Talk:Indicator function

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 Field: Foundations, logic, and set theory

wow -- great article -- this helped a lot.

Graph[edit]

The supplied graph image is pretty, but would be more correct if it were generated without interpolation. —Preceding unsigned comment added by 64.110.209.189 (talk) 22:25, 14 November 2008 (UTC)


Characteristic function[edit]

Who says "characteristic function" is "much less frequent now"? It's actually the only term I know for this (I had to guess what an "indicator function" might be, when it showed up in Talk:Boolean algebra). Also the notation I know is χA for the characteristic function of A. --Trovatore 15:26, 6 September 2005 (UTC)

I agree strongly. I had never hear of "indicator function" before I read the ergodic theory article and linked to this page from there. I propose that this page be renamed to "characteristic function". --Mosher 22:03, 23 September 2005 (UTC)

You would have to make it a disambiguation page. Characteristic function already refers to the Fourier transform of a distribution of a random variable, which is a standard usage.--CSTAR 22:20, 23 September 2005 (UTC)
I assume the name indicator function or characteristic function is geographic so I don't think it wise to rule one out or another. As it is called indicator function and not characteristic function where I am. Also, perhaps you should put into the article multiplying two indicator functions. I[a, b] * I[c, d] = I[ max(a,c), min(c, d)] This property is crucial for calculating convolution.

I don't think it's geographic. I think it's more a matter of which research area you work in. Michael Hardy 18:44, 3 August 2006 (UTC)

Maybe, I'm not sure. However, I also notice the notification is completely different as well as how the indicator function is described. Lectures never needed to speak about mapping, the explanation of course was made to be more simplistic and considering the caliber of people that might need to come here, it would better if the article were described in a manner more suitable to teaching the concept rather than stating it in the most obtuse format possible. Perhaps something where it starts off for the possible motivations for using the indicator function, for instance in circuit analysis to perform convolution... possibly different notations, like using the 1 with subscript versus a capital I with a subscript or followed by brackets to indicate the set it describes. A simple layman explanation, for instance, I [0, 1], means a function that is 1 from 0 to 1 and zero otherwise. Show that you might use it to multiply against an existing function to extract a piece of it, like f(x) * I[0,1] gives you the function from [0,1]. I'm personally wary of editing the article myself.

Perhaps the term indicator function is a shorthand for set indicator function, because the function f specifies or indicates the set { x | f(x) = 1 }. Bo Jacoby 23:09, 25 December 2006 (UTC).

Beware : other definition in convex analysis[edit]

I would like to point out that in convex analysis, the definition of a characteristic function is different from the definition of an indicator function. The indicator function of K is defined as follows:


\chi_K(x)=\left\{
\begin{array}{ll}
1 & \textrm{ if }\ \ x\in K \\
0 & Otherwise.
\end{array}
\right.

while the characteristic function is defined by:


\chi_K(x)=\left\{
\begin{array}{ll}
0 & \textrm{ if }\ \ x\in K \\
+\infty & Otherwise.
\end{array}
\right.

See for instance http://en.wikipedia.org/wiki/Characteristic_function_(convex_analysis)

It could be good to add this definition to this page.

The lemma of this page is "indicator function", not "characteristic function". Characteristic function is already a disambig. I think that for the sake of clarity, only concepts that are related to the indicator function should be explained on this page. But it could be mentioned that "characteristic function" has other unrelated meanings in other fields (now the only other meaning mentioned is in probability theory). There could also be a more prominent link to the disambig page.--88.73.31.222 (talk) 01:05, 8 February 2012 (UTC)

Proposed merge with Indicator vector[edit]

Seems to be a different way of viewing a finite indicator function. QVVERTYVS (hm?) 22:22, 10 February 2014 (UTC)

Yes, as a vector instead of a function. Merger with redirect is a good idea. Zaslav (talk) 23:26, 10 February 2014 (UTC)
Except that some fields use the vector format exclusively or primarily. It is also a common method in some areas of computer science. I work with selection vectors (which are simply another name for indicator vectors) almost every day. DES (talk) 23:31, 10 February 2014 (UTC)
So do I, but I think the use in computing belongs under Bit array rather than in a separate page that is purportedly about mathematics. Then again, if indicator vectors have interesting properties in terms of linear algebra, a separate page would be in order. QVVERTYVS (hm?) 00:02, 11 February 2014 (UTC)
No, as it would be confusing and taxing for the common user, unless we atypically use the vector as a special case, a generalization, at the bottom of the Indicator Function page. There are multitudes one-dimensional applications of indicator functions (limited to dimension 1) and it would be taxing to start with the higher dimensional ones. Limit-theorem (talk) 11:30, 20 March 2014 (UTC)
Withdrawing merge proposal. QVVERTYVS (hm?) 20:05, 7 October 2014 (UTC)