Hinge Functions
Hinge functions are a key part of MARS models. A hinge function takes the form
or
where is a constant, called the knot. The figure on the right shows a mirrored pair of hinge functions with a knot at 3.1.
A hinge function is zero for part of its range, so can be used to partition the data into disjoint regions, each of which can be treated independently. Thus for example a mirrored pair of hinge functions in the expression
creates the piecewise linear graph shown for the simple MARS model in the previous section.
One might assume that only piecewise linear functions can be formed from hinge functions, but hinge functions can be multiplied together to form non-linear functions.
Hinge functions are also called hockey stick functions. Instead of the notation used in this article, hinge functions are often represented by where means take the positive part.
Read more about this topic: Multivariate Adaptive Regression Splines
Famous quotes containing the words hinge and/or functions:
“It is one of the consolations of philosophy that the benefit of showing how to dispense with a concept does not hinge on dispensing with it.”
—Willard Van Orman Quine (b. 1908)
“Let us stop being afraid. Of our own thoughts, our own minds. Of madness, our own or others. Stop being afraid of the mind itself, its astonishing functions and fandangos, its complications and simplifications, the wonderful operation of its machinerymore wonderful because it is not machinery at all or predictable.”
—Kate Millett (b. 1934)