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Across the literature of artificial intelligence, especially machine learning, it is normal to treat the tuples of datasets as vectors.

Although there is a convention to treat them as data points. Treating them as vectors is also considerable.

It is easy to understand the tuples of datasets as points over space. But what is the purpose of treating them as vectors?

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    $\begingroup$ Beacuse it is how visualize the stuff i.e datapoints as vectors. I do not know the argument you are trying to propose, because there are many different kind of vector spaces with different properties, which can lead to a very complex argument to your answer. But normally we restrict ourselves to euclidean space and more generally the Hilbert Space. $\endgroup$
    – user9947
    Oct 28, 2020 at 10:39

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They are equivalent. When we consider a particular instance as a vector, we are not literally imagining it as an arrow with it's head at the point coordinates and tail at the origin. It's just when you are working with a tuple of numbers in a mathematical context, it is conventional to call it a vector. This language follows into machine learning which is usually based on associated linear algebra.

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