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Kernel Fisher discriminant analysis. In statistics, kernel Fisher discriminant analysis (KFD), [1] also known as generalized discriminant analysis [2] and kernel discriminant analysis, [3] is a kernelized version of linear discriminant analysis (LDA). It is named after Ronald Fisher .
One possible solution to this anchor point placement problem is to remove the histogram binning grid completely. In the left figure below, a kernel (represented by the grey lines) is centred at each of the 50 data points above. The result of summing these kernels is given on the right figure, which is a kernel density estimate.
Kernel density estimation of 100 normally distributed random numbers using different smoothing bandwidths.. In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights.
Kernel principal component analysis. In the field of multivariate statistics, kernel principal component analysis (kernel PCA) [1] is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space .
In functional analysis (a branch of mathematics ), a reproducing kernel Hilbert space ( RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Roughly speaking, this means that if two functions and in the RKHS are close in norm, i.e., is small, then and are also pointwise close, i.e., is small for all .
Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. "A spline is a function defined by polynomials in a piecewise manner." They were introduced to geometric design by Duchon. They are an important special case of a polyharmonic spline. Robust Point Matching (RPM) is a common extension and shortly known as ...
Kernel regression. In statistics, kernel regression is a non-parametric technique to estimate the conditional expectation of a random variable. The objective is to find a non-linear relation between a pair of random variables X and Y . In any nonparametric regression, the conditional expectation of a variable relative to a variable may be written:
In nonparametric statistics, a kernel is a weighting function used in non-parametric estimation techniques. Kernels are used in kernel density estimation to estimate random variables ' density functions, or in kernel regression to estimate the conditional expectation of a random variable. Kernels are also used in time-series, in the use of the ...