Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [radial-basis]

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.

A radial basis function (RBF) is a real-valued function whose value depends only on the distance from the origin, so that $\phi( x ) = \phi (\|x\|) $. Sums of radial basis functions are typically used to approximate given functions. Examples include Gaussian:

$$\phi( r ) =e^{-(\varepsilon r)^{2}}\;,$$

And others, and find application, for example, in simple neural networks, and for kernels in machine learning support vector machines.

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SVM: non-linear versus linear models

In the context of classification on somewhat large datasets (say at least 50Kx50K), I am wondering in which cases non-linear models are superior to linear ones to warrant the added complexity. I often see in my own research that for these larger…
ciri
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libsvm on MATLAB with rbf kernel: Compute distance from hyperplane

I have a One-Versus-All classification task with 80 different labels. In order to parallelize the problem to take advantage of multiple nodes on a computer cluster, I first trained 80 binary SVM classifiers in parallel with MATLAB's frontend of…
Jason
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Can someone explain the RBF Kernel to me?

I have read every explanation out there on this but nobody seems capable of explaining this in a way that I am able to understand. For an SVM RBF Kernel we often say that: But what does x and x' represent here? Let's say my input data x is of shape…
user1761806
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RBF kernel algorithm Python

I have this algorithm to compute the RBF kernel and it seems to work just fine. But I would like to understand what kind of operations are involved, for example: What are the trnorms vectors? What are they for? What is the meaning of creating the…
Lorenzo Norcini
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Weights of radial basis function networks

If I use radial basis function networks (RBFNs) for probability estimation by plugging the output of the RBFNs into the Logistic function are weights between 0 and 1 sufficient?
cs0815
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Binary classification using radial basis kernel SVM with a single feature

Is there any interpretation (graphical or otherwise) of a radial basis kernel SVM being trained with a single feature? I can visualize the effect in 2 dimensions (the result being a separation boundary that is curved rather than a linear line. (e.g…
user2422566
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How to build and use the kernel trick manually in python?

So... I have been trying to make a radial basis kernel for hours but I am not sure of what my final matrix should look like. I have 30 features and 200000 data points. Should my matrix K be 200000*200000 or 30*30 ? My code so far produces 30*30: def…
Albert James Teddy
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Optimal basis for regression problem

Consider the training set $\{(x_i; y_i)\}_{i=1}^N, x_i \in \mathbb{R}^n, y_i \in \mathbb{R}$. The goal is to find regression function, like, $f(x) = \sum_{i=1}^K a_i g_i(x) + a_0$. The least-squares solution is well known, if we know $g_i$…
TheBug
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Is it meaningful to compute a radial kernel density estimate from 2D data?

I am working with 2D spatial data, $(X_i, Y_i),\; i=1, \cdots, N$. My current research requires estimating the density of the distances between those data points in each of the two dimensions. So the underlying joint pdf that I am estimating is…
Gabriel
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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 derivate the polynomial function kernel…
Nip
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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 measure proportional to the kernel. In this case, by…
alienflow
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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 is partially motivated by the top answer of this…
guy
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100% training accuracy despite a low cv score

I am working on an assignment where we have to study the affect of gamma and C parameters on SVM with RBF kernel. I use python's sklearn library and grid search with 10 fold cross validation (with a test size of .2) to test different values of…
artemis
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Can one derive Radial Basis Functions (RBFs) with movable centers from Tikhonov regularization?

It is well know that the "usual" Radial Basis Function can be derived from Regularization that imposes small derivates. More precisely it is well known that the following: $$ f(x) = \sum^{N}_{n=1} w_n \phi( \| x - x_n\| ) = \sum^{N}_{n=1} w_n e^{ -…
Charlie Parker
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How to prove that Radial Basis Function can be derived by mapping function?

How to prove the radial basis function $k(u,v) = \int_{\mathbb{R}^d} \phi_t(u)\phi_t(v)dt $ can be integrated out by mapping function? $$\phi_{t}(u) = \frac{1}{(2\pi\Sigma)^{d/2}} \exp\left\{-\frac{\|u - t\|^2}{2\Sigma}\right\}$$ In other words, the…
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