Dimensionality reductionDimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable (hard to control or deal with).
CardinalityIn mathematics, the cardinality of a set is a measure of the number of elements of the set. For example, the set contains 3 elements, and therefore has a cardinality of 3. Beginning in the late 19th century, this concept was generalized to infinite sets, which allows one to distinguish between different types of infinity, and to perform arithmetic on them. There are two approaches to cardinality: one which compares sets directly using bijections and injections, and another which uses cardinal numbers.
Support vector machineIn machine learning, support vector machines (SVMs, also support vector networks) are supervised learning models with associated learning algorithms that analyze data for classification and regression analysis. Developed at AT&T Bell Laboratories by Vladimir Vapnik with colleagues (Boser et al., 1992, Guyon et al., 1993, Cortes and Vapnik, 1995, Vapnik et al., 1997) SVMs are one of the most robust prediction methods, being based on statistical learning frameworks or VC theory proposed by Vapnik (1982, 1995) and Chervonenkis (1974).
Joseph-Louis LagrangeJoseph-Louis Lagrange (born Giuseppe Luigi Lagrangia or Giuseppe Ludovico De la Grange Tournier; 25 January 1736 – 10 April 1813), also reported as Giuseppe Luigi Lagrange or Lagrangia, was an Italian mathematician, physicist and astronomer, later naturalized French. He made significant contributions to the fields of analysis, number theory, and both classical and celestial mechanics.
Card readerA card reader is a data input device that reads data from a card-shaped storage medium. The first were punched card readers, which read the paper or cardboard punched cards that were used during the first several decades of the computer industry to store information and programs for computer systems. Modern card readers are electronic devices that can read plastic cards embedded with either a barcode, magnetic strip, computer chip or another storage medium. A memory card reader is a device used for communication with a smart card or a memory card.
K-d treeIn computer science, a k-d tree (short for k-dimensional tree) is a space-partitioning data structure for organizing points in a k-dimensional space. k-d trees are a useful data structure for several applications, such as searches involving a multidimensional search key (e.g. range searches and nearest neighbor searches) and creating point clouds. k-d trees are a special case of binary space partitioning trees. The k-d tree is a binary tree in which every node is a k-dimensional point.
Credit cardA credit card is a payment card issued to users (cardholders) to enable the cardholder to pay a merchant for goods and services based on the cardholder's accrued debt (i.e., promise to the card issuer to pay them for the amounts plus the other agreed charges). The card issuer (usually a bank or credit union) creates a revolving account and grants a line of credit to the cardholder, from which the cardholder can borrow money for payment to a merchant or as a cash advance.
Doomsday ruleThe Doomsday rule, Doomsday algorithm or Doomsday method is an algorithm of determination of the day of the week for a given date. It provides a perpetual calendar because the Gregorian calendar moves in cycles of 400 years. The algorithm for mental calculation was devised by John Conway in 1973, drawing inspiration from Lewis Carroll's perpetual calendar algorithm. It takes advantage of each year having a certain day of the week upon which certain easy-to-remember dates, called the doomsdays, fall; for example, the last day of February, 4/4, 6/6, 8/8, 10/10, and 12/12 all occur on the same day of the week in any year.
TranslationTranslation is the communication of the meaning of a source-language text by means of an equivalent target-language text. The English language draws a terminological distinction (which does not exist in every language) between translating (a written text) and interpreting (oral or signed communication between users of different languages); under this distinction, translation can begin only after the appearance of writing within a language community.
Digital imagingDigital imaging or digital image acquisition is the creation of a digital representation of the visual characteristics of an object, such as a physical scene or the interior structure of an object. The term is often assumed to imply or include the , , , printing and display of such images. A key advantage of a , versus an analog image such as a film photograph, is the ability to digitally propagate copies of the original subject indefinitely without any loss of image quality.
Convex polytopeA convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the -dimensional Euclidean space . Most texts use the term "polytope" for a bounded convex polytope, and the word "polyhedron" for the more general, possibly unbounded object. Others (including this article) allow polytopes to be unbounded. The terms "bounded/unbounded convex polytope" will be used below whenever the boundedness is critical to the discussed issue.
Google TranslateGoogle Translate is a multilingual neural machine translation service developed by Google to translate text, documents and websites from one language into another. It offers a website interface, a mobile app for Android and iOS, as well as an API that helps developers build browser extensions and software applications. As of 2022, Google Translate supports languages at various levels; it claimed over 500 million total users , with more than 100 billion words translated daily, after the company stated in May 2013 that it served over 200 million people daily.
