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The proximal operator can be seen as a generalization of the projection operator. Indeed, in the specific case where f {\displaystyle f} is the 0- ∞ {\displaystyle \infty } characteristic function ι C {\displaystyle \iota _{C}} of a nonempty, closed, convex set C {\displaystyle C} we have that
In computer science there are binary and unary operators depending on the number of elements or records an operator acts on. In database searching there are Boolean and Proximity operators. Boolean operators are a subclass of logical operators (Logical operators are binary operators that manipulate data at the bit level.). A Boolean operator ...
Phrase search is one of many search operators that are standard in search engine technology, along with Boolean operators (AND, OR, and NOT), truncation and wildcard operators (commonly represented by the asterisk symbol), field code operators (which look for specific words in defined fields, such as the Author field in a periodical database ...
The basic linguistic assumption of proximity searching is that the proximity of the words in a document implies a relationship between the words. Given that authors of documents try to formulate sentences which contain a single idea, or cluster of related ideas within neighboring sentences or organized into paragraphs, there is an inherent, relatively high, probability within the document ...
The (standard) Boolean model of information retrieval (BIR) [1] is a classical information retrieval (IR) model and, at the same time, the first and most-adopted one. [2] The BIR is based on Boolean logic and classical set theory in that both the documents to be searched and the user's query are conceived as sets of terms (a bag-of-words model).
In topology, a proximity space, also called a nearness space, is an axiomatization of the intuitive notion of "nearness" that hold set-to-set, as opposed to the better known point-to-set notion that characterize topological spaces. The concept was described by Frigyes Riesz but ignored at the time. [1]
They are called proximal because each non-differentiable function among ,..., is involved via its proximity operator. Iterative shrinkage thresholding algorithm, [ 1 ] projected Landweber , projected gradient, alternating projections , alternating-direction method of multipliers , alternating split Bregman are special instances of proximal ...
The Web of Science (WoS; previously known as Web of Knowledge) is a paid-access platform that provides (typically via the internet) access to multiple databases that provide reference and citation data from academic journals, conference proceedings, and other documents in various academic disciplines.