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A neural network is a computational system that creates predictions based on existing data. Let us train and test a neural network using the neuralnet library in R.

## How To Construct A Neural Network?

A neural network consists of:

• Input layers: Layers that take inputs based on existing data
• Hidden layers: Layers that use backpropagation to optimise the weights of the input variables in order to improve the predictive power of the model
• Output layers: Output of predictions based on the data from the input and hidden layers ## Solving classification problems with neuralnet

In this particular example, our goal is to develop a neural network to determine if a stock pays a dividend or not.

As such, we are using the neural network to solve a classification problem. By classification, we mean ones where the data is classified by categories. e.g. a fruit can be classified as an apple, banana, orange, etc.

In our dataset, we assign a value of 1 to a stock that pays a dividend. We assign a value of 0 to a stock that does not pay a dividend. The dataset for this example is available at dividendinfo.csv.

Our independent variables are as follows:

• fcfps: Free cash flow per share (in $) • earnings_growth: Earnings growth in the past year (in %) • de: Debt to Equity ratio • mcap: Market Capitalization of the stock • current_ratio: Current Ratio (or Current Assets/Current Liabilities) We firstly set our directory and load the data into the R environment: setwd("your directory") mydata <- read.csv("dividendinfo.csv") attach(mydata)  Let’s now take a look at the steps we will follow in constructing this model. ### Data Normalization One of the most important procedures when forming a neural network is data normalization. This involves adjusting the data to a common scale so as to accurately compare predicted and actual values. Failure to normalize the data will typically result in the prediction value remaining the same across all observations, regardless of the input values. We can do this in two ways in R: • Scale the data frame automatically using the scale function in R • Transform the data using a max-min normalization technique We implement both techniques below but choose to use the max-min normalization technique. Please see this useful link for further details on how to use the normalization function. Scaled Normalization scaleddata<-scale(mydata)  Max-Min Normalization For this method, we invoke the following function to normalize our data: normalize <- function(x) { return ((x - min(x)) / (max(x) - min(x))) }  Then, we use lapply to run the function across our existing data (we have termed the dataset loaded into R as mydata): maxmindf <- as.data.frame(lapply(mydata, normalize))  We have now scaled our new dataset and saved it into a data frame titled maxmindf: We base our training data (trainset) on 80% of the observations. The test data (testset) is based on the remaining 20% of observations. # Training and Test Data trainset <- maxmindf[1:160, ] testset <- maxmindf[161:200, ] ### Training a Neural Network Model using neuralnet We now load the neuralnet library into R. Observe that we are: • Using neuralnet to “regress” the dependent “dividend” variable against the other independent variables • Setting the number of hidden layers to (2,1) based on the hidden=(2,1) formula • The linear.output variable is set to FALSE, given the impact of the independent variables on the dependent variable (dividend) is assumed to be non-linear • The threshold is set to 0.01, meaning that if the change in error during an iteration is less than 1%, then no further optimization will be carried out by the model Deciding on the number of hidden layers in a neural network is not an exact science. In fact, there are instances where accuracy will likely be higher without any hidden layers. Therefore, trial and error plays a significant role in this process. One possibility is to compare how the accuracy of the predictions change as we modify the number of hidden layers. For instance, using a (2,1) configuration ultimately yielded 92.5% classification accuracy for this example. #Neural Network library(neuralnet) nn <- neuralnet(dividend ~ fcfps + earnings_growth + de + mcap + current_ratio, data=trainset, hidden=c(2,1), linear.output=FALSE, threshold=0.01) nn$result.matrix
plot(nn)

We now generate the error of the neural network model, along with the weights between the inputs, hidden layers, and outputs:

nn$result.matrix 1 error 2.027188266758 reached.threshold 0.009190064608 steps 750.000000000000 Intercept.to.1layhid1 3.287965374794 fcfps.to.1layhid1 -1.723307330428 earnings_growth.to.1layhid1 -0.076629853467 de.to.1layhid1 1.243670462201 mcap.to.1layhid1 -3.520369700429 current_ratio.to.1layhid1 -3.068677865885 Intercept.to.1layhid2 3.618803162161 fcfps.to.1layhid2 1.109150492946 earnings_growth.to.1layhid2 -11.588713924832 de.to.1layhid2 -1.526458929898 mcap.to.1layhid2 -3.769192938001 current_ratio.to.1layhid2 -4.547481937028 Intercept.to.2layhid1 2.991704593713 1layhid.1.to.2layhid1 -7.372717428050 1layhid.2.to.2layhid1 -22.367528820159 Intercept.to.dividend -5.673537382132 2layhid.1.to.dividend 17.963989719804  ### Testing The Accuracy Of The Model As already mentioned, our neural network has been created using the training data. We then compare this to the test data to gauge the accuracy of the neural network forecast. In the below: • The “subset” function is used to eliminate the dependent variable from the test data • The “compute” function then creates the prediction variable • A “results” variable then compares the predicted data with the actual data • A confusion matrix is then created with the table function to compare the number of true/false positives and negatives #Test the resulting output temp_test <- subset(testset, select = c("fcfps","earnings_growth", "de", "mcap", "current_ratio")) head(temp_test) nn.results <- compute(nn, temp_test) results <- data.frame(actual = testset$dividend, prediction = nn.results$net.result)  The predicted results are compared to the actual results: results actual prediction 161 0 0.003457573932 162 1 0.999946522139 163 0 0.006824520245 ... 198 0 0.005474975456 199 0 0.003427332586 200 1 0.999985252611  ### Confusion Matrix Then, we round up our results using sapply and create a confusion matrix to compare the number of true/false positives and negatives: roundedresults<-sapply(results,round,digits=0) roundedresultsdf=data.frame(roundedresults) attach(roundedresultsdf) table(actual,prediction) prediction actual 0 1 0 17 0 1 3 20  A confusion matrix is used to determine the number of true and false positives generated by our predictions. The model generates 17 true negatives (0’s), 20 true positives (1’s), while there are 3 false negatives. Ultimately, we yield an 92.5% (37/40) accuracy rate in determining whether a stock pays a dividend or not. ## Solving regression problems using neuralnet We have already seen how a neural network can be used to solve classification problems by attempting to group data based on its attributes. However, what if we wish to solve a regression problem using a neural network? i.e. one where the dependent variable is an interval one and can take on a wide range of values? Let us now visit the gasoline.csv dataset. In this example, we wish to analyze the impact of the explanatory variables capacity, gasoline, and hours on the dependent variable consumption. Essentially, we wish to determine the gasoline spend per year (in$) for a particular vehicle based on different factors.

Accordingly, our variables are as follows:

• consumption: Spend (in $) on gasoline per year for a particular vehicle • capacity: Capacity of the vehicle’s fuel tank (in litres) • gasoline: Average cost of gasoline per pump • hours: Hours driven per year by owner ### Data Normalization Again, we normalize our data and split into training and test data: # MAX-MIN NORMALIZATION normalize <- function(x) { return ((x - min(x)) / (max(x) - min(x))) } maxmindf <- as.data.frame(lapply(fullData, normalize)) # TRAINING AND TEST DATA trainset <- maxmindf[1:32, ] testset <- maxmindf[33:40, ]  ### Neural Network Output We then run our neural network and generate our parameters: #4. NEURAL NETWORK library(neuralnet) nn <- neuralnet(consumption ~ capacity + gasoline + hours,data=trainset, hidden=c(2,1), linear.output=TRUE, threshold=0.01) nn$result.matrix
1
error                     0.158611967443
reached.threshold         0.007331578682
steps                    66.000000000000
Intercept.to.1layhid1     1.401987575173
capacity.to.1layhid1      1.307794013481
gasoline.to.1layhid1     -3.102267882386
hours.to.1layhid1        -3.246720660493
Intercept.to.1layhid2    -0.897276576566
capacity.to.1layhid2     -1.934594889387
gasoline.to.1layhid2      3.739470402932
hours.to.1layhid2         1.973830465259
Intercept.to.2layhid1    -1.125920206855
1layhid.1.to.2layhid1     3.175227041522
1layhid.2.to.2layhid1    -2.419360506652
Intercept.to.consumption  0.683726702522
2layhid.1.to.consumption -0.545431580477



### Model Validation

Then, we validate (or test the accuracy of our model) by comparing the estimated gasoline spend yielded from the neural network to the actual spend as reported in the test output:

results <- data.frame(actual = testset$consumption, prediction = nn.results$net.result)
results
actual   prediction
33 0.7556029883 0.6669224684
34 0.7801494130 0.6458686668
35 0.8356456777 0.6549105183
36 0.8399146211 0.6646982158
37 0.8431163287 0.6631168047
38 0.8890074707 0.6629885579
39 0.9124866596 0.6649999344
40 1.0000000000 0.6665075920


### Accuracy

In the below code, we are then converting the data back to its original format, and yielding an accuracy of 90% on a mean absolute deviation basis (i.e. the average deviation between estimated and actual gasoline consumption stands at a mean of 10%). Note that we are also converting our data back into standard values given that they were previously scaled using the max-min normalization technique:

predicted=results$prediction * abs(diff(range(consumption))) + min(consumption) actual=results$actual * abs(diff(range(consumption))) + min(consumption)
comparison=data.frame(predicted,actual)
deviation=((actual-predicted)/actual)
comparison=data.frame(predicted,actual,deviation)
accuracy=1-abs(mean(deviation))
accuracy
 0.9017828022


You can see that we obtain 90% accuracy using a (2,1) hidden configuration. This is quite good, especially considering that our dependent variable is in the interval format. However, let’s see if we can get it higher!

What happens if we now use a (5,2) hidden configuration in our neural network? Here is the generated output:

nn <- neuralnet(consumption ~ capacity + gasoline + hours,data=trainset, hidden=c(5,2), linear.output=TRUE, threshold=0.01)
nn$result.matrix 1 error 0.049463073770 reached.threshold 0.009079608691 steps 183.000000000000 Intercept.to.1layhid1 -0.484165225327 capacity.to.1layhid1 3.271476705612 gasoline.to.1layhid1 -13.185417334090 hours.to.1layhid1 0.926588147188 Intercept.to.1layhid2 -0.931405056650 capacity.to.1layhid2 0.527977084370 gasoline.to.1layhid2 5.893120354012 hours.to.1layhid2 -0.435230849092 Intercept.to.1layhid3 0.389302962895 capacity.to.1layhid3 -1.502423111329 gasoline.to.1layhid3 -4.684748555999 hours.to.1layhid3 -6.319048800780 Intercept.to.1layhid4 -0.094490811578 capacity.to.1layhid4 -2.399916325456 gasoline.to.1layhid4 -4.115161295471 hours.to.1layhid4 5.013344559754 Intercept.to.1layhid5 0.759624731279 capacity.to.1layhid5 -0.565467044104 gasoline.to.1layhid5 -7.076912238164 hours.to.1layhid5 -6.709144936619 Intercept.to.2layhid1 0.157424617083 1layhid.1.to.2layhid1 7.364054381868 1layhid.2.to.2layhid1 -3.671237007644 1layhid.3.to.2layhid1 6.295218032535 1layhid.4.to.2layhid1 -0.303371875453 1layhid.5.to.2layhid1 12.271950628363 Intercept.to.2layhid2 0.353976458576 1layhid.1.to.2layhid2 -2.460042549015 1layhid.2.to.2layhid2 0.062791089253 1layhid.3.to.2layhid2 2.376623876363 1layhid.4.to.2layhid2 -2.385599836002 1layhid.5.to.2layhid2 5.234292659554 Intercept.to.consumption 0.921627990820 2layhid.1.to.consumption -0.524918897571 2layhid.2.to.consumption -0.669503028647 results <- data.frame(actual = testset$consumption, prediction = nn.results$net.result) results actual prediction 33 0.7556029883 0.6554040151 34 0.7801494130 0.7781191265 35 0.8356456777 0.7611519348 36 0.8399146211 0.7980981880 37 0.8431163287 0.8027250788 38 0.8890074707 0.8047567120 39 0.9124866596 0.7969363797 40 1.0000000000 0.7802800479 predicted=results$prediction * abs(diff(range(consumption))) + min(consumption)
actual=results\$actual * abs(diff(range(consumption))) + min(consumption)
comparison=data.frame(predicted,actual)
deviation=((actual-predicted)/actual)
comparison=data.frame(predicted,actual,deviation)
accuracy=1-abs(mean(deviation))
accuracy
 0.9577401232


We see that our accuracy rate has now increased to nearly 96%, indicating that modifying the number of hidden nodes has enhanced our model!

## Conclusion

In this tutorial, you have learned how to use a neural network to solve classification problems.

Specifically, you saw how we can:

• Normalize data for meaningful analysis
• Classify data using a neural network
• Test accuracy using a confusion matrix
• Determine accuracy when the dependent variable is in interval format

Many thanks for viewing this tutorial. Please visit my blog for this and other posts.

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