Space (mathematics)In mathematics, a space is a set (sometimes called a universe) with some added structure. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself. A space consists of selected mathematical objects that are treated as points, and selected relationships between these points. The nature of the points can vary widely: for example, the points can be elements of a set, functions on another space, or subspaces of another space.
Linear discriminant analysisLinear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.
Pattern recognitionPattern recognition is the automated recognition of patterns and regularities in data. While similar, pattern recognition (PR) is not to be confused with pattern machines (PM) which may possess (PR) capabilities but their primary function is to distinguish and create emergent pattern. PR has applications in statistical data analysis, signal processing, , information retrieval, bioinformatics, data compression, computer graphics and machine learning.
Information theoryInformation theory is the mathematical study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field, in applied mathematics, is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering. A key measure in information theory is entropy.
Automatic transmissionAn automatic transmission (sometimes abbreviated AT) is a multi-speed transmission used in motor vehicles that does not require any input from the driver to change forward gears under normal driving conditions. The most common type of automatic transmission is the hydraulic automatic, which uses a planetary gearset, hydraulic controls, and a torque converter. Other types of automatic transmissions include continuously variable transmissions (CVT), automated manual transmissions (AMT), and dual-clutch transmissions (DCT).
Scale (ratio)The scale ratio of a model represents the proportional ratio of a linear dimension of the model to the same feature of the original. Examples include a 3-dimensional scale model of a building or the scale drawings of the elevations or plans of a building. In such cases the scale is dimensionless and exact throughout the model or drawing. The scale can be expressed in four ways: in words (a lexical scale), as a ratio, as a fraction and as a graphical (bar) scale.
Natural language generationNatural language generation (NLG) is a software process that produces natural language output. A widely-cited survey of NLG methods describes NLG as "the subfield of artificial intelligence and computational linguistics that is concerned with the construction of computer systems than can produce understandable texts in English or other human languages from some underlying non-linguistic representation of information". While it is widely agreed that the output of any NLG process is text, there is some disagreement about whether the inputs of an NLG system need to be non-linguistic.
Natural language processingNatural language processing (NLP) is an interdisciplinary subfield of linguistics and computer science. It is primarily concerned with processing natural language datasets, such as text corpora or speech corpora, using either rule-based or probabilistic (i.e. statistical and, most recently, neural network-based) machine learning approaches. The goal is a computer capable of "understanding" the contents of documents, including the contextual nuances of the language within them.
Computer engineeringComputer engineering (CoE or CpE) is a branch of electronic engineering and computer science that integrates several fields of computer science and electronic engineering required to develop computer hardware and software. Computer engineers require training in electronic engineering, computer science, hardware-software integration, software design, and software engineering. It uses the techniques and principles of electrical engineering and computer science, and can encompass areas such as artificial intelligence (AI), robotics, computer networks, computer architecture and operating systems.
Inner product spaceIn mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in . Inner products allow formal definitions of intuitive geometric notions, such as lengths, angles, and orthogonality (zero inner product) of vectors. Inner product spaces generalize Euclidean vector spaces, in which the inner product is the dot product or scalar product of Cartesian coordinates.
Hierarchical clusteringIn data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two categories: Agglomerative: This is a "bottom-up" approach: Each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy. Divisive: This is a "top-down" approach: All observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.
Diffusion equationThe diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's laws of diffusion). In mathematics, it is related to Markov processes, such as random walks, and applied in many other fields, such as materials science, information theory, and biophysics. The diffusion equation is a special case of the convection–diffusion equation, when bulk velocity is zero.
