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In the lower plot, both the area and population data have been transformed using the logarithm function. In statistics, data transformation is the application of a deterministic mathematical function to each point in a data set—that is, each data point z i is replaced with the transformed value y i = f(z i), where f is a function.
In computer science, graph transformation, or graph rewriting, concerns the technique of creating a new graph out of an original graph algorithmically. It has numerous applications, ranging from software engineering ( software construction and also software verification ) to layout algorithms and picture generation.
This means that the inverse function will only give values in the domain of the function, but restricted to a single period. Hence, the range of the inverse function is only half a full circle. Note that one can also use r = x 2 + y 2 θ ′ = 2 arctan y x + r {\displaystyle {\begin{aligned}r&={\sqrt {x^{2}+y^{2}}}\\\theta '&=2\arctan ...
The transformation of graphs is often formalized and represented by graph rewrite systems. Complementary to graph transformation systems focusing on rule-based in-memory manipulation of graphs are graph databases geared towards transaction-safe, persistent storing and querying of graph-structured data.
Affine transformation (Euclidean geometry) Bäcklund transform; Bilinear transform; Box–Muller transform; Burrows–Wheeler transform (data compression) Chirplet transform; Distance transform; Fractal transform; Gelfand transform; Hadamard transform; Hough transform (digital image processing) Inverse scattering transform; Legendre ...
ΔY- and YΔ-transformations are a tool both in pure graph theory as well as applications. Both operations preserve a number of natural topological properties of graphs. . For example, applying a YΔ-transformation to a 3-vertex of a planar graph, or a ΔY-transformation to a triangular face of a planar graph, results again in a planar graph.
A composition of four mappings coded in SVG, which transforms a rectangular repetitive pattern into a rhombic pattern. The four transformations are linear.. In mathematics, a transformation, transform, or self-map [1] is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X.
The existence of the inverse Möbius transformation and its explicit formula are easily derived by the composition of the inverse functions of the simpler transformations. That is, define functions g 1 , g 2 , g 3 , g 4 such that each g i is the inverse of f i .