Concepts inOnline and batch learning of pseudo-metrics
E-learning
E-learning comprises all forms of electronically supported learning and teaching. The information and communication systems, whether networked learning or not, serve as specific media to implement the learning process. The term will still most likely be utilized to reference out-of-classroom and in-classroom educational experiences via technology, even as advances continue in regard to devices and curriculum.
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Online algorithm
In computer science, an online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e. , in the order that the input is fed to the algorithm, without having the entire input available from the start. In contrast, an offline algorithm is given the whole problem data from the beginning and is required to output an answer which solves the problem at hand.
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Positive-definite matrix
In linear algebra, a positive-definite matrix is a matrix that in many ways is analogous to a positive real number. The notion is closely related to a positive-definite symmetric bilinear form (or a sesquilinear form in the complex case). The proper definition of positive-definite is unambiguous for Hermitian matrices, but there is no agreement in the literature on how this should be extended for non-Hermitian matrices, if at all. (See the section Non-Hermitian matrices below.)
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Supervised learning
Supervised learning is the machine learning task of inferring a function from supervised (labeled) training data. The training data consist of a set of training examples. In supervised learning, each example is a pair consisting of an input object (typically a vector) and a desired output value (also called the supervisory signal).
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Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. In this context, a computational problem is understood to be a task that is in principle amenable to being solved by a computer (which basically means that the problem can be stated by a set of mathematical instructions).
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Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example, is a quadratic form in the variables x and y. Quadratic forms occupy a central place in various branches of mathematics, including number theory, linear algebra, group theory, differential geometry, differential topology, and Lie theory.
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Constraint (mathematics)
In mathematics, a constraint is a condition that a solution to an optimization problem is required by the problem itself to satisfy. There are two types of constraints: equality constraints and inequality constraints. The set of candidate solutions that satisfy all constraints is called the feasible set.
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