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 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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110 views

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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562 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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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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19 views

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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18 views

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. ...
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1answer
26 views

Is SVM RBF applied to both classes?

Lets say i have following 1D data (position on x), color is target class and I need a classifier which classifies green from red: I decided to use SVM. Data is clearly not linearly separable, so i ...
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69 views

Gaussian RBF vs KNN explanation

I was studying SVM ML alghorythm and I was wondering about solution for non-linear cases. As I understand it for know, SVM tries to find hyperplane or object in defined n-dimensional space, which ...
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11 views

Labeling KPCA in R

The function $\texttt{biplot}$ in R is very useful for creating visualizations when performing PCA. However, when performing kernel PCA in R, I cannot find a way to label the loadings on the graph. ...
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34 views

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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63 views

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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43 views

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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87 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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173 views

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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428 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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16 views

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 ...
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10 views

Implementation of a Gauss Kernel in Python possibly using RBF Client

I want to implement the following Gauss kernel in Python: I could implement the structure in Python up to this point. However, the last piece missing is the calculation of the parameter tau squared. ...
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Resource for understanding kernel trick, kernel method, kernel functions?

So far my understanding about kernel methods is that they are ways to map our features to a higher dimension space - allowing us to fit non-linear data using linear models. I don't understand much ...
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17 views

Relation between Bayesian Linear Regression (Fixed base: Gaussian RBF) and SVM RBF?

I am trying to get my head around Bayesian Linear Regression. I am looking at a Gaussian radial basis function, which I assume acts as our prior. I have the following diagram: My current ...
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Why do Support Vector Data Description and One Class Support Vector Machine produce the same results?

Quoating from Chapter 5 of Kernel Methods in Computer Vision by Christoph H. Lampert 'A quick geometric check shows that if all data points have the same feature space norm and can be separated ...
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Relation between choice of kernel for the affinity matrix in spectral clustering and embedding into a higher dimensional space, using feature maps

So I've been studying spectral clustering where they use some affinity function related to a pre-constructed graph of the sample points or data $\{x_1,...x_n\}$. If we call the affinity function $W$, ...
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1answer
26 views

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 ...
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Binary classification Task : Least Squares kernel regression(squared loss) Vs SVM (hinge loss)

In binary classification, the solution function, in order to fit the training data, it just needs to acquire values that have the same polarity as the desired values, rather than accurately acquiring ...
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RBF-Kernel: Handling missing values

I want to compute the RBF-Kernel for a dataset which contains missing values: ...
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18 views

SVM and RBF Kernel

I have read that high gamma value in SVM(rbf kernel) can lead to high bias. But I have seen high gamma overfits the decision boundary. Why is it not called high variance?
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Significance of initialisation of Kernel in sklearn.gaussian_process.kernels

I have been going through Gaussian Processes. In one of the code I stumbled upon there is this statement, I am not quite sure of the parameters that are passed to initialise it. Please help me. ...
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How would phi of the gaussian rbf kernel map a 100-by-3 dimensional feature matrix?

Would a 100-by-3 dimensional feature matrix be mapped into a 100 dimensional or into a infinite dimensional feature space, if the mapping would not be bypassed by the Gaussian RBF Kernel? Following ...
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28 views

Reproducing kernels: how do I numerically compute the decomposition?

Suppose I'm given a kernel, $$ K(x,y) : \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R} $$ In order to describe/understand the (unique) associated RKHS, I seek its eigenfunctions, as per Mercer'...
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87 views

R - Gamma estimates in Kernel Ridge Regression

I am running a Kernel Ridge Regression in R. Mathematically, the minimization problem to be solved is the following: $$ \min_{\boldsymbol{\beta} \in \mathbb{R}^{d}} \ \sum_{i = 1}^{n} (y_{i} - \left \...
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1answer
172 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.