Issue Regarding KL divergence Implementation in MATLAB

21 ビュー (過去 30 日間)
Muhammad Nauman Nasir 2017 年 8 月 4 日

I have some issue regarding KL divergence as i am confused that if i am going in right way or not .
I am explaining my issue by an example as my data set is too big so just for clarity of concept i am providing an example.
I have one reference sensor signal and 1 measured value of some sensor.
I want to find out the error or difference between Ref and Measured sensor signal Values.
So I am using KL divergence.
First I normalized my reference and sensor signal histogram and then applied KL divergence.
My data is too much and complicated means it contains a lot of zeroes and negative values and also 0.001 like these values also.
I was applying KL divergence but unfortunately was not being able to get some good results so I was wondering that may be I did not able to get the good concept of KL divergence or I am doing wrong at some point in The code.
It will nice of people if someone help me out in this. I shall be grateful.
Am i on right way or there is some fault in my concepts .
Code
ref = [2 3 4 5 6 7 8 9 -2 -3 -4];
measured_sensor = [3 3 4 5 7 8 9 9 -1 -2 -3];
%normalized histograms for
C= hist( ref);
C1 = C ./ sum(C);
D = hist(measured_sensor);
D1 = D ./ sum(D);
figure(1)
ax11=subplot(321);
bar(C1)
ax12=subplot(322);
bar(D1)
d = zeros(size(C1));
goodIdx = C1>0 & D1>0;
d1 = sum(C1(goodIdx) .* log(C1(goodIdx) ./ D1(goodIdx)))
d2 = sum(D1(goodIdx) .* log(D1(goodIdx) ./ C1(goodIdx)))
d(goodIdx) = d1 + d2
Mean Based Gaussian Hysterisis (Means Error Finding)
ref = [5 6 7 5 8 7 8 9 -2 -3 -4];
measured_sensor = [3 3 4 5 7 8 9 9 -1 -2 -3];
sig_diff = ref - measured_sensor ;
m = mean(sig_diff)
deviation = std(sig_diff);
pos = sig_diff(sig_diff>0)
neg = sig_diff(sig_diff<0)
m_pos = mean(pos)
m_neg = mean (neg)
hysterisis = abs( m_pos)+ abs(m_neg)
figure(6)
ax11=subplot(321);
histfit(sig_diff)
hold on
plot([m m],[0 5000],'r')
plot([m-deviation m-deviation],[0 5000],'r')
plot([m+deviation m+deviation],[0 5000],'r')
hold off
The error value or Hysterisis value that I am getting with mean based Gaussian Distribution is 3.2500.
So I am expecting the error values from KL divergence near to 3.2500 value or in the range with some tolerance is also accepted.

サインインしてコメントする。

採用された回答

Chris Perkins 2017 年 8 月 9 日

KL Divergence produces a number between 0 and 1, where 0 indicates the expectation of extremely similar behavior between the two distributions and 1 indicates that the two distributions behave extremely differently. See more here: https://en.wikipedia.org/wiki/Kullback-Leibler_divergence
As your given sample data mirrors each other very closely, we would expect a KL Divergence value close to zero.
I hope this helps clear up some confusion.

サインインしてコメントする。

その他の回答 (1 件)

Muhammad Nauman Nasir 2017 年 8 月 21 日
Thanks a lot this was a solved my issue.

サインインしてコメントする。

カテゴリ

Find more on Digital Filter Analysis in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by