Greg Corrado, Ilya Sutskever and Jeff Dean at Google, and published in 2013. Word2vec represents a word as a high-dimension vector of numbers which capture relationships between words. In particular, words which appear in similar contexts are mapped to vectors which are nearby as measured by cosine similarity. This indicates the level of semantic similarity between the words, so for example the vectors for ''walk'' and ''ran'' are nearby, as are those for "but" and "however", and "Berlin" and "Germany". Approach Word2vec is a ... [...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) or the M-mode SVD. The algorithm to which the literature typically refers when discussing the Tucker decomposition or the HOSVD is the M-mode SVD algorithm introduced by Vasilescu and Terzopoulos, but misattributed to Tucker or De Lathauwer etal. 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 o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term ''Fourier transform'' refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Polyadic Decomposition
In multilinear algebra, the tensor rank decomposition or rank-''R'' decomposition is the decomposition of a tensor as a sum of ''R'' rank-1 tensors, where ''R'' is minimal. Computing this decomposition is an open problem. Canonical polyadic decomposition (CPD) is a variant of the tensor rank decomposition, in which the tensor is approximated as a sum of ''K'' rank-1 tensors for a user-specified ''K''. The CP decomposition has found some applications in linguistics and chemometrics. It 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). Note that the PARAFAC2 rank decomposition is a variation of the CP decomposition. 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, comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analogical
Analogy is a comparison or correspondence between two things (or two groups of things) because of a third element that they are considered to share. In logic, it is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction. It is also used where at least one of the premises, or the conclusion, is general rather than particular in nature. It has the general form ''A is to B as C is to D''. In a broader sense, analogical reasoning is a cognitive process of transferring some information or meaning of a particular subject (the analog, or source) onto another (the target); and also the linguistic expression corresponding to such a process. 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 human thought processes. It has been argued that analogy lies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
