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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### Would l-1 regularization with kernel trick induce sparsity on feature map's features?

Would l-1 regularization with kernel trick induce sparsity on the infinite dimensional feature map's features in the case of gaussian kernel?
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### Radial Basis Network and Multilayer Perceptron Network regression in R

I am new to R and I try to make a simple regression problem using a radial basis neural network and a multilayer perceptron neural network. With the following code: ...
1 vote
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### Are radial basis kernels able to model interactions between predictors?

I have been doing research using Support Vector Regression for some time, especially using radial basis kernel, for predicting a response variable from a set of numeric predictors. As a consequence of ...
1 vote
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### Relationship between structural or statistical properties and hardness of classification

I am trying to understand the relationship between structural or statistical properties of training dataset and hardness of classification in the context of binary classification with SVM using RBF ...
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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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### 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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### 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 ...
1 vote
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### 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" ...
1 vote
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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 ...
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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 ...