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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, a geometric property of a pair of sets of points in Euclidean geometry; Recursively inseparable sets, in computability theory, pairs of sets of natural numbers that cannot be "separated" with a recursive set
The left image shows 100 points in the two dimensional real space, labelled according to whether they are inside or outside the circular area. These labelled points are not linearly separable, but lifting them to the three dimensional space with the kernel trick, the points becomes linearly separable. Note that in this case and in many other ...
Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation.. In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
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 ]
In field theory, a branch of algebra, an algebraic field extension / is called a separable extension if for every , the minimal polynomial of over F is a separable polynomial (i.e., its formal derivative is not the zero polynomial, or equivalently it has no repeated roots in any extension field). [1]
Thus more sophisticated formulations are required. The separability problem is a subject of current research. A separability criterion is a necessary condition a state must satisfy to be separable. In the low-dimensional (2 X 2 and 2 X 3) cases, the Peres-Horodecki criterion is actually a