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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Correlation between two Gaussian Processes
I have a space-time series, so it is in 2D. So, the signal model $\mathbf{S}$ is a matrix. If I fix the space, the time series at that point in space is a complex GP:
$$ \mathbf{S}[x, :] \sim \...
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What is normalized winning frequency in kernel self organizing map(SOM)?
In the k-means based kernel SOM, proposed by MacDonald and Fyfe (2000), the update of the mean is based on a soft learning algorithm
mi(t + 1) = mi(t) + Λ[φ(x) − mi(t)]
where Λ is the normalized ...
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Prove that modified RBF function satisfies Mercer conditions
Suppose that I have a modified RBF kernel function.
$k(\mathbf{x},\mathbf{y}) = \exp{(-||\mathbf{x}-P\mathbf{y}||^2 })$
where $\mathbf{x},\mathbf{y}$ represent $d$ dimensional inputs and $P$ is the ...
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Interpreting the formula for Riemannian metric tensor
In Improving support vector machine classifiers by modifying kernel functions, the authors defined Riemannian metric tensor for a kernel as follows:
$$
\begin{align}
g(\vec{x}) &= \text{det}|g_{ij}...
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Weighted sum of RBF kernels with different length scales
When applying Gaussian Processes to applied problems, the choice of length-scale parameter parameter for the radial basis function (RBF, ie Gaussian) kernel makes a big difference. In practice, I have ...
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Is it enough to prove that the Kernel matrix is positive semidefinite to know that the function is a kernel?
Is it enough to prove that the Kernel matrix is positive semidefinite to know that the function is a kernel? Or is it also necessary to prove that the matrix is symmetric?
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Hyperparameter estimation of a Gaussian process when the total length of observation is less than the correlation length?
If a Gaussian process has a kernel covariance function that is parametrized by a correlation length-like parameter (Like in RBF of an SM kernel), to estimate the hyperparameters, it is common ...
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learning guarantees for gaussian weighting of training points
I have my training data for binary classification that consists of $N$ pairs $$(x_i\in R^F, y_i \in {-1, 1})$$ $i\in [1,\dots,N]$. My classification rule of a new point $x$ is simply
$$
\hat{y}(x) = \...
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Squared Exponential Kernel Matrix is not Positive Definite
Related to this question, but adding a nugget isn't helping. Possibly I'm just making a silly coding mistake:
...
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Why does Kernel PCA works with validation data?
Assume that you have a matrix $X$ and you want to do Principal Component Analysis on that data. But the data contains nonlinearities, so you decided to use Kernel Principal Component Analysis instead.
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Does the ID class vector change in Kernel Linear Discriminant Analysis?
Assume that I have a matrix $X$ that has the size $m * n$ and a class ID vector with the length $n$.
If I want to apply Kernel Linear Discriminant Analysis (KLDA) onto the matrix $X$ and vector $y$, ...
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Result after applying kernel trick
I understand when the data is not linearly separable, it has to transformed into higher dimensional space, to make it linearly separable. Applying kernel trick can perform it without even computing ...
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Kernel PCA on each data set, not the whole matrix - Possible?
I have a matrix $X$ that has $M * n$ in size. I'm going to apply that with PCA. The problem is that $X$ contains nonlinear structures. So one good thing is to use The Kernel Trick.
My data is ...
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is it possible to use RBF sampler to construct kernel and use it for prediction at new data point?
I would like to construct a kernel from very large samples which makes it impossible to construct the N by N kernel matrix. I can use RBF sampler (random fourier features) to make the dimension more ...
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What kernel to use for Gaussian Process Regression on data with large flat region?
The problem I'm working on has a region that's largely accurately modeled by a GP model using a squared exponential kernel. However, there is a large region in the "truth" model that is ...
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