Page 333 - Computational Statistics Handbook with MATLAB

322 Computational Statistics Handbook with MATLAB

covset = cov(setosa);
muvir = mean(virginica);
covvir = cov(virginica);
muver = mean(versicolor);
covver = cov(versicolor);

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If it is not appropriate to assume the features for a class follow a known dis-
tribution, then we can use the nonparametric density estimation techniques
from Chapter 8. These include the averaged shifted histogram, the frequency
polygon, kernel densities, finite mixtures and adaptive mixtures. To obtain
the class-conditional probabilities, we take the set of measured features from
each class and estimate the density using one of these methods. This is illus-
trated in Example 9.2, where we use the product kernel to estimate the prob-
ability densities for the iris data.
Example 9.2
We estimate the class-conditional probability densities for the iris data
using the product kernel, where the univariate normal kernel is used for each
dimension. We illustrate the use of two functions for estimating the product
kernel. One is called cskern2d that can only be used for bivariate data. The
output arguments from this function are matrices for use in the MATLAB
plotting functions surf and mesh. The cskern2d function should be used
when the analyst wants to plot the resulting probability density. We use it on
the first two dimensions of the iris data and plot the surface for Iris virginica
in Figure 9.2.
load iris
% This loads up three matrices:
% setosa, virginica and versicolor
% We will use the product kernel to estimate densities.
% To try this, get the kernel estimate for the first
% two features and plot.
% The arguments of 0.1 indicate the grid size in
% each dimension. This creates the domain over
% which we will estimate the density.
[xset,yset,pset]=cskern2d(setosa(:,1:2),0.1,0.1);
[xvir,yvir,pvir]=cskern2d(virginica(:,1:2),0.1,0.1);
[xver,yver,pver]=cskern2d(versicolor(:,1:2),0.1,0.1);
mesh(xvir,yvir,pvir)
colormap(gray(256))

© 2002 by Chapman & Hall/CRC