Hi Jonne,
I have reproduced your code at my end, and I am currently using R2023A version of MATLAB. Kindly note the following differences, and I will paste the code below as well. I have attached the required PDF graph here.
- In the "nnPdf" function, you have used “standardize” but it isn’t defined in MATLAB. The function “zscore” can perform the task of standardizing.
- While sorting, you haven’t assigned the values back to v, and hence it isn’t working. Code:
[v(i,:), ~] = sort(v(i,:));
- The line where you calculate the window size "V(i)" is incorrect. Instead of dividing by "v(i,k)", you should divide by the distance to the k-th nearest neighbor, which is "v(i,k+1)" (since MATLAB indexing starts from 1).
Finally the code which gave me the attached result is:
x = [0.553766713954610,0.683388501459509,0.274115313899635,0.586217332036812,0.531876523985898,0.369231170369473,0.456640797769432,0.534262446653865,0.857839693972576,0.776943702988488];
d = size(x,1);
d2 = size(x,2);
% k samples inside the Parzen window
k = 3; % sqrt(N) is a good guess for optimal k
% plotting the samples and the estimated pdf
xAxis = linspace(0,1,100);
plot(xAxis,nnPdf(xAxis,x,k));
title('t122 on the real line with nn-estimated pdf');
hold on;
plot(x,0,'o','MarkerSize',25);
legend(sprintf('%d nearest neighbours pdf',k),'t122');
% k nearest neighbours 1D pdf-estimator function nnPdf()
% inputs:
% x0 = interval for the pdf
% x = data for which the pdf is estimated
% k = number of samples in every Parzen window
% output:
% V = 1D-pdf estimated with k nearest neighbours
function V = nnPdf(x0,x,k)
v = zeros(length(x0),size(x,2)); % for distances to all samples
V = zeros(length(x0),1); % for distance needed to include k samples
if k > size(x,2)
disp('*Invalid value for k: not so many samples in the data.');
return
end
zscore(x);
for i = 1:length(x0)
for j = 1:size(x, 2)
% distance from interval point to all samples
v(i, j) = abs(x0(i) - x(j));
end
% sorted distances so v_ik is the distance for reaching to the
% kth sample from the point x0_i
[v(i, :), ~] = sort(v(i, :));
% window size V at point x0_i based on the distance (volume in 1D)
V(i) = (k / size(x, 2)) * (1 / v(i, k+1));
end
end
Hope it helps!
