# Questions tagged [rbf-kernel]

The RBF kernel, i.e., radial-basis-function kernel, occurs in the context of kernel methods in machine learning.

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### Is it efficient to use kernel trick in primal form of SVM?

I know we can use Kernel trick in the primal form of SVM. So the hypothesis will be - and optimization objective - We can optimize the above equation using gradient descent, but in this equation ...
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### How to obtain the inverse of the Gram (kernel) matrix?

We're working with a similar dual SVR problem that involves the inversion of a Gram (kernel) matrix: $\boldsymbol{S}_{i,j} = e^{ -\gamma ||\vec{x_i} - \vec{x_j}||_2^2}$ With some data-sets (e.g.: UCI ...
1 vote
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### Can someone clarify what the linear assumption of PCA is?

For the past few hours I've been trying to search what this linear assumption is. Some of the articles states that that your independent variables have to be linear in relationship and need some type ...
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### Why use RBF kernel if less is needed?

I have seen online theorem's such as Cover's theorem Wikipedia which prove how given $p$ points in $\mathbb{R}^N$ the linear separability is almost certain as the fraction $\dfrac{p}{N}$ is kept close ...
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### About Gaussian kernel for distances other than Euclidian

I have a question about Gaussian kernel. I read the following site. https://datascience.stackexchange.com/questions/17352/why-do-we-use-a-gaussian-kernel-as-a-similarity-metric My question is whether ...
1 vote
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### How to use sklearn's Gaussian Process Regression parameters?

I have been trying to play around with Gaussian process Regression. I have constructed a fake 1D data for this. I am using a Squared exponential kernel. I solved the regression problem using inbuilt ...
1 vote
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### How to extend kernel-based classifier to non-euclidean space like SO3

What is the proper way to extend kernel-based classifier to non-euclidean space like SO3? This kind of situation happens a lot in robotics, where the data points all live in a specific manifold. (Note:...
1 vote
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### Can someone improve my feeble understanding of feature maps and kernels?

I am taking the course and the extent in which we've discussed feature maps and kernels is as follows: Given Obviously we cannot use linear regression. Instead we map it to a space where it becomes ...
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1 vote
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### Finding optimal kernel parameters

I want to perform multiple kernel learning on my dataset and apply each (rbf) kernel to a different subset of features to then combine them. I do not want to have the same kernel with a range of ...
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### Applying different kernels to parts of a dataset and merging the output [duplicate]

I am trying to create a classifier using SVM on a dataset that is composed of 6 sets of data for each of my observations. When I train the SVM (rbf kernel), I get a better performance of the ...
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### Calculate Gamma for RBF Kernel to get Gaussian Kernel

In order to measure the information density like proposed in section 3.2 of this paper I need a symmetric positive definite Kernel function. For this purpose I want to use the Gaussian Kernel like ...
1 vote
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### hyperparameters optimisation with linear kernel

I want to conduct an SVM model-regression (i.e., support vector regression), using a linear kernel function. Does it make sense to perform a cross-validation hyperparameter optimization when the ...
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### Cannot use SVM with RBF Kernel

I'm new in R. I have an original dataset with 25771 variables and 118 samples. I already performed feature selection and split the dataset into 70 30 so i have 82 samples in my training data and 36 in ...
1 vote
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### What is the role of length scale bound in sklearn Radial Basis Function

The radial basis function provided by SkLearn (reference) has two parameters: length scale and length scale bounds. I understand that the length scale controls the importance of the coordinates of the ...
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### What is the expanded representation, $\phi(X)$, required to obtain the RBF kernel?

For the two-dimensional case, where $\boldsymbol X=[x_1, x_2]$ and its corresponding expanded represetation $\boldsymbol\phi(X)= [1, \sqrt2 x_1, \sqrt2 x_2, x_1^2, x_2^2, \sqrt2x_1x_2]$, we can ...
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### Adaptive Gamma in RBF Kernel

The RBF Kernel is defined by $K(x,y)=\exp(-\gamma ||x-y||^2)$ Wouldnt it be better to find a suited gamma value for each dimension? $K(x,y)=\exp(-\sum_i \gamma_i * (x_i-y_i)^2 )$ This would add ...
1 vote
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### Is it good idea to generate features from data points similarity comparison?

I know about polynomial features in machine learning, which can introduce nonlinearity to original dataset. I also heard about binning, which also allows us to create new features from existing ones. ...