In consideration of this problem, we propose an improved distance measure based on
kernel space. The original data are mapped to the feature space of high dimension by kernel function, which makes the data separable.
Solving singular two-point boundary problem in reproducing
kernel space. Journal of Computational and Applied Mathematics, 205(1):6-15, 2007.
where [phi] : [R.sup.D] [right arrow] [R.sup.t] means the kernel function; it maps the original feature space into a high dimensional
kernel space.
The present method can approximate the solutions and their derivatives at every point of the range of integration; also it has several advantages such that the conditions for determining solutions can be imposed on the reproducing
kernel space, the conditions about the nonlinearity of the forcing function f are simple and may include u, [u.sup.i], or any others operator of u, and the iterative sequence [u.sub.n](x) of approximate solutions converges in C to the solution u(x).
In this section, we show some fundamental theories of the reproducing
kernel space [11, 12].
Substituting the expansion of p in (10) into 9), this transformation leads to nonlinear generalization of fuzzy inference system in
kernel space which can be called as kernel fuzzy inference system (K-FIS).
MI (K, D) measures the importance of feature subset F' in the
kernel space to distinguish different classes.
For a countable dense set [{[x.sub.i]}.sup.[infinity].sub.i=1] of [a, b], let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [[psi].sub.i](x) = [L.sup.*] [[phi].sub.i](x) where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the reproducing
kernel space of [W.sup.1.sub.2][a, b] and [L.sup.*] is the adjoint operator of L.
The formula the left represents the center frequency of the filter, kv = [k.sub.max]/[f.sup.v], ([phi]u = [pi]u/8, [k.sub.max] Represents the maximum frequency, in the frequency domain,
kernel space factor is f Filter of direction selectivity is decision by [[phi].sub.u].
For the feature [y.sub.ci] = [phi]([x.sub.ci]) in the
kernel space, we define its informative energy according to the graph energy model.