# Neural networks, mapping features to polar coordinates to deal with uncertain inputs

Let's say you've got a neural network which takes in a vector of real numbers as input. Additionally, let's say you're uncertain about the values of some components of the vector, and your level of certainty is a number between $$0$$ and $$1$$. It's a promising idea to map the $$(\text{certainty}, y)$$ values to $$(u,v)$$ values in such a way that when $$\text{certainty} = 0$$, $$f(\text{certainty}, y)$$ doesn't change with $$y$$.

Two ideas:

Idea 1: $$f(\text{certainty}, y) = (\text{certainty} \times\cos(y),\text{certainty}\times\sin(y))$$. The closer $$\text{certainty}$$ is to $$0$$, the closer the points in the image will be to each other. It seems to me that this idea works best when the space of $$y$$ values is topologically a circle.

Idea 2: $$f(\text{certainty}, y) = (\text{certainty}, \text{certainty} \times y)$$. Again, degenerate when $$certainty = 0$$, as we want it to be. Works best when the space of $$y$$ values is topologically the same as $$\mathbb R$$.

• Has this been tried? I would be very surprised if it hasn't.
• Is it a good way to deal with missing values in time series analysis?
• Any relationship to dropout?