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In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane ) by thinking of one set of points as being colored blue and the other set of points as being colored red.
Kirchberger's theorem is a theorem in discrete geometry, on linear separability.The two-dimensional version of the theorem states that, if a finite set of red and blue points in the Euclidean plane has the property that, for every four points, there exists a line separating the red and blue points within those four, then there exists a single line separating all the red points from all the ...
Linear separability is testable in time ((/), (), ()), where is the number of data points, and is the dimension of each point. [ 35 ] If the training set is linearly separable, then the perceptron is guaranteed to converge after making finitely many mistakes. [ 36 ]
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
Separable filter, a product of two or more simple filters in image processing; Separable ordinary differential equation, a class of equations that can be separated into a pair of integrals; Separable partial differential equation, a class of equations that can be broken down into differential equations in fewer independent variables
In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.
LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition.
In statistics, separation is a phenomenon associated with models for dichotomous or categorical outcomes, including logistic and probit regression.Separation occurs if the predictor (or a linear combination of some subset of the predictors) is associated with only one outcome value when the predictor range is split at a certain value.