How to compute gaussian kernel matrix efficiently?

88 次查看（过去 30 天）
Deepak Nayak
Deepak Nayak 2012-10-28
评论： amel kaouane 2022-6-20
Hi,
I have a matrix X(10000, 800). I want to compute gramm matrix K(10000,10000), where K(i,j)= exp(-(X(i,:)-X(j,:))^2).
First i used double for loop, but then it just hangs forever. Then I tried this:
[N d] = size(X); aa = repmat(X',[1 N]); bb = repmat(reshape(X',1,[]),[N 1]); K = reshape((aa-bb).^2, [N*N d]); K = reshape(sum(D,2),[N N]); But then it uses a lot of extra space and I run out of memory very soon. Is there any efficient vectorized method for this. I am sure there must be something as this is quite a standard intermediate step for many kernel svms and also in image processing.
  2 个评论
Matt J
Matt J 2012-10-28
编辑：Matt J 2012-10-28
Your expression for K(i,j) does not evaluate to a scalar. Are you sure you don't want something like
exp(-norm( X(i,:) - X(j,:) ))^2);
Also, please format your code so it's more readable.
Shahid Mahmood
Shahid Mahmood 2019-11-21
can you explain the whole procedure in detail to compute a kernel matrix in matlab

请先登录，再进行评论。

请先登录，再回答此问题。

回答（2 个）

Matt J
Matt J 2012-10-28
编辑：Matt J 2012-10-28
Assuming you really want exp(-norm( X(i,:) - X(j,:) ))^2), then one way is
nsq=sum(X.^2,2);
K=bsxfun(@minus,nsq,(2*X)*X.');
K=bsxfun(@plus,nsq.',K);
K=exp(-K);
  3 个评论
显示 1更早的评论
Matt J
Matt J 2015-3-10
编辑：Matt J 2015-3-10
Just pre-normalize X1 and X2 by sigma.
Farzan Zaheer
Farzan Zaheer 2015-8-4
编辑：Farzan Zaheer 2015-8-4
I am working on Kernel LMS, and I am having issues with the implementation of Kernel. I want to know what exactly is "X2" here. I am implementing the Kernel using recursion.
I am using the following statement,
for n=2:K-1
Kernel(n)=exp(-0.5*(dist(x(:,2:n),x(:,n)')/ker_bw^2));
end
where ker_bw is the kernel bandwidth/sigma and x is input of (1000,1) and I have reshaped the input x as
x = [x(1:end-1),x(2:end)];
as mentioned in the research paper I am following. Any help will be highly appreciated.

请先登录，再进行评论。

Image Analyst
Image Analyst 2012-10-28
If you have the Image Processing Toolbox, why not use fspecial()?
h = fspecial('gaussian', hsize, sigma) returns a rotationally symmetric Gaussian lowpass filter of size hsize with standard deviation sigma (positive). hsize can be a vector specifying the number of rows and columns in h, or it can be a scalar, in which case h is a square matrix. The default value for hsize is [3 3]; the default value for sigma is 0.5.
  4 个评论
显示 2更早的评论
Image Analyst
Image Analyst 2022-6-20
Ran in:
@amel kaouane it comes from your mind. You think up some sigma that might work, assign it like
sigma = 5;
hsize = 21;
h = fspecial('gaussian', hsize, sigma)
h = 21×21
0.0001 0.0002 0.0003 0.0003 0.0005 0.0006 0.0007 0.0008 0.0009 0.0009 0.0009 0.0009 0.0009 0.0008 0.0007 0.0006 0.0005 0.0003 0.0003 0.0002 0.0001 0.0002 0.0003 0.0004 0.0005 0.0007 0.0008 0.0010 0.0011 0.0012 0.0013 0.0014 0.0013 0.0012 0.0011 0.0010 0.0008 0.0007 0.0005 0.0004 0.0003 0.0002 0.0003 0.0004 0.0005 0.0007 0.0009 0.0012 0.0014 0.0016 0.0018 0.0019 0.0019 0.0019 0.0018 0.0016 0.0014 0.0012 0.0009 0.0007 0.0005 0.0004 0.0003 0.0003 0.0005 0.0007 0.0010 0.0012 0.0016 0.0019 0.0021 0.0024 0.0025 0.0026 0.0025 0.0024 0.0021 0.0019 0.0016 0.0012 0.0010 0.0007 0.0005 0.0003 0.0005 0.0007 0.0009 0.0012 0.0016 0.0020 0.0024 0.0028 0.0031 0.0033 0.0033 0.0033 0.0031 0.0028 0.0024 0.0020 0.0016 0.0012 0.0009 0.0007 0.0005 0.0006 0.0008 0.0012 0.0016 0.0020 0.0025 0.0030 0.0035 0.0038 0.0041 0.0042 0.0041 0.0038 0.0035 0.0030 0.0025 0.0020 0.0016 0.0012 0.0008 0.0006 0.0007 0.0010 0.0014 0.0019 0.0024 0.0030 0.0036 0.0042 0.0046 0.0049 0.0050 0.0049 0.0046 0.0042 0.0036 0.0030 0.0024 0.0019 0.0014 0.0010 0.0007 0.0008 0.0011 0.0016 0.0021 0.0028 0.0035 0.0042 0.0048 0.0053 0.0056 0.0057 0.0056 0.0053 0.0048 0.0042 0.0035 0.0028 0.0021 0.0016 0.0011 0.0008 0.0009 0.0012 0.0018 0.0024 0.0031 0.0038 0.0046 0.0053 0.0058 0.0062 0.0063 0.0062 0.0058 0.0053 0.0046 0.0038 0.0031 0.0024 0.0018 0.0012 0.0009 0.0009 0.0013 0.0019 0.0025 0.0033 0.0041 0.0049 0.0056 0.0062 0.0066 0.0067 0.0066 0.0062 0.0056 0.0049 0.0041 0.0033 0.0025 0.0019 0.0013 0.0009
imshow(h, []);
axis('on', 'image')
If you don't like 5 for sigma then just try others until you get one that you like. It's not like I can tell you the perfect value of sigma because it really depends on your situation and image.
amel kaouane
amel kaouane 2022-6-20
am looking to get similarity between two time series by using this gaussian kernel, i think it's not the same situation, right?!

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Mathematics and Optimization 的更多信息

标签

产品

Community Treasure Hunt

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

Start Hunting!

Translated by