5 ms·

"Normalized". That's what we call data that have been scaled to fit on a tidy axis.

AstralStorm 6y ago
This has a nice confusion factor because IEEE calls such floats denormalized. Because they may have extra precision and different format.
- MaxBarraclough 6y ago
  Perhaps I'm misunderstanding you, but with floating point, denormalized/denormal numbers aren't just numbers with a magnitude less than 1, they're numbers so small that it's no longer possible to adjust the exponent in the usual way, so leading zeroes are used in the mantissa. This reduces precision. https://en.wikipedia.org/wiki/IEEE_754-1985#Examples https://en.wikipedia.org/wiki/IEEE_754-1985#Examples https://wiki.sei.cmu.edu/confluence/display/c/FLP05-C.+Do+not+use+denormalized+numbers https://wiki.sei.cmu.edu/confluence/display/c/FLP05-C.+Do+no...
0b01 6y ago
Normalized could also imply demeaned.
- joshvm 6y ago
  You could also call that centred to clear up confusion, or mean-subtracted to be more specific. I think if you're specifically dealing with statistical quantities it should be obvious, e.g. standardised if you also scale to unit variance. Personally if I saw normalised I would assume scaled by a constant, not offset (as in subtraction).
quietbritishjim 6y ago
One problem with the word normalised is that it implies that there is some true original value from before normalisation that isn't necessarily between 0 and 1. Of course if that's true then the word is ideal, but if not then it's confusing.
- tcldr 6y ago
  Genuine question, i'm no math expert: if you're using the value by multiplying it with some other value, does that not imply it qualifies as normalised? i.e. say you have a width of 500 and you want to move half way across so you have this value of 0.5 to get 250. By dividing 250 by 500, aren't we in fact normalising it?
  - chub500 6y ago
    I think generally normalized quantities maintain their original units whereas in your ratio case the unit is dropped. Units in the abstract sense I guess, such as this is a measurement along this vector or this is a ratio of any vector.
    - quietbritishjim 6y ago
      I think it's the opposite way round: normalisation results in units being dropped. The typical, most common, definition of normalisation is value ÷ max possible value, giving a result in [0,1]. (More general definitions of normalisation exist e.g. if you rescale so the standard deviation is a fixed value, or even use non linear rescaling, that could count, but never mind all that.) The parent comment's example of "position along width ÷ total width" certainly fits that bill. Whenever you divide something by the max of that something, the max is going to have the same units as the original value and you're bound to end up cancelling them. Or put another way, if you rescale 10cm into 0.5, it's certainly not 0.5cm so the units are either dropped or, at least, changed e.g. you could argue you've got 0.5x where x is the unit equal to 20cm.
      - f154hfds 6y ago
        Hmm when I think of 'normalizing' I don't think of dividing by a max at all - in my experience it is more taking a quantity (perhaps in English measurement) and transferring to a more 'standard' unit (say metric). In general I don't think normalization always includes a sense of being in a bounded interval. From a mathematical perspective you could perhaps say normalization is achieved by multiplying your quantity by a 1D operator. You can't change the dimensionality this way, but are certainly changing 'units' a la mm in the x direction -> m in the x direction for example. I guess what I'm saying is that 'normalized' and the like are not the best fit for the SO question. If I could take my own shot at the SO challenge from a mathematical perspective it would perhaps be sigmoid. Where the result of a normalization function takes a 1D value and maps it to a similar 1D value, the sigmoid takes a 1D value and maps it to a similar 1D value between (0, 1). So if I want to drop the previous information and only keep the resulting map, I can say 'this is my sigmoided value' - IE it is impossible for it to be outside of that range. Unfortunately sigmoid also connotates a differentiable curve which is extraneous information... https://en.wikipedia.org/wiki/Normalization_(statistics) https://en.wikipedia.org/wiki/Normalization_(statistics) https://en.wikipedia.org/wiki/Sigmoid_function https://en.wikipedia.org/wiki/Sigmoid_function
MaxBarraclough 6y ago
That's a good suggestion. 'Normalizing' is also used to refer to taking a vector and scaling it to make its length equal to 1. Google tells me it's also used in an analogous way elsewhere in maths. https://mathworld.wolfram.com/NormalizedVector.html https://mathworld.wolfram.com/NormalizedVector.html
uniqueid 6y ago
That's what I use, too: "normalized floats." I would prefer a better word, though. I work a lot with audio, and "signed normalized floats" doesn't exactly roll off the tongue.
prox 6y ago
I am trying to think of what the opposite word is of normalization.
- kevingadd 6y ago
  In the spaces I work in, people just say denormalized / denormalization.
  - prox 6y ago
    That was easier than I imagined, thanks :)
- w0mbat 6y ago
  Weirdization or maybe WeirdAlization if you like Weird Al.
pantelisk 6y ago
"Normalized from 0 to 1" is what I say as a non-native english speaker
vortico 6y ago
I use this term for https://github.com/VCVRack/Rack https://github.com/VCVRack/Rack. Sometimes I say "`x` is a normalized float between 0 to 1" to somewhat reveal the definition of the term.
MagnumOpus 6y ago
That isn't the right term. The standard meaning of "normalisation" in most scientific and engineering domains is shifting and scaling to get the sample mean to 0 and sample standard deviation to 1. I.e. it will almost always include both negative numbers and numbers larger than 1.
- FabHK 6y ago
  FWIW, I'd call that the z-score.
vertere 6y ago
I don't think "normalised" is specific enough. Normalising can refer to division by values other than the maximum. I'm also not convinced it implies non-negativity. (My vote's with "proportion" BTW.) https://en.wikipedia.org/wiki/Normalization_(statistics) https://en.wikipedia.org/wiki/Normalization_(statistics)
noodlenotes 6y ago
This would be like calling numbers constrained between 0 and 100 "multiplied". Yes, in some common situations you normalize data and it ends up between 0 and 1. And in some common situations you multiply and end up with numbers between 0 and 100 (like percentages). But normalization doesn't always result in numbers between 0 and 1 and multiplication doesn't always result in numbers between 0 and 100. Similarly, not all numbers constrained between 0 and 1 have been normalized and not all numbers constrained between 0 and 100 have been multiplied. Add in the fact that the normalization statisticians most commonly use is z-score standardization (subtracting by the mean and dividing by standard deviation, resulting in data centered around 0), and you're going to end up with a lot of confusion. In fact, this example highlights that while normalization does mean "to scale" it doesn't mean that the result will always be bounded to a particular interval.

This has a nice confusion factor because IEEE calls such floats denormalized. Because they may have extra precision and different format.

MaxBarraclough 6y ago
Perhaps I'm misunderstanding you, but with floating point, denormalized/denormal numbers aren't just numbers with a magnitude less than 1, they're numbers so small that it's no longer possible to adjust the exponent in the usual way, so leading zeroes are used in the mantissa. This reduces precision. https://en.wikipedia.org/wiki/IEEE_754-1985#Examples https://en.wikipedia.org/wiki/IEEE_754-1985#Examples https://wiki.sei.cmu.edu/confluence/display/c/FLP05-C.+Do+not+use+denormalized+numbers https://wiki.sei.cmu.edu/confluence/display/c/FLP05-C.+Do+no...

0b01 6y ago

Normalized could also imply demeaned.

joshvm 6y ago
You could also call that centred to clear up confusion, or mean-subtracted to be more specific. I think if you're specifically dealing with statistical quantities it should be obvious, e.g. standardised if you also scale to unit variance. Personally if I saw normalised I would assume scaled by a constant, not offset (as in subtraction).

quietbritishjim 6y ago

One problem with the word normalised is that it implies that there is some true original value from before normalisation that isn't necessarily between 0 and 1. Of course if that's true then the word is ideal, but if not then it's confusing.

tcldr 6y ago
Genuine question, i'm no math expert: if you're using the value by multiplying it with some other value, does that not imply it qualifies as normalised? i.e. say you have a width of 500 and you want to move half way across so you have this value of 0.5 to get 250. By dividing 250 by 500, aren't we in fact normalising it?
- chub500 6y ago
  I think generally normalized quantities maintain their original units whereas in your ratio case the unit is dropped. Units in the abstract sense I guess, such as this is a measurement along this vector or this is a ratio of any vector.
  - quietbritishjim 6y ago
    I think it's the opposite way round: normalisation results in units being dropped. The typical, most common, definition of normalisation is value ÷ max possible value, giving a result in [0,1]. (More general definitions of normalisation exist e.g. if you rescale so the standard deviation is a fixed value, or even use non linear rescaling, that could count, but never mind all that.) The parent comment's example of "position along width ÷ total width" certainly fits that bill. Whenever you divide something by the max of that something, the max is going to have the same units as the original value and you're bound to end up cancelling them. Or put another way, if you rescale 10cm into 0.5, it's certainly not 0.5cm so the units are either dropped or, at least, changed e.g. you could argue you've got 0.5x where x is the unit equal to 20cm.
    - f154hfds 6y ago
      Hmm when I think of 'normalizing' I don't think of dividing by a max at all - in my experience it is more taking a quantity (perhaps in English measurement) and transferring to a more 'standard' unit (say metric). In general I don't think normalization always includes a sense of being in a bounded interval. From a mathematical perspective you could perhaps say normalization is achieved by multiplying your quantity by a 1D operator. You can't change the dimensionality this way, but are certainly changing 'units' a la mm in the x direction -> m in the x direction for example. I guess what I'm saying is that 'normalized' and the like are not the best fit for the SO question. If I could take my own shot at the SO challenge from a mathematical perspective it would perhaps be sigmoid. Where the result of a normalization function takes a 1D value and maps it to a similar 1D value, the sigmoid takes a 1D value and maps it to a similar 1D value between (0, 1). So if I want to drop the previous information and only keep the resulting map, I can say 'this is my sigmoided value' - IE it is impossible for it to be outside of that range. Unfortunately sigmoid also connotates a differentiable curve which is extraneous information... https://en.wikipedia.org/wiki/Normalization_(statistics) https://en.wikipedia.org/wiki/Normalization_(statistics) https://en.wikipedia.org/wiki/Sigmoid_function https://en.wikipedia.org/wiki/Sigmoid_function

MaxBarraclough 6y ago

That's a good suggestion. 'Normalizing' is also used to refer to taking a vector and scaling it to make its length equal to 1. Google tells me it's also used in an analogous way elsewhere in maths. https://mathworld.wolfram.com/NormalizedVector.html https://mathworld.wolfram.com/NormalizedVector.html

uniqueid 6y ago

That's what I use, too: "normalized floats." I would prefer a better word, though. I work a lot with audio, and "signed normalized floats" doesn't exactly roll off the tongue.

prox 6y ago

I am trying to think of what the opposite word is of normalization.

kevingadd 6y ago
In the spaces I work in, people just say denormalized / denormalization.
- prox 6y ago
  That was easier than I imagined, thanks :)
w0mbat 6y ago
Weirdization or maybe WeirdAlization if you like Weird Al.

pantelisk 6y ago

"Normalized from 0 to 1" is what I say as a non-native english speaker

vortico 6y ago

I use this term for https://github.com/VCVRack/Rack https://github.com/VCVRack/Rack. Sometimes I say "`x` is a normalized float between 0 to 1" to somewhat reveal the definition of the term.

MagnumOpus 6y ago

That isn't the right term. The standard meaning of "normalisation" in most scientific and engineering domains is shifting and scaling to get the sample mean to 0 and sample standard deviation to 1. I.e. it will almost always include both negative numbers and numbers larger than 1.

FabHK 6y ago
FWIW, I'd call that the z-score.

vertere 6y ago

I don't think "normalised" is specific enough. Normalising can refer to division by values other than the maximum. I'm also not convinced it implies non-negativity. (My vote's with "proportion" BTW.) https://en.wikipedia.org/wiki/Normalization_(statistics) https://en.wikipedia.org/wiki/Normalization_(statistics)

noodlenotes 6y ago

This would be like calling numbers constrained between 0 and 100 "multiplied". Yes, in some common situations you normalize data and it ends up between 0 and 1. And in some common situations you multiply and end up with numbers between 0 and 100 (like percentages). But normalization doesn't always result in numbers between 0 and 1 and multiplication doesn't always result in numbers between 0 and 100. Similarly, not all numbers constrained between 0 and 1 have been normalized and not all numbers constrained between 0 and 100 have been multiplied. Add in the fact that the normalization statisticians most commonly use is z-score standardization (subtracting by the mean and dividing by standard deviation, resulting in data centered around 0), and you're going to end up with a lot of confusion. In fact, this example highlights that while normalization does mean "to scale" it doesn't mean that the result will always be bounded to a particular interval.