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I'm having trouble understanding the use of Vector in machine learning to represent a group of features.

If one looks up the definition of a Vector, then, according to wikipedia, a Vector is an entity with a magnitude and direction.

This can be understood when applying Vectors to for example physics to represent force, velocity, acceleration, etc...: the components of the Vector represent the components of the physical property along the axes in space. For example, the components of a velocity vector represent the velocity along the x, y and z axes

However, when applying Vectors to machine learning to represent features, then those features can be totally unrelated entities. They can have totally different units: one feature can be the length in meters of a person and another can be the age in years of the person.

But then what is the meaning of the Magnitude of such a Vector, which would then be formed by a summation of meters and years? And the Direction?

I do know about normalization of features to make them have similar ranges, but my question is more fundamental.

That is what sort of confuses me: "not an Euclidean one". If it is not an Euclidean, then what kind is it? Hence the title: "What kind of Vector is ...." Or am I being to specific in interpreting "Euclidean"? – Serge Desmedt – 2018-11-14T15:11:24.950

The vector representation just facilitates the processing and statistical analysis. If you are looking for an interpretation, this is not anymore a technical question and I think you just need to think in a more abstract way, as if you try to represent yourself what an n-dimensional Euclidean space is. (n>3) – Atani – 2018-11-14T15:37:36.180