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.

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Multilayer Perceptron and Radial Basis Function

I've just studied how MLP neural networks and RBF neural networks work. However, I wasn't able to find any comparison that explains in layman terms when should I use MLP or RBF. Could you tell me?
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Can we optimize heterogeneous parameters of RBF Network using Gradient Descent?

There're three parameters in the Radial Basis Function Networks (RBFN). Centers of RBFs Width of RBFs Weights of RBFs It's a fact that Weights can be easily updated using a simple Gradient Descent. ...
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38 views

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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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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100 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 ...
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540 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" ...
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64 views

How to prove 1-norm radial function is kernel?

How should I prove that is a valid kernel: $K(x,y)=exp(-\alpha||x-y||_1) $ As I understand, there are three ways to prove that prove $K(x,y)=<\phi(x) ,\phi(y) >$ prove $\sum_{j,k=1}^n a_j\,...
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223 views

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 ...
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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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142 views

Why are Radial basis function networks not particularly suitable for extrapolation?

Assuming you have a regression problem where the test data is quite likely to be outside the range of the training data; hence, the model needs to extrapolate from the training set. Why are RBF ...
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1answer
802 views

How to interpret a SVM plot

Hi, so i'm using support vector machine for some statistical project and this is a plot of from a using a sigmoid kernel. There are 9 variables and 300 data points. The way i interpret this plot is ...
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7k views

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' ...
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145 views

SVM: (Using the RBF as a Kernel) vs (Using the RBF to create a new set of features)

I apologize for the verbose description, but (after searching several places for an answer) maybe the best way to phrase it is to lay things out explicitly. Say we are trying to build an SVM model ...
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70 views

Coefficient in GLM, find the important factor

I am using the GLM to model my data. The response variable is binary and there are two predictors, namely, speed (cm/s) and position (cm). First of all I have used the Zernic basis functions to model ...
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964 views

How to choose bandwidth parameter for RBF

I am implementing a logistic regression with RBF (Gaussian) kernel. Here are the steps I tried: first finding centers with k-means perform the transformation using $e^{-(||x-c_i||)^2/2\sigma^2}$ ...
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3k views

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*...
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1answer
782 views

How to calculate decision boundary from nonlinear svm in R?

As a follow up to this question - How to obtain decision boundaries from linear SVM in R? Is it possible to do the same with non linear SVM? (Radial for example). What do the weights represent?
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9k views

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 ...
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2answers
2k views

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 ...
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202 views

Weighted Minkowski RBF kernel

The radial basis function (RBF) kernel is given by $$K_{\text{RBF}}(\mathbf{x}, \mathbf{y})=\exp[-\gamma\|\mathbf{x}-\mathbf{y}\|^2_2]$$ where $\|\mathbf{x}-\mathbf{y}\|^2_2$ is the squared ...
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285 views

RBF transformation on a Normally Distributed Random Variable

I have a random vector $\mathbf{X} \sim \mathcal{N}(\mathbf{m,\Sigma})$ which is transformed by a Gaussian Radial Basis Function into the random variable $\mathbf{Y} = K(\mathbf X) = \exp(-\lambda ||\...
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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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93 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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160 views

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} ...
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148 views

Gaussian shape link function for glm binomial regression?

Link functions are typically sigmoid. The idea being that the underlying data is fitted to the curve with an increase in the predictor summation gives an increase in the response. However, could one ...
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190 views

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 ...
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152 views

Are RSM and RBFN essentially GLM?

Is response surface methodology (RSM) the same as a generalized linear model (GLM) with quadratic terms and normal error distribution? Is radial basis function network (RBFN) also the same as a ...
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106 views

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{\|...
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1answer
303 views

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 ...
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3k views

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 ...
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How to interpret basis function that yields vector in machine learning algorithm?

I'm struggling to understand what $\phi(x_{N+1})$ is in this excerpt of an algorithm (namely Linear Bayesian Regression embedded in other algorithm): $c_i = \gamma_i / \sum^L_{j} \gamma_j$ $V_i^{N+1}...
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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 ...
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1answer
974 views

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 ...
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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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581 views

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?
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188 views

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 ...