Fitting Routines
There are four characteristics of the RBF that need to be decided:
weights, centers, width, and
. Each of these can have significant impact on
the quality of the resulting fit, and good values for each of them
need to be determined. The weights are always determined by specifying
the centers, width, and
, and then solving an appropriate linear system
of equations. However, the problem of determining good centers, width,
and
in the first place is far from simple, and is
complicated by the strong dependencies among the parameters. For example,
the optimal
varies considerably as the width parameter changes.
A global search over all possible center locations, width, and
is computationally prohibitive
in all but the simplest of situations.
To try to combat this problem, the fitting routines come in
three different levels.
At the lowest level are the algorithms that choose appropriate
centers for given values of width and
. The centers are chosen one at
a time from a candidate set (usually the set of data points or a subset
of them). The resulting centers are therefore ranked in a rough order
of importance.
At the middle level are the algorithms that choose appropriate
values for
and the centers, given a specified width.
At the top level are the algorithms that aim to find good values
for each of the centers, width, and
. These top-level algorithms test
different width values. For each value of width, one of the middle-level
algorithms is called that determines good centers and values for
.
These algorithms and their fit parameters are described in the
following sections:
Center Selection Algorithms
Lambda Selection Algorithms
Width Selection Algorithms
 | Types of Radial Basis Functions | | Center Selection Algorithms |  |
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