How can I compute kernels?
12 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
Hello
I want to calculate weighted kernels (for using in a SVM classifier) in Matlab but I'm currently compeletely confused.
I would like to implement the following weighted RBF and Sigmoid kernel:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/163701/image.gif)
//
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/163705/image.gif)
x and y are vectors of size n, gamma and b are constants and w is a vector of size n with weights.
The problem now is that the fitcsvm method from Matlab need two matrices as input, i.e. K(X,Y). For example the not weighted RBF and sigmoid kernel can be computed as follows:
K_rbf = exp(-gamma .* pdist2(X,Y,'euclidean').^2)
K_sigmoid = tanh(gamma*X*Y' + b);
X and Y are matrices where the rows are the data points (vectors).
How can I compute the above weighted kernels efficiently in Matlab?
Can I just apply the weights before computing the kernel? And if yes, how can this be done?
0 Kommentare
Akzeptierte Antwort
John BG
am 8 Mai 2016
Bearbeitet: John BG
am 8 Mai 2016
instead of pdist2, that performs rest sqrt, and then back ^2, you could simply use the operators .^ and .* to operate element wise on W X and Y:
K_rbf = exp(-gamma * sum(sum(W.*((X-Y).^2))))
you don't mention it, but gamma seems to be a scalar, so gamma does not need the element wise product .*
2 sum() because sum only sums along a given dimension.
Why do you write that K(x,y)=exp( .. is same as K(x,y)=tanh( .. ?
If you find this answer of any help solving your question,
please click on the thumbs-up vote link,
thanks in advance
John
3 Kommentare
John BG
am 8 Mai 2016
my mistake, not '.-', just '-'
the following seems to work
N=10;X=randi(101,1,N)/100;Y=randi(101,1,N)/100
X =
0.67 0.04 0.86 0.95 0.69 0.77 0.76 0.40 0.67 0.18
Y =
0.72 0.04 0.28 0.05 0.10 0.84 0.71 0.33 0.96 0.04
W=[.1 .5 .21 .43 .1 .4 .4 .4 .4 .2]
gamma=42e-3
K_rbf = exp(-gamma * sum(sum(W.*((X-Y).^2))))
=
0.98
Is the result supposed to be scalar?
What are the units of the result, energy?
or is it just probability?
Weitere Antworten (0)
Siehe auch
Kategorien
Mehr zu Statistics and Machine Learning Toolbox finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!