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While learning about neural networks, I stumbled upon this really cool resource where you can tinker around with NN's architecture and hyperparameters in a point classification problem.

What I'm confused about is the meaning of the input layer which they call the "features."

enter image description here

Since the data is just points, I would assume there could only be two features: the X value and the Y value of each point.

My question: What do their features mean and why aren't they just using the (X,Y) coordinates of the points as the input data?

Are they perhaps transforming the (X,Y) values into these other features? If so, what are the actual numerical values they are getting transformed into?

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You're right, they are transformed, hand-crafted features, obtained from the original ones, $X_1,X_2$, according to the figure. They could have used only the original features and let the neural network decide which ones to invent. Though this is a tougher process, this is usually what's being done in current deep learning literature. We don't usually have input pixels being squared etc. Or, if you think the hand-crafted features are important by domain knowledge, you can include them to not reinvent the wheel. The transformed values depend on the transformation. For example, if you use $\sin(X_1)$ the value range will be $[-1, 1]$ irrespective of $X_1$'s range.

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  • $\begingroup$ If X1 simply refers to raw value of the x coordinate, what do the colors mean in the little thumbnail? In other words, why is the left side orange and right side blue? $\endgroup$
    – Nova
    Commented Nov 12, 2022 at 18:58
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    $\begingroup$ The blogpost has a colorbar. Orange to blue means -1 to 1. Colors represent possible transformed values of each (x,y) points. That's why $X_1^2$ has no orange and it's white-ish around $0$ because values around $0$ correspond to white in the colorbar. $\endgroup$
    – gunes
    Commented Nov 14, 2022 at 18:14

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