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A radial basis function (RBF) is a real-valued function whose value depends only on the distance from the origin. Gaussian function is one example.

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For what values of $\beta \in \mathbb{R}$ is $t(x-x')=-||x-x'||^\beta$ a kernel?

For what values of $\beta \in \mathbb{R}$ is $t(x-x')=-||x-x'||^\beta$ a kernel? I know that kernels of type $t(x-x')$ where $t$ is function that inverts the dissimilarity $x-x'$ into a similarity ...
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Weights from RBF Support Vector Regression

I was doing some research on Support Vector Regressions with Radial Kernels and I have consistently come across that the weights from the RBF cannot be calculated implicitly because of the ...
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how to use RFB for primal svam model?

I know if we want to solve primal model of non-linear SVM, we have to generate new features. for example for kernel (1+xz)^2 for primal problem for any pair of features x1 and x2 we have to generate: ...
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encoding the true labels of radial basis neural network for binary classsification

I am working on a binary classification problem (my class labels are 1 or 0) and I have three layers (input, hidden, output) radial basis neural network. I put two neurons, one per class, in the ...
28 views

Using k-means clustering to train radial basis neural network for highly imbalanced dataset

I am trying to find prototype neurons for my radial basis neural network. My dataset has 30 attributes (of which 28 of them are the result of a single PCA) and 300.000 observations. It is a binary ...
133 views

What is the basis for the default sigma value used by svmRadial in caret? [closed]

I am looking at the source code (I think) for the "svmRadial" function in the caret package. It looks like the default sigma values are calculated by first using the kernlab package's "sigest" ...
78 views

How to use a gaussian basis function

I am trying to build a linear regression model and one of my features when plotted against the output looks like a bell curve. So intuitively I figured that if I use the raw data for that feature my ...
40 views

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 ...
39 views

Mairhuber-Curtis Theorem, Adaptive Bases and Neural Networks

I am reading the paper Positive Definite Kernels: Past, Present and Future by GE Fasshauer in which he describes computing with PD kernels. In section 3.2 he mentions the Mairhuber-Curtis Theorem, ...
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How does one extend radial basis function (RBF) networks formally from regularization but with vector valued outputs?

I was reading the following paper on hyper & radial basis function (HBFs & RBFs) networks and also this one that kind of summarizes the first one and was trying to understand how to extend ...
92 views

How should one learn the centers for an hyper basis function network (HBF)?

I was reading the following paper on hyper basis function (HBF) (similar to radial basis function RBF network) and was trying to figure out how one learns the movable centers of the hyper basis ...
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SVM RBF performance on “dissimilar” data

I've been studying the performance of machine learning algorithms on "dissimilar" data (that is, prediction on new data that are not that "similar" to the training set) and I came up with this ...