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i have managed to implement my own backpropagation algorithm. I was able to train my neural network to resolve OR/AND/XOR problems so far. I am using a sigmoid function. For my school project I am looking for an idea of simple graphical demonstration of this algorithm. I need something simple but effective.

My idea is to implement a demo where i can place points into cartesian plane and then separate them by curve. For linearly separable problems, perceptron weights could be used as a vector to find line which separates the points (Two dimensions = 3 inputs = 3 weights, one is 1). For example in 2D:

w2*x2 + w1*x1 + w0*1 = 0
  • How can i find the curve polynom that separates the points (2D) (so i can also separate linearly inseparable points solvable by BP)?
  • Or is there easier way to demonstrate it's functionality?

Curve

Thank you.

Smarty77
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  • This might be of interest: http://tjo-en.hatenablog.com/entry/2014/01/06/234155 – runDOSrun Oct 29 '15 at 01:07
  • Sorry, but this article does not contain anything about math behind drawing the curves. – Smarty77 Oct 29 '15 at 10:58
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    You asked about a way to present the problem. The rest is a bit vague. Are you trying to make a contrast between single and multi-layer perceptrons? For multiple layers and non-linearity the equation becomes nested as in z = f(sum(w y)) = f(sum(w f(w x))). Since sigmoid(0)=0.5, your decision boundary is thus all the points x that lead to z = 0. Maybe [this](http://www.cs.cmu.edu/afs/cs/academic/class/15381-s07/www/slides/042407neuralNetworks.pdf) helps (around slide 27). – runDOSrun Oct 29 '15 at 11:45
  • Oh thank you! I see it now, so in multilayer NN the curve(respectively the function which decides where the point goes to) is a composition of activation functions right? (sigmoids in my case). Sorry for vagueness, english is not my native language :(. – Smarty77 Oct 30 '15 at 18:13
  • Pretty much, or to be a bit more precise the composition is of the layers in which the activations take place. No need to be sorry! – runDOSrun Oct 30 '15 at 20:42

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