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Is there a difference between the words transform (noun) and transformation?

Let me describe my problem. I have a mathematical model which I can transform into a better model with help of a data matrix. Should I call this matrix a transform, or should I call it a transformation?

An example sentence where I would use this is:

To recognize with the optimized model, first the transform(ation) is applied and then the likelihoods are calculated.

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In the particular domain you're referencing, both transform and transformation have an established history of usage.

For example, we speak of the Hough transform or the Fourier transform. We also talk about affine transformations or homothetic transformations.

I'm not aware of any specific rules, but in general, I've noticed that "named" objects tend to be referenced as the foo transform, while unnamed or otherwise generic ones use the foo transformation.

In this case, I would probably use transformation since it appears you're referring to a generic transformation matrix. So:

To recognize with the optimized model, first the transformation is applied and then the likelihoods are calculated.

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    It should be noted that transform as a noun is rare outside of mathematics and a few related domains. – JSBձոգչ Nov 23 '10 at 15:39
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    @JSBangs - which is why I started with "in the particular domain you're referencing" =D – Dusty Nov 23 '10 at 15:43
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As @Dusty said, this is relevant to your specific domain...

However, I felt that there was a more specific difference:

You use a transform to perform a transformation.

That is, if you're outlining the model of which you speak it would be "transform".
However, if you're referring to the actual effect (in runtime, so to speak), its transformation.

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In my opinion, it is more convenient to use "transformation". One of the reasons is "transform" is used usually as a verb, and rarely as a noun. For example, we say "linear transformation" instead of saying "linear transform". Another reason is "transform (noun)" was first used in 1853 [1] whereas "transformation" was first used in 15th century [2]. So I would prefer:

To recognize with the optimized model, first the transformation is applied and then the likelihoods are calculated.

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    The age of the words is not relevant. As others have said, 'transform' as a noun is common in certain fields and almost unknown elsewhere. – Colin Fine Nov 23 '10 at 17:20
  • "Fourier transform" is the standard term; "Fourier transformation" is almost unheard of. – ShreevatsaR Jun 22 '11 at 6:05
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I'm very familiar with using the word transform in the mathematical domain. In you case, you should use the word transformation because you are "applying" it. Transform is a result of a transformation.

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