Dear Vijay,

You question may be interpreted in two ways, one of which is how to predict the X's (the inputs) from the output (Y), given the ANN equation. This was Belcaid Anass interpretation but I guess it is not what you wanted. Furthermore, there is no single solution for that inverse function. If I guessed correctly, you want to predict Y from some X's. To the best of my knowledge the software used to

train the ANN will also allow you to feed the trained network with "new" data and get the prediction (I never came across a software that only allowed to train the ANN).

No matter the case is, if you want to perform the calculations yourself you should use the sigmoid functions as you state these were the transfer functions in your network (not their inverse).

To simplify,

The N1 output is: N1=1/(1+10^(-b1-sum(xi*wi))

in which xi are the scaled inputs 1 to 5 and wi the corresponding weights and b1 the bias, from node 1:

N1= 1 /(1 + 10^-(0.193-0.364*i1-0.583*i2-0.314*i3+0.965*i4+0.66*i5)

Perform similar calculations for N2 to 4 and then calculate the output by using

Y=1/(1+10^(-(-1.511+1.066*N1-0.235*N2+1.243*N3+1.178*N4)))

You need to be aware that, most probably, your input data was (automatically or manually) scaled (perhaps to the -1 to 1 range, or close) and that your output data was also scaled. As such you need to scale the inputs before using them in the above equations and the output needs to be converted to the "real world" values by back-scaling them.

You need that information too.

Find attached an Excel worksheet with the above calculations (but without taking into consideration the scaling for which you did not provide any information).

Kind regards, Luis

Suppose you have a single layer ( generalization is straighforward by function composition)

y = sigmoid(Ax +b)

The inverse of the sigmoid function is the logit (logit(x) = ln(x/(1-x) ) )

Then we could simply write

x = A-1( logit(y) - b)

For muliple layer you compose the inverse of each layer.

Dear Vijay,

You question may be interpreted in two ways, one of which is how to predict the X's (the inputs) from the output (Y), given the ANN equation. This was Belcaid Anass interpretation but I guess it is not what you wanted. Furthermore, there is no single solution for that inverse function. If I guessed correctly, you want to predict Y from some X's. To the best of my knowledge the software used to

train the ANN will also allow you to feed the trained network with "new" data and get the prediction (I never came across a software that only allowed to train the ANN).

No matter the case is, if you want to perform the calculations yourself you should use the sigmoid functions as you state these were the transfer functions in your network (not their inverse).

To simplify,

The N1 output is: N1=1/(1+10^(-b1-sum(xi*wi))

in which xi are the scaled inputs 1 to 5 and wi the corresponding weights and b1 the bias, from node 1:

N1= 1 /(1 + 10^-(0.193-0.364*i1-0.583*i2-0.314*i3+0.965*i4+0.66*i5)

Perform similar calculations for N2 to 4 and then calculate the output by using

Y=1/(1+10^(-(-1.511+1.066*N1-0.235*N2+1.243*N3+1.178*N4)))

You need to be aware that, most probably, your input data was (automatically or manually) scaled (perhaps to the -1 to 1 range, or close) and that your output data was also scaled. As such you need to scale the inputs before using them in the above equations and the output needs to be converted to the "real world" values by back-scaling them.

You need that information too.

Find attached an Excel worksheet with the above calculations (but without taking into consideration the scaling for which you did not provide any information).

Kind regards, Luis

Thanks, Luis F. Gouveia for such an illustrative answer. I can't express how useful it is for me as I am not from a typical mathematical field. I just want to ask you one more thing that use to scale down the inputs and how to scale up the outputs. I have attached the raw input data.

Please see: Parameters used in Neural Net

training cycles = 200000

learning rate = 0.001

momentum = 0.999

error epsilon = 1.0E-4

Thanks in advance!

Regards

Vijay

Dear Vijay, from the csv file you attached I got a bit confused regarding what you are trying to predict! Please confirm the "Per Capita Trip Rate Excluding Walk Trips" is what you are trying to predict based on the:

X1: Modal Split

X2: Adminstrative Area (sq.km) Municipal Area

X3: Maximum Floor Space Index (FSI) Permissible

X4: Average Trip Length of City (Km) excluding Walk Trips

X5: Average Density of City (Persons/Sq.Km)

Is that so?

Are the cases in the ANN.csv the ones used to train your network or are cases not used during training?

Kind regards, Luis

Respected Luis F. Gouveia sir, I am trying to predict "Per Capita Trip Rate Excluding Walk Trips"based on the following:

X1: Modal Split

X2: Administrative Area (sq.km) Municipal Area

X3: Maximum Floor Space Index (FSI) Permissible

X4: Average Trip Length of City (Km) excluding Walk Trips

X5: Average Density of City (Persons/Sq.Km)

80% of the cases in "ANN.csv" are used to train the network and 20% are used to validate the model.

Regards

Vijay Meena