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This occurs quite a lot in image processing, where the work is predominantly with silhouettes; there are a whole lot of redundant features that just have the same value for every instance in the dataset, i.e, features of zero variance. Such features are usually removed during the preprocessing stage.

Is there a conventional terminology to denote such features?

amoeba
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Ébe Isaac
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    Constant, as opposed to variable, maybe? – Momo Mar 08 '17 at 09:00
  • @Momo I used to refer to them as constant attributes or static features but I was wondering if there is any other term used in the statistics jargon. – Ébe Isaac Mar 08 '17 at 09:09
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    I think both terms are fine; just constant is also fine. I don't know of any other name and am not sure one exists at all, as in statistics we are usually interested in things that vary. – Momo Mar 08 '17 at 19:16

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It is simply a constant. In mathematics "constant means non-varying." We have constant variables and constant functions: $f(x) =c$. Moreover, even if you want to frame your problem in terms of random variables, then you can think of constant as of variable following degenerate distribution, i.e. $\Pr(X=c)=1$, or Dirac delta $f(x) = \delta(x-c)$ in continuous case. There is no need to create new term for it.

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Tim
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  • Well, a constant could be taken to mean necessarily not varying. It could be that it only is constant in the sample, but coud be varying in the population. I woud say zero-variance. – kjetil b halvorsen Apr 15 '17 at 22:30
  • @kjetilbhalvorsen the same could be said about zero-variance: is it zero variance in the sample or population? – Tim Apr 16 '17 at 06:05