Computational Methods for Data Analysis – 2014/15
Lab 5: Neural Networks in R
In this lab we’ll see how to train a neural net for classification, using the package
nnet.1
Starting
In this lab we’ll use the nnet library; you should start by loading it into your R
environment using library (and installing the package using
install.packages if you haven’t installed them yet).
Loading the cheese dataset
In this exercise we’ll use the cheese dataset, containing information about taste,
acetic component, lactic component, etc of several types of cheese.
Exercise: Download the cheese data from the Lab5 directory on the course
website.
Exercise: Load the cheese data into a variable called cheese in your workspace.
Exploring the data
Exercise: Use the commands
cheese
names(cheese)
summary(cheese)
to get a feel for the data.
Create and analyze a perceptron
Fit a simple neural net to predict with no hidden layer and linear activation
function using the function nnet(). nnet() takes as arguments
- a formula specifying output and input variables (just as in linear regression)
1
The lab follows closely the presentation in
http://www.louisaslett.com/Courses/Data_Mining/ST4003-Lab5Introduction_to_Neural_Networks.pdf
- a parameter data specifying the data frame to be used
- a parameter size specifiying the number of hidden units (0 in this case)
- a parameter skip specifying whether the inputs are directly connected with
the outputs or now
- a parameter linout specifying whether a linear activation function is
desired.
(see http://cran.r-project.org/web/packages/nnet/nnet.pdf for full details of all
the arguments)
For example, the following command creates a perceptron with three input
variables, one output variable, and using a linear activation function instead of
the logistic function.
> fitnn1 = nnet(taste ~ Acetic + H2S + Lactic, cheese,
size=0, skip=TRUE, linout=TRUE)
> summary(fitnn1)
In the output of summary(), i1, i2 and i3 are the input nodes (so acetic, H2S
and lactic respectively); o is the output node (taste); and b is the bias. The values
under the links are the weights.
Evaluating the predictions of a perceptron
Let us now use the J cost function implemented in Lab 1 to evaluate the model:
J = function (model) {
return(mean(residuals(model) ^ 2) / 2)
}
Exercise Compute J of fitnn1
Let us now compare this to the fit we get by doing standard least squares
regression:
fitlm = lm(taste ~ Acetic + H2S + Lactic, cheese)
summary(fitlm)
Exercise Compute J of fitlm
Adding a Hidden Layer With a Single Node
We now add a hidden layer in between the input and output neurons, with a
single node.
> fitnn3 = nnet(taste ~ Acetic + H2S + Lactic, cheese,
size=1, linout=TRUE)
During backpropagation you should see values like the following:
# weights: 6
initial value 25372.359476
final value 7662.886667
converged
You can visualize the structure of the network created by nnet using the function
plot.nnet(), in the devtools library
library(devtools)
The following encantation enables devtools:
source_url('https://gist.githubusercontent.com/fawda123
/7471137/raw/466c1474d0a505ff044412703516c34f1a4684a5/n
net_plot_update.r')
We can now plot the architecture of fitnn3 with the following command:
plot.nnet(fitnn3)
(NB plot.nnet() doesn’t seem to work with perceptrons)
Train and Test subsets
In this exercise we are going to use part of our data for training, part for testing.
First of all, download the Titanic.csv dataset into a variable called data. This
dataset provides information on the fate of passengers on the maiden voyage of
the ocean liner ‘Titanic’. Explore the dataset.
Then split the dataset into a training set consisting of 2/3 the data and a test set
consisting of the other 1/3 using the method seen in Lab 4.
n <- length(data[,1])
indices <- sort(sample(1:n, round(2/3 * n)))
train <-data[indices,]
test <- data[-indices,]
The nnet package requires that the target variable of the classification (in this
case, Survived) be a two-column matrix: one column for No, the other for Yes
— with a 1 in the No column for the items to be classified as No, and a 1 in the
Yes column for the items to be classified as 0:
No Yes
Yes  0 1
Yes  0 1
No  1
Yes  0
0
1
Etc. Luckily, the class.ind utility function in nnet does this for us:
train$Surv = class.ind(train$Survived)
test$Surv = class.ind(test$Survived)
(Use head to see what the result is on train for instance.) We can
now use train to fit a neural net. The softmax parameter specifies a logistic
activation function.
fitnn = nnet(Surv~Sex+Age+Class, train, size=1,
softmax=TRUE)
fitnn
summary(fitnn)
And then test its performance on test:
table(data.frame(predicted=predict(fitnn, test)[,2] > 0.5,
actual=test$Surv[,2]>0.5))
Download

Exercise Compute J of fitnn1 - clic