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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RBF networks and epsilon-NN

Will an RBF network with a Window kernel correspond to an epsilon-NN classifier? I know that kNN only considers the k nearest data points while RBF uses all the data. How does this relate to epsilon-...
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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 ...
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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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63 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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146 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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848 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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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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323 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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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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894 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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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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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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86 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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1k 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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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
880 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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13k 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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219 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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300 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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86 views

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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162 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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164 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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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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166 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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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
307 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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1k 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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439 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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650 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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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 ...