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The margin for an iterative boosting algorithm given a dataset with two classes can be defined as follows: the classifier is given a sample pair (,), where is a domain space and = {, +} is the sample's label.
Eigen is a high-level C++ library of template headers for linear algebra, matrix and vector operations, geometrical transformations, numerical solvers and related algorithms. . Eigen is open-source software licensed under the Mozilla Public License 2.0 since version 3.1
A vector field V defined on an open set S is called a gradient field or a conservative field if there exists a real-valued function (a scalar field) f on S such that = = (,,, …,). The associated flow is called the gradient flow , and is used in the method of gradient descent .
In vector calculus, a conservative vector field is a vector field that is the gradient of some function. [1] A conservative vector field has the property that its line integral is path independent; the choice of path between two points does not change the value of the line integral. Path independence of the line integral is equivalent to the ...
A (,)-tensor field is a differential -form, a (,)-tensor field is a vector field, and a (,)-tensor field is -vector field. While differential forms are widely studied as such in differential geometry and differential topology , multivector fields are often encountered as tensor fields of type ( 0 , k ) {\displaystyle (0,k)} , except in the ...
Given two C 1 vector fields V and W on d-dimensional Euclidean space R d, let [V, W] denote their Lie bracket, another vector field defined by [,] = () (),where DV(x) denotes the Fréchet derivative of V at x ∈ R d, which can be thought of as a matrix that is applied to the vector W(x), and vice versa.
The most vexing parse is a counterintuitive form of syntactic ambiguity resolution in the C++ programming language. In certain situations, the C++ grammar cannot distinguish between the creation of an object parameter and specification of a function's type. In those situations, the compiler is required to interpret the line as a function type ...
A margin classifier is a classification model that utilizes the margin of each example to learn such classification. There are theoretical justifications (based on the VC dimension) as to why maximizing the margin (under some suitable constraints) may be beneficial for machine learning and statistical inference algorithms.