# Made a [basis-function] tag

We have 700+ Q/A referring to basis functions, and a subset radial-basis tag. There appears to be considerable head-scratching as to what a basis function is, so, I made a tag the following excerpt:

A basis function is an element of a set of functions that span a function space.

The full wiki is:

Basis functions are spanning sets of functions. These include sums of sine waves to match any waveform, radial basis functions used for artificial neural networks, basis vectors of a linear algebra, and $\Sigma_0^{n-1} t^i$ to span a polynomial of degree $n-1$. For the latter, $\Sigma t^i$ is called a cardinal or standard basis because the coefficients of $t^i$ are all 1's.

What is needed now? Do I need to put in 100 or so tags onto Q? What do I do about the synonym structure where radial-basis is a subset of basis-function, anything? There are pluses and minuses to doing that, request advice.

• 700 seems to be a gross overestimate. This search stats.stackexchange.com/… yields 93. And I am not sure what fraction is covered by [kernel-trick] (probably substantial)... Nevertheless, the new tag is probably fine. Nov 3 '17 at 15:07
• @amoeba My apologies, your search was literal for "basis function", mine was for basis+function and frequently users do not know that often basis+function="basis-function" so perhaps $~90<n<~700$. However, that is not as important as the advice I am seeking, please?
– Carl
Nov 3 '17 at 15:13
• I'd say wait a couple of days to see if anybody protests against your new tag, and if nobody raises any concerns, then you can go ahead and put this tag on some questions. I don't recommend hunting down all questions possibly related to this tag. Rather, I would suggest to find a dozen or two most prominent (most upvoted or otherwise most important) threads and tag those. This will be enough to "establish" the tag. Nov 3 '17 at 21:49
• @amoeba Thank-you, much obliged. What about synonym? My instinct would be to leave it alone rather than force synonym on people who may learn what a basis function is via a radial basis function, even if, or perhaps because, the order in which a statistician learns physics seems outstanding.
– Carl
Nov 4 '17 at 0:25
• Re synonym, turns out this issue is more complicated than it could seem, because we have rbf-network along with radial-basis, and lots of radial-basis questions are actually about RBF networks. I would suggest to retag these threads to [rbf-network] (these would be at least 15). Nov 4 '17 at 23:13
• Further, most of the remaining threads in radial-basis are about RBF kernel in the context of kernel methods in machine learning (kernel trick). I am wondering if we should move all that to kernel-trick. Perhaps we could also create [rbf-kernel] as a synonym to [kernel-trick]. This will leave only a handful (if it all!) of questions left in [radial-basis] and I would retag those to [basis-function] and eliminate the [radial-basis] entirely :-) Nov 4 '17 at 23:17
• @amoeba I'm working on it, it will take a while, and not yet sure that rbf-network overlaps radial-basis entirely. Conceptually they do not appear to, and user interest may be dumped if we eliminate radial-basis, but in practice maybe they are equivalent. So, I will go about this gradually.
– Carl
Nov 6 '17 at 19:03
• Carl, but I did not say that these two tags overlap entirely! Wait, let me post my suggestion as an answer, so that other people could discuss it as well. Nov 6 '17 at 19:25

Wait a couple of days to see if anybody protests against your new tag, and if nobody raises any concerns, then you can go ahead and put this tag on some older questions. I don't recommend hunting down all questions possibly related to this tag. Rather, I would suggest to find a dozen or two most prominent (most upvoted or otherwise most important) threads and tag those. This will be enough to "establish" the tag.

Related tags

I don't like ×39 tag too much.

1. Around half of its questions seem to be about ×21, which has its own tag. Those clearly should be retagged.

2. Most of the remaining questions seem to be about RBF kernel in the context of kernel methods in machine learning. I suggest we create [rbf-kernel] tag and map it as a synonym to ×434. I don't think it would be useful to keep it separate.

3. After questions about RBF networks and about RBF kernel are moved out of the [radial-basis] tag, there will be almost no threads left there. If anything remains, it can be retagged with your new tag.

• Thanks much. Much obliged.
– Carl
Nov 6 '17 at 20:19
• If you are going to carry this out, then ping me please once this is done. Cheers. (Of course let's see first if anybody protests.) Nov 6 '17 at 20:23
• Hi Carl. So what do you think about this? Do you agree with my assessment? If you do, shall we go ahead? Do you want to implement that? Nov 12 '17 at 14:15
• Yes, I agree with your assessment and have been slowly implementing it. The reason why I did not respond was because you requested a ping upon completion, and I did not finish making changes. For me, this has proved to be a slow process because the material is new to me and I have to work to understand each Q/A. If you wish to pitch in, feel free to do so. It is less important who does what, when, than it is to create a hierarchic dialectic.
– Carl
Nov 12 '17 at 14:33
• @Carl Ah, OK great. Sure, no pressure. I might retag something at some moment, but I am happy to let you do it too. Some are pretty straightforward (e.g. see this search stats.stackexchange.com/…) but of course if you want to carefully review each Q then it takes time. Nov 12 '17 at 14:37