What can I classify with 1 layer neural network?

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Assume that we are using 1 layer neural network described as a system of a equation:

$$b = f(x)$$

Where $x$ is a vector of dimension $\Re^n$ and $b$ is a vector of dimension $\Re^m$ We know the function $f()$ and it's a matrix of $\Re^{m x n}$.

Assume that $x$ is a vector from an image and $b$ is the identity number of that image. When I apply the picture $x$ into the matrix $f()$, i will receive the indentity number $b$. It's classification.

But what can I classify with 1 layer neural network if $x$ is a vector from an image?

  • Can I classify simple shapes such as square, rectangular, triangle, circle?
  • Can I classify the majority color?
  • Can I classify patterns?
  • Can I classify amout of colors?

I'm not talking about a 1 layer neural network that can classify ALL things at the same time. I'm talking about 1 layer neural network that are specified in classify certain subjects. For example:

  • Layer 1 classify ONLY shapes
  • Layer 2 classify ONLY majority color
  • Layer 3 classify ONLY patters
  • Layer 4 classify ONLY amount of colors

Combine these results from these 4 different models can give me a result of what they together see. Is that possible?

Question:

What can I classify with 1 layer neural network?