# Basis Functions

### Some articles on basis, basis functions, functions, function, basis function:

Curvelet
... Wavelets generalize the Fourier transform by using a basis that represents both location and spatial frequency ... directional wavelet transforms go further, by using basis functions that are also localized in orientation ... In particular, fine-scale basis functions are long ridges the shape of the basis functions at scale j is by so the fine-scale bases are skinny ridges with a precisely determined orientation ...
Predictive Analytics - Statistical Techniques - Multivariate Adaptive Regression Splines
... In multivariate and adaptive regression splines, basis functions are the tool used for generalizing the search for knots ... Basis functions are a set of functions used to represent the information contained in one or more variables ... Regression Splines model almost always creates the basis functions in pairs ...
Practical Assembly of The Stiffness Matrix
... method on a computer, one must first choose a set of basis functions and then compute the integrals defining the stiffness matrix ... The basis functions are then chosen to be polynomials of some order within each element, and continuous across element boundaries ... for most values of i and j, for which the corresponding basis functions are zero within Tk ...
Polynomial Regression - Alternative Approaches
... Polynomial regression is one example of regression analysis using basis functions to model a functional relationship between two quantities ... A drawback of polynomial bases is that the basis functions are "non-local", meaning that the fitted value of y at a given value x = x0 depends strongly on data values with x far from x0 ... In modern statistics, polynomial basis-functions are used along with new basis functions, such as splines, radial basis functions, and wavelets ...
Empirical Orthogonal Functions
... and signal processing, the method of empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which ... The ith basis function is chosen to be orthogonal to the basis functions from the first through i − 1, and to minimize the residual variance ... That is, the basis functions are chosen to be different from each other, and to account for as much variance as possible ...

### Famous quotes containing the words functions and/or basis:

The English masses are lovable: they are kind, decent, tolerant, practical and not stupid. The tragedy is that there are too many of them, and that they are aimless, having outgrown the servile functions for which they were encouraged to multiply. One day these huge crowds will have to seize power because there will be nothing else for them to do, and yet they neither demand power nor are ready to make use of it; they will learn only to be bored in a new way.
Cyril Connolly (1903–1974)

Painting dissolves the forms at its command, or tends to; it melts them into color. Drawing, on the other hand, goes about resolving forms, giving edge and essence to things. To see shapes clearly, one outlines them—whether on paper or in the mind. Therefore, Michelangelo, a profoundly cultivated man, called drawing the basis of all knowledge whatsoever.
Alexander Eliot (b. 1919)