What does an ellipses graph show?

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That is to say: a graph with multiple feature variables showing different ellipses plots for class groups. What do the ellipses actually tell us? How are the ellipses graphed? What does overlap among ellipses mean? What basic graphing theory techniques are ellipse graphs based on?

I look at ellipse graphs and just think: huh – it looks like clustering but I know it isn’t clustering. I have no idea what this is saying and it is awful confusing.

[Example](https://machinelearningmastery.com/machine-learning-in-r-step-by-step/)

Scroll to section 4.2. The first plot there is the one I am asking about.

In: Mathematics
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It’s been awhile, but isn’t an ellipse:
1) the intersection of a plane going through one half of a cone,
2) such that it doesn’t cross at the perpendicular (such that it forms a circle) nor
3) at such a steep angle that the plane goes through both halves of the whole cone and forms a parabola or a hyperbola?

Can you link an example of the type of graph you’re talking about? You seem to be talking about some specific type of graph, and I’m not familiar with the term, or the field where it’s used. This sounds like something in either statistics or data science?

[Like this?](https://upload.wikimedia.org/wikipedia/commons/e/e4/Venn_diagram_gr_la_ru.svg)

Those are venn diagrams. Each circle represents a set, a collection of things. In this case, they’re uppercase glyphs (the ‘drawing’ you make to create a letter). Where the circles overlap, it means the things inside the overlap are shared by the two sets. For insta’ce N, I and Z are qhared by the Latin and Greek alphabet. The middle bit with O, M, H and all, means it’s shared by all alphabets.

[Here’s a complicated one about Europe](https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Supranational_European_Bodies-en.svg/1200px-Supranational_European_Bodies-en.svg.png). This one also has circles inside circles, which means that every element of the ‘smaller’ set is also an element of the ‘larger’ one (like how all natural numbers are integers, but not vice versa).

Like [this?](https://lh3.googleusercontent.com/proxy/FAdDfPz3j3dUoc5GrtCo0G-lVekqn4JqAlbx7CaDO5S5HlJLdUKp4QG3eDoW7Y6tTrDDimHAkiU34_-ATSZZUMlddUsFNgVTn73IElHTfk0vRmucU2lzz2PJ2IxxQos_fb7a91Dm-iAgNOmZBWaN81eq-Wo) That type of graph is less for quantitative consumption, and more for qualitative consumption. Here you’re seeing that rubbers/composites/metals are tougher than porcelain/glass/ceramic and that ceramic/metals/brick are stronger than wood/foam/rubber as classes. If you wanted specific data about a particular type or wood or metal, you need a different chart. This one just shows the ranges.

This graph is elliptical on two axes. You can find ones that are only in one axis as well.