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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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Kernel function with a feature space equipped with an inner product that is not the dot product

Premise: A function $K: \mathbb R^d \times \mathbb R^d \to \mathbb R$ is called a kernel function on $\mathbb{R}^d$ if there exists a Hilbert space $\mathcal{H}$ and a map $\phi: \mathbb R^d \...
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Possible error in evaluating kernel gradient in scikit-learn's GPR

Perhaps I am missing something very obvious, but in the standard kernels associated with scikit-learn's Gaussian process regression framework, the radial basis function (RBF), $$f = e^{-x^2/2l^2},$$ ...
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Is this a valid Gaussian Process kernel?

$\mathcal{K}\Big( \; (x,y), (x',y') \; \Big) = \sigma_f^2 \exp{ \frac{(x-x')^2}{2l^2 \cdot (y+y')^2} } $, where $l > 0$ The variance associated with each training point (given by a vector) is a ...
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Estimate RBF-kernel mapping function given graph/space

Problem Provide a mapping function $𝜑(x)$ that enables us to draw a linear separator between the two classes in the mapped space. Attempt I tried to use a radial basis function by finding 4 ...
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Svm grid search tunes itself to 100% training accuracy?

Im using rbf svm classifier with nested cross validation (5 kfold to tune hyperparameters and then leave the last 10% for testing). When tuning hyperparameters the best cv accuracy trains to around 56%...
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SVM Classifier with RBF kernel works well with cross validation on training data, but fails on test data. What's going on?

According to the Practical Guide: We propose that beginners try the following procedure first: Transform data to the format of an SVM package Conduct simple scaling on the data Consider the RBF ...
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What is the most intuitive proof that Gaussian kernel is positive definite?

I have general form of Gaussian kernel $K(x,x')=\exp(-\|x-x'\|^{2})$ (just not considering $\sigma$). I tried to prove its positive definiteness via Gram matrix properties, but couldn't. Is there any ...
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Convergence of the Matérn covariance function to the squared exponential

The Matérn covariance function converges to the squared exponential covariance function. Many sources, amongst them the GPML book and Wikipedia, state this result. None of them provide details. I ...
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Probabilistic Interpretation of Radial Basis Function

I was wondering if someone could flesh out the probabilistic interpretation of using the Radial Basis Function to compute the probability between an observation and some reference value. My question ...
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48 views

SVM and correlation

Can anyone guide me about the feature selection based on correlation using SVM? RBF kernel check the correlation too or not? I am using weka and matlab. Any help would be appreciated.
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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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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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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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Is RBF SVM an ideal classier? [closed]

After reading up on RBF kernel, and seeing several SE posts (like this and this), I wonder if RBF kernel (and RBF network) can be called an "ideal" classifier? My logic is: RBF can be expanded into an ...
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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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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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Denoising with Kernel PCA, with handwritten digit denoising

When using Kernel pca and denoising handwritten images, basically every number gets denoised very well, and just with 1 PC, we have a clean denoised image. Yet, the number 7 gets somewhat an extra ...
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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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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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Optimization of firefly algorithm (FA) parameters

just need a hint (still learning) I'd like to use FA for optimization of three parameters of SVR-rbf. However, the FA algorthm itself has few parameters that need to be stated: # of fireflies - (...
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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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238 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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446 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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286 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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385 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 ...