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
