[SciPy-User] R: Re: R: Re: R: Re: Epanechnikov kernel
Patrick Marsh
patrick.marsh@noaa....
Sat Jan 19 11:40:26 CST 2013
I've previously coded up a Cython version of the Epanechnikov kernel. You
can find the function here:
https://gist.github.com/4573808
It's certainly not optimized. It was a quick hack for use with rare
(spatial) meteorological events. As the grid density increases, the
performance decreases significantly. At this point, your best bet would be
to create a grid that has the weights of the Epanechnikov kernel, and do a
FFT convolve between the two grids. A pseudocode example (that I believe
should work) is shown below...
============================================
import numpy as np
import scipy as sp
import epanechnikov (from the gist linked to above)
data_to_kde = ... # Your 2D array
# Create a grid with a value of 1 at the midpoint
raw_epan_grid = np.zeros((51, 51), dtype=np.float64)
raw_epan_gird[25, 25] = 1
# Convert this binary grid into the weights of the Epanechnikov kernel
bandwidth = 10
dx = 1
epan_kernel = epanechnikov(raw_epan_grid, bandwidth, dx)
# Use FFTCONVOLVE to do the smoothing in Fourier space
data_smoothed = sp.signal.fftconvolve(data_to_kde, epan_kernel, mode='same')
============================================
This is slower than the function linked above for sparse grids, but faster
for dense grids. (The runtime of fftconvolve is dependent upon the size of
your arrays, not the density.)
Hope this helps
Patrick
---
Patrick Marsh
Ph.D. Candidate / Liaison to the HWT
School of Meteorology / University of Oklahoma
Cooperative Institute for Mesoscale Meteorological Studies
National Severe Storms Laboratory
http://www.patricktmarsh.com
On Sat, Jan 19, 2013 at 9:18 AM, francescoboccacci@libero.it <
francescoboccacci@libero.it> wrote:
> Thanks Josef, i will investigate on it.
> I'm using scipy version '0.9.0' so i need to update it.
> If i have some problems i will ask you again :).
> Thanks for your time
>
> Francesco
>
> >----Messaggio originale----
> >Da: josef.pktd@gmail.com
> >Data: 19/01/2013 16.06
> >A: "francescoboccacci@libero.it"<francescoboccacci@libero.it>, "SciPy
> Users
> List"<scipy-user@scipy.org>
> >Ogg: Re: [SciPy-User] R: Re: R: Re: Epanechnikov kernel
> >
> >On Sat, Jan 19, 2013 at 9:57 AM, francescoboccacci@libero.it
> ><francescoboccacci@libero.it> wrote:
> >> Hi,
> >> i would like to use a Epanechnikov kernel because i would like
> replicate
> an R
> >> function that use Epanechnikov kernel.
> >> Reading in depth a documentation below documentation:
> >>
> >>
> >> http://rgm3.lab.nig.ac.jp/RGM/r_function?p=adehabitatHR&f=kernelUD
> >>
> >> i found that i can use normal kernel (i think guaussion kernel).
> >> Below i write a pieces of my code:
> >>
> >>
> >> xmin = min(xPoints)
> >> xmax = max(xPoints)
> >> ymin = min(yPoints)
> >> ymax = max(yPoints)
> >> X,Y = np.mgrid[xmin:xmax:40j, ymin:ymax:40j]
> >> positions = np.vstack([X.ravel(), Y.ravel()])
> >> values = np.vstack([xPoints,yPoints])
> >> # scipy.stats.kde.gaussian_kde --
> >> # Representation of a kernel-density estimate using
> Gaussian
> >> kernels.
> >> kernel = stats.kde.gaussian_kde(values)
> >>
> >> Z = np.reshape(kernel(positions).T, X.T.shape)
> >>
> >> If i understood in right way the missing part that i have to implement
> is
> the
> >> smoothing paramter h:
> >>
> >> h = Sigma*n^(-1/6)
> >>
> >> where
> >>
> >> Sigma = 0.5*(sd(x)+sd(y))
> >>
> >>
> >> My new question is:
> >>
> >> How can set smooting parameter in stats.kde.gaussian_kde function? is it
> >> possible?
> >
> >In a recent scipy (since 0.10 IIRC) you can directly set the bandwidth
> >without subclassing
> >
> >
> http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gaussian_kde.
> html#scipy.stats.gaussian_kde
> >
> http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html#kernel-density-
> estimation
> >
> >Josef
> >
> >>
> >> Thanks
> >>
> >> Francesco
> >>
> >>
> >>>----Messaggio originale----
> >>>Da: jsseabold@gmail.com
> >>>Data: 19/01/2013 15.21
> >>>A: "francescoboccacci@libero.it"<francescoboccacci@libero.it>, "SciPy
> Users
> >> List"<scipy-user@scipy.org>
> >>>Ogg: Re: [SciPy-User] R: Re: Epanechnikov kernel
> >>>
> >>>On Sat, Jan 19, 2013 at 8:48 AM, francescoboccacci@libero.it
> >>><francescoboccacci@libero.it> wrote:
> >>>> Hi,
> >>>> is there a possibility to multivariate KDE using Epanechnikov
> kernel? my
> >>>> variables are X Y (point position)
> >>>>
> >>>
> >>>As Josef mentioned there is no way for the user to choose the kernel
> >>>at present. The functionality is there, but it needs to be hooked in
> >>>with a suitable API. I didn't keep up with these discussions, so I
> >>>don't know the current status. If it's something you're interested in
> >>>trying to help with, I'm sure people would be appreciative and you can
> >>>ping the statsmodels mailing list.
> >>>
> >>>Practically though, the reason this hasn't been done yet is that the
> >>>choice of the kernel is not all that important. Bandwidth selection is
> >>>the most important variable and other kernels perform similarly given
> >>>a good bandwidth. Is there any particular reason you want Epanechnikov
> >>>kernel in particular?
> >>>
> >>>Skipper
> >>>
> >>>> Thanks
> >>>>
> >>>> Francesco
> >>>>
> >>>>>----Messaggio originale----
> >>>>>Da: jsseabold@gmail.com
> >>>>>Data: 19/01/2013 14.32
> >>>>>A: "SciPy Users List"<scipy-user@scipy.org>
> >>>>>Ogg: Re: [SciPy-User] Epanechnikov kernel
> >>>>>
> >>>>>On Sat, Jan 19, 2013 at 7:49 AM, <josef.pktd@gmail.com> wrote:
> >>>>>> On Sat, Jan 19, 2013 at 6:34 AM, francescoboccacci@libero.it
> >>>>>> <francescoboccacci@libero.it> wrote:
> >>>>>>> Hi all,
> >>>>>>>
> >>>>>>> I have a question for you. Is it possible in scipy using a
> Epanechnikov
> >>>>>>> kernel function?
> >>>>>>>
> >>>>>>> I checked on scipy documentation but i found that the only way to
> >>>> calculate
> >>>>>>> kernel-density estimate is possible only with using Gaussian
> kernels?
> >>>>>>>
> >>>>>>> Is it true?
> >>>>>>
> >>>>>> Yes, kde in scipy.stats only has gaussian_kde
> >>>>>>
> >>>>>> Also in statsmodels currently only gaussian is supported for
> >>>>>> continuous data
> >>>>>> http://statsmodels.sourceforge.net/devel/nonparametric.html
> >>>>>> (It was removed because in the references only the bandwidth
> selection
> >>>>>> made much difference in the estimation, but not the shape of the
> >>>>>> kernel. Other kernels for continuous variables will come back
> >>>>>> eventually.
> >>>>>
> >>>>>If you're interested in univariate KDE, then we do have the
> Epanechnikov
> >>>> kernel.
> >>>>>
> >>>>>http://statsmodels.sourceforge.net/devel/generated/statsmodels.
> >> nonparametric.
> >>>>
> kde.KDEUnivariate.fit.html#statsmodels.nonparametric.kde.KDEUnivariate.
> fit
> >>>>>
> >>>>>Skipper
> >>>>>_______________________________________________
> >>>>>SciPy-User mailing list
> >>>>>SciPy-User@scipy.org
> >>>>>http://mail.scipy.org/mailman/listinfo/scipy-user
> >>>>>
> >>>>
> >>>>
> >>>> _______________________________________________
> >>>> SciPy-User mailing list
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> >>>
> >>
> >>
> >> _______________________________________________
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> >
>
>
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