fastmath.kernel — generateme/fastmath 2.4.0

Various kernel functions.

• RBF (double -> double functions)
• vector kernels (vector x vector -> double function; may be positive definite, conditional positive definite, positive semi-definite, mercer)
• density estimation
• some kernel operations

approx clj

(approx k)

(approx k precision)

Kernel wrapper. Round value returned by kernel using fastmath.core/approx function.

cauchy-density-kernel clj

(cauchy-density-kernel x)

cosine-density-kernel clj

(cosine-density-kernel x)

cpd->pd clj

(cpd->pd k)

Convert conditionally positive definite kernel into positive definite.

Formula is based on this SO answer. x0 is equal 0.

Doesn't work well.

epanechnikov-density-kernel clj

(epanechnikov-density-kernel x)

exp clj

(exp k)

(exp k t)

Kernel wraper. exp of kernel k with optional scaling value t.

fields clj

(fields k f)

(fields k f1 f2)

Kernel wrapper. Apply vector field for each input before applying kernel function.

gaussian-density-kernel clj

(gaussian-density-kernel x)

kernel clj multimethod

Crated vector kernel.

Kernels can be Mercer, positive definite, conditional positive definite, positive semi-definite or other.

Optional parameters:

For :gaussian, :exponential, :laplacian, :rational-quadratic, :multiquadratic, :inverse-multiquadratic, :circular, :spherical, :wave, :power, :log, :cauchy, :generalized-t-student, :hyperbolic-secant, :thin-plate, :mattern-12, :mattern-32, :mattern-52 and ::hyperbolic-secant you can provide scaling parameter and distance (see fastmath.distance, default is [[euclidean]]).

Others:

• :linear - alpha, scaling parameter
• :polynomial - alpha (scaling), c (shift) and d (power)
• :anova - sigma (scaling), k and d (power)
• :hyperbolic-tangent - alpha (scaling), c (shift)
• :periodic - sigma (scaling), periodicity and distance
• :bessel - sigma (scaling), n and v (power factors) and distance
• :generalized-histogram - alpha and beta (power factors)
• :dirichlet - N
• :pearson - sigma (scaling) and omega (power)

Additionally there are two special kernels build from funcitons:

• :scalar-functions - provide one or two double->double functions
• :variance-function - provide any variance function (smooth, vector->double type)

The rest of the kernels do not require parameters.

kernel->rbf clj

(kernel->rbf k)

(kernel->rbf k center)

Convert vector kernel to RBF kernel. center is fixed y vector (default contains [[EPSILON]] values).

kernel-density clj multimethod

Create kernel density estimator.

Parameters:

• kernel name, see kernel-density-list.
• sequence of data values
• optional: bandwidth (by default, bandwidth is estimated using nrd method)

kernel-density-ci clj

(kernel-density-ci method data)

(kernel-density-ci method data bandwidth)

(kernel-density-ci method data bandwidth alpha)

Create function which returns confidence intervals for given kde method.

Check 6.1.5 http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/tutorials/xlghtmlnode33.html

Parameters:

• method - kernel name
• data - sequence of data values
• bandwidth
• alpha - confidence level parameter

Returns three values: density, lower confidence, upper confidence

kernel-density-list clj

kernels-list clj

laplace-density-kernel clj

(laplace-density-kernel x)

logistic-density-kernel clj

(logistic-density-kernel x)

mult clj

(mult k1)

(mult k1 k2)

(mult k1 k2 k3)

(mult k1 k2 k3 & r)

Kernel wrapper. Multiply two or more kernels.

quartic-density-kernel clj

(quartic-density-kernel x)

rbf clj multimethod

RBF kernel creator. RBF is double->double function.

Parameters:

All kernels accept scale parameter (as last parameter).

Following kernels also accept beta: :multiquadratic, :inverse-multiquadratic, :truncated-power, :radial-powers and :thin-plate.

rbf->kernel clj

(rbf->kernel rbf-kernel)

(rbf->kernel rbf-kernel distance)

Treat RBF kernel as vector kernel using distance function (default [[euclidean]].

rbf-list clj

scale clj

(scale k scale)

Kernel wrapper. Scale kernel result.

sigmoid-density-kernel clj

(sigmoid-density-kernel x)

silverman-density-kernel clj

(silverman-density-kernel x)

smile-mercer clj

(smile-mercer k)

Create Smile Mercer Kernel object

Used to pass to Smile constructors/functions.

smile-rbf clj

(smile-rbf rbf-fn)

Create RBF Smile object.

Used to pass to Smile constructors/functions.

triangular-density-kernel clj

(triangular-density-kernel x)

tricube-density-kernel clj

(tricube-density-kernel x)

triweight-density-kernel clj

(triweight-density-kernel x)

uniform-density-kernel clj

(uniform-density-kernel x)

wadd clj

(wadd kernels)

(wadd weights kernels)

Kernel wrapper. Add kernels (weighted).

wigner-density-kernel clj

(wigner-density-kernel x)