Marcel February 2016
### Basics: How does a neural network work? (Decision)

first of all: I know that there are similar questions like this. But I wanna know the plain basics. Somehow I do miss something important.

Let's assume I Have some data `(x,y) -> z`

where z can be 0 or 1 and `x,y in [0,1].`

Now I wanna train a neural network with that data and my desired output should be a boundary or a line or curved line in the x,y space where it splits the zeros from the ones (e.g. male/female or whatever).

So, I wanna have one hidden layer. I guess I somehow understand how to feed the network:

- feed it with
`X = (x,y)`

to the first layer - Do some computation with weights and bias atc.
- Compute an Error or Loss function
- train the network with e.g. gradiant descent (i.e. updating the weights, etc)
*yeah, now comes my problem :D*

What is the output in the end? With a given data set the network tries to reproduce my z values for given x,y, right? So, how do I get a Fit or decision boundary or whatever? What is the stuff that one "plots" in the end in the x,y space?

How do I generate "new data" by the network, or is that not possible?

So, my main question is: What is the output? And how do I handle the output? And what are the steps to get a logistic regression plot in the end (that can be found everywhere in the internet, but they do not say what they plot in the end :D)

I really do not get it:D Sorry^^.

Thanks in advance,

Marcel

Marcel February 2016

So, after a discussion with a friend (who was not around the last days) I finally think I got it.

After training I can just use the network as a function F(x,y) to make new predictions.

To find a decision boundary (the hyperplane in the X space) I can just solve F(x,y) = 1/2 for x(y) or vice versa and plot it. Then I am done:D

Cheers,

Marcel speaking to myself :D

Raj Samant February 2016

Let's consider an example of famous XOR problem

```
Training Data
X | Y | Z
0 | 0 | 0
0 | 1 | 1
1 | 0 | 1
1 | 1 | 0
```

Now create a neural network, leat's assume MLN (2,4,1). Train it with your training data till convergence.

Now for the decision Boundary Plot.

Create Test Data

```
**x** [0 0.01 0.02 0.03 .... 1] (100x1)
**y** [0 0.01 0.02 0.03 .... 1] (100x1)
```

Then find **z** for each (x, y) pair, (0,0) (0.01,0) (0.02,0)...(0,0.01) (0,0.02), so **z** will be 100x100 matrix.

For XOR we know output space is 0 or 1. so we quantize **z**

```
if (z(x,y)>0.5)
zq(x,y) = 1
else
zq(x,y) = 0
```

Now plot x,y,zq. which will give you a decision surface.

if you want decision boundary. check where ever z = 0.5 and mark that point. line created by all points will be decision boundary.

Asked in February 2016

Viewed 2,071 times

Voted 9

Answered 2 times

Viewed 2,071 times

Voted 9

Answered 2 times