the adaptive kernel density estimate of samples in several dimensions, the regularised EM mixture of Botev et al.; MATLAB’s kdeN

Syntax

pdf, bw = kdeN(X, grid)

Ceil(sqrt(n)) Gaussians.

pdf, bw = kdeN(X, grid, gam=50, rng=np.random.default_rng(1))

More Gaussians, reproducible.

Description

A mixture of gam Gaussians is fitted by the regularised EM iteration to the data scaled to their bounding box widened by a tenth on every side, and evaluated at the rows of grid. The start is random: rng makes it reproducible. Rows with a NaN are dropped. MATLAB returns the 2d grid it builds when none is given; here the grid is required and the bandwidth is returned instead. calcDensity of a matrix of samples calls it on a regular grid.

Input

`X`	ndarray of shape (n, d), one sample per row
`grid`	ndarray of shape (m, d), the points to evaluate at

Keywords

keyword	default	description
`gam`	`None`	the number of Gaussians, below n; larger may be more accurate and is slower
`rng`	`None`	the numpy random generator of the start

Output

`pdf`	the density at the rows of grid
`bw`	the bandwidth per dimension

References

Z. I. Botev, J. F. Grotowski, D. P. Kroese, Kernel density estimation via diffusion, Annals of Statistics 38 (2010) 2916-2957

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/kdeN_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

kdeN