- #1

CraigH

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http://img59.imageshack.us/img59/6414/puag.png [Broken]

The picture above is used to help understand artificial neural networks, however for now this doesn't matter as i'm only concerned with the maths.

A number is input at the start of each both horizontal lines at the left hand side. The numbers travel along the lines from left to right and at each node (circle) the numbers at that node are summed together and sent out the other side.

Each line also has an associated "weight", this weight is multiplied with the number traveling along the line before it is sent to the attached node. For example if the numbers (2,2,2) are inputted, and all of the lines have a weight of 2, then the final output will be 192.

This is all I understand so far. The rest I have guessed using the information given in the picture above.

I'm guessing that i is a variable that ranges from 1 to 3, j is a variable that ranges from 1 to 2, and k is a variable that is always 1.

so in the formula

[itex]x_{j}=\sum_{i}w_{ij}*I_{i}[/itex]

[itex]x_{j}[/itex] is the value of the 'j'th hidden node

and

[itex]I_{i}[/itex] is the value of the 'i'th input

e.g [itex]I_{1}[/itex] will be the 1st input (going into the top horizontal line)

[itex]w_{ij}[/itex] will be the "weight" of the line before the node, however I do not understand what to do when there are two subscripts next to it.

So for example the value of the 2nd hidden node will be

[itex]x_{2}=\displaystyle\sum\limits_{i=1}^3 w_{i2}*I_{i}[/itex]

I just do not understand how you evaluate the sum when you have 2 subscripts under a variable as is the case with [itex]w_{ij}[/itex]

can someone please explain?

Or have I completely misunderstood the whole network and i'm getting everything wrong?

Thanks!

The picture above is used to help understand artificial neural networks, however for now this doesn't matter as i'm only concerned with the maths.

A number is input at the start of each both horizontal lines at the left hand side. The numbers travel along the lines from left to right and at each node (circle) the numbers at that node are summed together and sent out the other side.

Each line also has an associated "weight", this weight is multiplied with the number traveling along the line before it is sent to the attached node. For example if the numbers (2,2,2) are inputted, and all of the lines have a weight of 2, then the final output will be 192.

This is all I understand so far. The rest I have guessed using the information given in the picture above.

I'm guessing that i is a variable that ranges from 1 to 3, j is a variable that ranges from 1 to 2, and k is a variable that is always 1.

so in the formula

[itex]x_{j}=\sum_{i}w_{ij}*I_{i}[/itex]

[itex]x_{j}[/itex] is the value of the 'j'th hidden node

and

[itex]I_{i}[/itex] is the value of the 'i'th input

e.g [itex]I_{1}[/itex] will be the 1st input (going into the top horizontal line)

[itex]w_{ij}[/itex] will be the "weight" of the line before the node, however I do not understand what to do when there are two subscripts next to it.

So for example the value of the 2nd hidden node will be

[itex]x_{2}=\displaystyle\sum\limits_{i=1}^3 w_{i2}*I_{i}[/itex]

I just do not understand how you evaluate the sum when you have 2 subscripts under a variable as is the case with [itex]w_{ij}[/itex]

can someone please explain?

Or have I completely misunderstood the whole network and i'm getting everything wrong?

Thanks!

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