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 this a valid kernel function?

I devised a distance function similar to this form. K(x,y)=(-||x-y||+xy+1)/2 And now I want to prove it is a kernel function.I have read about Mercer's condition and positive semi definiteness, but I ...
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Use the features selected with RFE SVM linear for prediction of SVM rbf

I was wondering if the features selected with RFE with SVM linear kernel are still "good" features when we use a non linear model, like SVM rbf kernel. This comes in practice when you want to use SVM ...
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619 views

How to perform kFold cross validation in Libsvm's precomputed kernel in MATLAB?

I understand that Libsvm provides 'v 10' option for 10-fold cross-validation in...
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Kernel functions with vector output

Kernel functions are used commonly with SVMs to make classification of non linearly separable data possible - i.e. the Kernel function provides the linear separability. But from looking at Kernel ...
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Adding new center in an RBF network without memorizing previous training examples

Suppose we train an RBF by minimizing the LSE on a couple of training points and we are doing it incrementally in an online fashion. So basically we update the QR factorization using e.g. Givens ...
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886 views

linear vs non-linear kernel SVM

The dataSet contains 213 examples of 7 classes . Each example are 25000 features. I want to learn model with SVM (test scenario used are 10-fold cross validation). I am a beginner in machine learning, ...
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410 views

What is the motivation or objective for adopting Kernel methods? Is kernel trick a feature engineering method?

I come to know that kernel methods can be used in not only SVM but also many machine learning algorithms. I understanding that in SVM, the reason for using kernel trick is that some data are linearly ...
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128 views

Kernels property: integral of kernel product $\propto k(x,y)$

Let $k$ be a kernel function (symmetric and semi-positive definite function). Does the following relationship hold: $\int_{-\infty}^{+\infty}k(x,u)k(y,u) du \propto k(x,y)$ ? Or for what type of ...
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Kernel and regularization parameter of James–Stein estimator

Consider a FIR model of the form $y= Ug_0+e$ with $e$ white noise with variance $\sigma^2$. We assume that we have collected N input-output measurements $y$ and $U$. The James–Stein estimator is ...
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475 views

How to tune bandwidth in machine learning kernel model?

Gaussian kernel $k(x,y) = \exp(-\lVert x-y \rVert^2/\sigma^2)$ has a hyperparameter $\sigma$. I know grid search cross validation, but this would require a lot of computation since computational ...
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Does Mercer's theorem work in reverse?

A colleague has a function $s$ and for our purposes it is a black-box. The function measures the similarity $s(a,b)$ of two objects. We know for sure that $s$ has these properties: The similarity ...
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738 views

How to understand effect of RBF kernel for kernel PCA

I understand the math in kernel PCA and with RBF kernel, and I also understand that the RBF kernel map the data into a infinite dimensional space. I know that for SVM, mapping the data into a higher ...
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Why a large gamma in the RBF kernel of SVM leads to a wiggly decision boundary and causes over-fitting?

The hyperparameter $\gamma$ of the Gaussian/rbf kernel controls the tradeoff between error due to bias and variance in your model. If you have a very large value of gamma, then even if your two ...
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The gamma parameter (or kernel width) for RBF Gaussian kernel in kernel PCA

Is there any general way or rule of thumb of how to determine the kernel width for KPCA?
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651 views

Regularized linear vs. RKHS-regression

I'm studying the difference between regularization in RKHS regression and linear regression, but I have a hard time grasping the crucial difference between the two. Given input-output pairs $(x_i,y_i)...
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626 views

Calculation of nu and gamma in one-class SVM with rbf kernel

I am using python sklearn's one-class svm classifier for anomaly detection. I would like to know can I accurately calculate the required value for nu and gamma for rbf kernel. Is there any equation or ...
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Gamma as inverse of the variance of RBF kernel

I would like to fix the parameter gamma by using the following heuristic and then select C using GridSearch: taking the inverse of variance of RBF. ...
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598 views

Is Bias term required for RBF with Gaussian kernel?

For standard logistic regression, we add a bias term (1) in the features. Is it required when RBF is used with Gaussian Kernel?
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Heavy-tailed RBF kernel function

I'm trying to run a SVM regression on some data and I want to use ksvm from kernlab or svm ...
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439 views

How to select a radial basis function?

Currently I am investigating interpolation of 3D data with radial basis functions (RBF) and I am wondering that there are quite a few families of such (see table1 here). However, I cannot find any ...

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