k

Back Propagation

Neural Network

For the multi

–

layer neural network that you will be implementing in the following problems, you may use

either the hyperbolic tangent or the sigmoid for the activation function. Obviously you will be implementing

the back propagation method to train the n

etwork. Your code should include an arbitrary method that allows

you to code it for any number of input dimensions, hidden layers, neurons and output neurons, (i.e. you need

it to be able to allow you to change a variable and it changes the number of laye

rs, or the number of neurons

at a given layer, or the number of dimensions, or the number of output layers…in other words this cannot be

hard coded

for a specific data set

).

1.

(25pts)

Develop a multi

–

layer neural network to solve the

regression problem: f

(x) = 1/x

, (for only the

positive values of x)

. Be sure to create a testing and training set.

I am

NOT

providing you with data.

The

number of hidden layers and neurons

is your discretion, however, you must provide an explanation as to why

the number of l

ayers and nodes you used was a good choice. You will need to create multiple different

structures that you train and p

lot this error for the different models to show why you chose the final model

that you did for this problem.

Report your network configu

ration, and comment on your observations

regarding the performance of your network as you try to determine the number of hidden layers and hidden

nodes of your final network, once you determine the correct model

:

a.

(10pts)

T

rack

your training and testing history.

This means that you

check your training performance

and your testing performance at multiples of some fixed number of

iterations

(and over many Epochs

also)

[thus you will provide a graph of this information]

, implement

the online learning method.

Be

sure to label plots appropriately.

(Remember to scale the data in the range that provides the best

results for your activation function

… normalization is a must)

b.

(5pts)

What did you observe regarding the value of the learni

ng parameter and how the network

performed given

:

(do one of each)

i.

(2.5pts)

a fixed value,

ii.

(2.5pts)

and a time decreasing value

c.

(2.5pts)

Choose a couple of points beyond your training set (i.e., if your max training input

is

x=10,

try testing your netw

ork with, say, x=10.5, x=

12

, and x=

30

). What do you observe regarding the

networks ability to generalize for data that is beyond its training set (note, you may have to increase

the v

alue of x

to a large number

to get a good idea

to answer this

)

.

d.

(2.5pts)

Briefly comment on

the extrapolation capability

compared

to the interpolation capability

of

the network.

e.

(5pts)

Plot the final results

showing the capability of your network to determine the function f(x) =

1/x versus the function f(x) = 1/x.

2.

(25pts)

Develop a multi

–

layer neural network to

classif

y

the

IRIS

data set.

Use K

–

Fold Cross Validation for

this problem.

The code you use for thi

s problem will be an extension of the code you created for problem 1.

a.

(12pts) Implement the NN and r

eport your network configuration: number of hidden layers, number

of nodes per hidden layer, learning rate/learning schedule, encoding of the output

, etc.

b.

(

5pts)

Plot

the

error metric versus the number of training steps (similar to problem

1

).

c.

(8pts)

Comment on how well your network learned the data. Things to think about: did the network

classify the data well (or not), and why (or why not); how well did it

classify each class independently

(you might consider contingency

table

s for this

); and what observation do you have regarding number

of training samples

: was the normalization technique I used adequat

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