Introduction to Pattern Recognition: A Matlab Approach

1.8 k-Nearest Neighbor Density Estimation 21

h=0.1;

pdfx_approx=Parzen_gauss_kernel(X,h,-5,5);

plot(-5:h:5,pdfx_approx,'r');

Exercise 1.7.1

Repeat the experiment in Example 1.7.1 with h = 0.01, N = 1000 and h =0.1, N = 10,000. Comment on the

results. The choice of h for a given N needs careful consideration. Tips related to this choice are provided in

[Theo 09, Sectio n 2.5.6] and the references therein.

Exercise 1.7.2

Generate N = 1000 data points from the following 2-dimensional pdf:

p(x) ≡p(x(1),x(2)) =

1

3

1

2πσ

2

exp



−

x

2

(1) +x

2

(2)

2σ

2



+

2

3

1

2πσ

2

exp



−

x

2

(1) +(x(2) −2)

2

2σ

2



Repeat the experiment in Example 1.7.1.

Exercise 1.7.3

Use the setup for the classificat ...