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Questions tagged [kernel]

The tag has no usage guidance.

1
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1answer
50 views

Is the absolute value of the difference a kernel?

In particular is $$ k(x_i,x_j)=|x_i-x_j|, \quad x_i,x_j\in \mathbb{R}$$ a valid kernel?
1
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2answers
24 views

Why is the convolution of two box kernels a triangle kernel? [duplicate]

Can anyone show the mathematical steps proving $K_{box}*K_{box} = K_{triangle}$
2
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0answers
21 views

Gaussian Processes, Prior function of constant, Linear and Polynomial Kernel

In my university course slide, regarding the exponential and Gaussian kernel there are these two relevant pictures. They show the prior function of each kernel: You can see that the resulting prior ...
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0answers
17 views

Linear Algebra: Dimension of kernel [migrated]

Suppose that we have the vector space $V=\{f/f:R\rightarrow R, \text{every class derivative is defined in R}\}$ and $φ: V\rightarrow W$ with $φ(f)=f+f'$ is linear. I want to find the dimension of ...
0
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0answers
21 views

Weighted kernel density

I would like to produce a 3-d plot based on density of 2-d data. This can be achieved for example in R using the kde2d function from the ...
1
vote
0answers
16 views

Prove this Kernel 1 - 2* angle(x,y)/pi is positive semi definite [closed]

How should we prove this kernel is positive semi definite? K(x,y) = 1- 2*ang(x,y)/pi ang(x,y) is the angle between vector x and y
0
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0answers
11 views

Does Kernel Function Only Apply To Support Vector In SVM?

We know that the if α=0 in below equation it is not a support vector, only if α!=0, it is the support vector. L(w, b, α) = Xm i=1 αi − 1 2 Xm i,j=1 y(i)y(j)αiαj(x(i))T x(j). However, for the Kernel ...
2
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0answers
26 views

Normal Kernel Estimation in R [closed]

I'm given the following data: ...
4
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1answer
119 views

Uniqueness of Reproducing Kernel Hilbert Spaces

Digging in the definition of Reproducing Kernel Hilbert Spaces (RKHS) I came across the following example taken from pages 49-51 of [1]: Given the kernel $k(x,y) = \langle x,y\rangle^2$, with $x,y\in ...
0
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0answers
13 views

Is a kernel density estimate meaningful if > 25% of my data are duplicates?

The title pretty much says it all. I have data that consists of 80 samples but there are always at least four samples that have exactly the same value. I want to assess, whether the data is unimodal. ...