In this tutorial a neural network (or Multilayer perceptron depending on naming convention) will be build that is able to take a number and calculate the square root (or as close to as possible). Later tutorials will build upon this to make forcasting / trading models.The R library ‘neuralnet’ will be used to train and build the neural network.

There is lots of good literature on neural networks freely available on the internet, a good starting point is the neural network handout by Dr Mark Gayles at the Engineering Department Cambridge University http://mi.eng.cam.ac.uk/~mjfg/local/I10/i10_hand4.pdf, it covers just enough to get an understanding of what a neural network is and what it can do without being too mathematically advanced to overwhelm the reader.

The tutorial will produce the neural network shown in the image below. It is going to take a single input (the number that you want square rooting) and produce a single output (the square root of the input). The middle of the image contains 10 hidden neurons which will be trained.

The output of the script will look like:

Input Expected Output Neural Net Output

   Input 	Expected Output		 Neural Net Output
      1               1     		 0.9623402772
      4               2     		 2.0083461217
      9               3     		 2.9958221776
     16               4     		 4.0009548085
     25               5     		 5.0028838579
     36               6     		 5.9975810435
     49               7    		 6.9968278722
     64               8    		 8.0070028670
     81               9    		 9.0019220736
    100              10    		 9.9222007864

As you can see the neural network does a reasonable job at finding the square root, the largest error in in finding the square root of 1 which is out by ~4%

Onto the code:

install.packages('neuralnet')
library("neuralnet")
 
#Going to create a neural network to perform sqare rooting
#Type ?neuralnet for more information on the neuralnet library
 
#Generate 50 random numbers uniformly distributed between 0 and 100
#And store them as a dataframe
traininginput <-  as.data.frame(runif(50, min=0, max=100))
trainingoutput <- sqrt(traininginput)
 
#Column bind the data into one variable
trainingdata <- cbind(traininginput,trainingoutput)
colnames(trainingdata) <- c("Input","Output")
 
#Train the neural network
#Going to have 10 hidden layers
#Threshold is a numeric value specifying the threshold for the partial
#derivatives of the error function as stopping criteria.
net.sqrt <- neuralnet(Output~Input,trainingdata, hidden=10, threshold=0.01)
print(net.sqrt)
 
#Plot the neural network
plot(net.sqrt)
 
#Test the neural network on some training data
testdata <- as.data.frame((1:10)^2) #Generate some squared numbers
net.results <- compute(net.sqrt, testdata) #Run them through the neural network
 
#Lets see what properties net.sqrt has
ls(net.results)
 
#Lets see the results
print(net.results$net.result)
 
#Lets display a better version of the results
cleanoutput <- cbind(testdata,sqrt(testdata),
                         as.data.frame(net.results$net.result))
colnames(cleanoutput) <- c("Input","Expected Output","Neural Net Output")
print(cleanoutput)