Talk:Radial basis function

message: Does this have something to do with basis function? --Abdull 17:08, 21 February 2006 (UTC)
replies: text: Yes. Radial basis functions are basis functions of a particular form. They depend on the distance to a center associated with each basis function. Unlike many basis functions, these sets are not complete. Complexica 18:52, 23 February 2006 (UTC)
thread_title: Basis function

message: Hi, 
It's one of my first intervention, I hope I won't do anything not aligned with the wikipedia policy.
1) Neural Networks are not always composed of three layers, there could be no hidden layer, one or two, even more for 'exotic cases'.
:I found an answer to this question here, it says "In principle, they could be employed in any sort of model (linear or nonlinear) and any sort of network (single-layer or multi-layer). However, since Broomhead and Lowe's 1988 seminal paper [3], radial basis function networks (RBF networks) have traditionally been associated with radial functions in a single-layer network" Paskari 21:06, 1 December 2006 (UTC)
replies: text: Good idea about the kernels. I am planning an extensive extension of the article. I will add, unless you want to. Perhaps something also should be added about layers. Please feel free to add what you think. Also, it is good to sign your comments with 4 ~. This puts a date stamp and an identifier on your comment. Complexica 20:14, 31 March 2006 (UTC)
replies: text:  Ok, thanks for the tips. I will think at something for the NN layers. Nicogla 12:32, 3 April 2006 (UTC)
thread_title:  Overview comments 

message: I'm not sure how to go about this but I was thinking of contributing something about using radial basis functions to interpolate scattered data samples. The current page is focused on their application in Neural Networks, which is a significant application - but not their only use.
:Perhaps the best place for this is as an example, maybe the first example.Complexica 20:20, 17 August 2006 (UTC)
thread_title:  Query 

message: I'm very familiar with RBFs as basis functions for meshless multivariate interpolation and the contents of this web page are totally unfamiliar.  This page presents their application to neural networks as what RBFs are all about and also uses jargon specific to that application ("streams of data", "learning") to describe general properties, which is very confusing and misleading.  There is almost nothing here which is from Holger Wendland's "Scattered Data Approximation", which is probably the most authoritative book on RBFs.
:Please feel free to add what you think is missing. That is what the wiki is about, isn't it? Complexica
::I am not a master of RBF but I have sets of rationalized pi the aproximations of pi are multiples of 10 thus and RBF is needed for Circular Arrays on decimal Distribution where is decimal digit is represented by a circle. The arrays are not standard square indexing. Thus, from pi*pi/pi the Circumference/Diameter set the divisor is x digits of pi -> For the x index of the circle array thus 4 digits of pi circle 9869/3141 or 9870/3141 if you look at 5th digit of pi*pi. Thus, I get a set of unit circles where x*x + y*y = (pi/2)*(pi/2). If I snap pi*pi+1/(pi*pi) = 1; I am getting the pi rationalization I am interested in for video game computing I call this oipi. This is used for Circular Bounding Box Recognition of Colision Detection. Because the square in circle has lot of error. This is a metaphor for square array math versus RBF Circular Arrays distributed on BASE notation.
openInvent 13:25, 12 April 2021 (PST)
17:29, 14 September 2006 (UTC)
replies: text: I agree in that the use of the terms 'streams of data' and 'complete data sets' is misleading', I think the introduction to any page should be as basic as possible, such that all readers, not just scientists and mathematicians, should understand. Paskari 19:43, 1 December 2006 (UTC)
thread_title:  wrong focus, inappropriate domain-specific jargon 

message: I admire the fact that you have spent such a long time organizing all the formulas, but you have to simplify at least the intro and the overview, otherwise no one will be able to follow Paskari 19:50, 1 December 2006 (UTC)
thread_title: Intro and Overview

message: User:Orie0505 objects to the writing of statements like \phi(\mathbf{x}) = \phi(||\mathbf{x}||), on the basis that the function φ can't act both on a scalar and a vector.
I think that's being unreasonably picky.  The point about an RBF is to define a mapping from a vector to scalars, which depends only on the norm ||x|| of the vector; in fact a family of mappings, indexed by the centres {c}, depending only on the norms ||x-c||.  But the fact that these are mappings from V to R is important.
In view of how closely related they are, it is natural (and common practice) to use the same letter φ for φ(x,c), φ(x) and φ(||x||).  Yes, these are three different functions, becuase they act on three different types of inputs.  But such operator overloading -- using the same letter for different, but closely related functions, identified by their different types of inputs, is not unusual.  In computer science it's a commonplace, of course.  But even in physical sciences and applied maths, it's not unusual to write things like ψ(r,θ)=ψ(r) to indicate there is no theta dependence.
In this case it would be much more confusing to use different letters for the different functions, because they are so closely related.  It is also, as I wrote, the standard practice in the field, and the article should reflect that.
At the end of the day RBFs depend only on a scalar.  But the whole name, "basis function", refers to a mapping of all the points in a space to scalars.   The article should reflect that.   Jheald 15:39, 5 October 2007 (UTC)
thread_title: RBFs: Functions of scalars or vectors? 

message: I have deleted the formulae for the h(x) formulations of the common RB functions, because what the h(x) functions refer to is described nowhere, and appears to use a somewhat different notation from the rest of the article. I would have tried to remedy these problems instead of merely deleting the functions, but try as I might, I cannot determine to what they refer.  —Preceding unsigned comment added by 69.144.206.47 (talk) 04:00, 5 August 2008 (UTC)
thread_title:  h(x) formulae 

message: Please delete this section when resolved.  
Critical radius is not a standard term so you should explain it mathematically. From the context I'm guessing that it's the square of the standard deviation? I have no way of knowing and I can't google the term or look it up in Wikipedia.  — Preceding unsigned comment added by Structurebiologist (talk • contribs) 05:15, 5 September 2018 (UTC)
replies: text: The term that is used in the interpolation literature is shape parameter. I believe that if the function has a compact support that the function is only non-zero for r < 1/\varepsilon . It makes sense why someone would call this a critical radius and it is consistent with their assertion. I'm not sure if this term is used at all so if someone finds it in a source somewhere it would be nice to mention it in the article again and provide a citation. Shawsa7 (talk) 10:17, 30 March 2019 (UTC)
thread_title:  Epsilon and critical radius