### Missing volume in kde_density solution

Verfasst:

**3. Jun 2010 16:02**Hey,

maybe it's just me, but im missing the Volume in the solution for Assignment 2 Problem 2 Task A: kde_density.m.

The slides define a Kernel Density Estimation as:

\(p(x) = \frac{1}{Nh^d}\sum\limits_{n=0}^N{k\left(\frac{||x-x_n||}{h}\right)}\)

the distance matrix is the norm \(\frac{||x-x_n||}{h}\) from the formular

normpdf is the used Kernel function which is nothing else but \(k(x) = \frac{1}{\sqrt{2\pi}}\exp{\left(-\frac{x^2}{2}\right)}\).

\(\frac{\sum\limits_{n=0}^N}{N}\) is just the mean.

So we get \(p(x)= \frac{mean(normpdf(distance))}{h^d}\) but the solution only computes \(p(x)= mean(normpdf(distance))\)

I am Missing the the volume \(V = h^d\).

I know this doesn't matter for classification as long as each estimator uses the same bandwidth, but the density estimations themselves are incorrect.

And if I only want to classify with an estimation above a certain threshold my calssifier wouldn't work like it should.

If the volume isn't missing, but i'm missing something i would love to be corrected.

Alexis.

maybe it's just me, but im missing the Volume in the solution for Assignment 2 Problem 2 Task A: kde_density.m.

The slides define a Kernel Density Estimation as:

\(p(x) = \frac{1}{Nh^d}\sum\limits_{n=0}^N{k\left(\frac{||x-x_n||}{h}\right)}\)

the distance matrix is the norm \(\frac{||x-x_n||}{h}\) from the formular

normpdf is the used Kernel function which is nothing else but \(k(x) = \frac{1}{\sqrt{2\pi}}\exp{\left(-\frac{x^2}{2}\right)}\).

\(\frac{\sum\limits_{n=0}^N}{N}\) is just the mean.

So we get \(p(x)= \frac{mean(normpdf(distance))}{h^d}\) but the solution only computes \(p(x)= mean(normpdf(distance))\)

I am Missing the the volume \(V = h^d\).

I know this doesn't matter for classification as long as each estimator uses the same bandwidth, but the density estimations themselves are incorrect.

And if I only want to classify with an estimation above a certain threshold my calssifier wouldn't work like it should.

If the volume isn't missing, but i'm missing something i would love to be corrected.

Alexis.