Help Manual


Sigma Magic Help Version 17

Neural Networks


A neural network model is made up of an interconnected set of neurons, similar to how a human brain is structured. It does not work linearly but can be pretty powerful in modeling complex data sets. A neural network model is characterized by an activation function that transforms inputs into outputs. The first layer of the neural network receives the raw input, processes it, and passes it on to the hidden layers. The hidden layers pass the information to the output layer. A neural network learns from the information provided when the outcome is known and trains itself to make better predictions in the future with unknown outcomes. During the learning process, the errors at the output units are back-propagated through the system to optimize the weights at each connection. However, it is hard for humans to understand and explain to others exactly how a neural network makes a decision - and it is usually treated as a black box.

The current implementation of Neural Network in Sigma Magic software is based on the neuralnet package in R. Make sure that all the input and output variables are numeric and the predictors are normalized before using this package. To add the Neural Network template to your worksheet, click on Analytics and then select Neural Networks.


Click on Analysis Setup to open the menu options for this template. A sample screenshot of the menu is shown below: Neural Input Menu 1
Training Set: Specify the data to be used for training the algorithms.
AutoRandom method for selection of the training data set is used./td>
RandomA random number algorithm is used to select the training set.
SequentialA sequential set of samples are picked. For example: 1st point, 3rd point, 5th point etc.
Training Size: Specify what % of the data points should be picked for the training set. These are used to build the model and the remaining points are used to test the model.
Algorithm: Specify the algorithm for generating the neural network. The following options are available:
AutoUsed the BackProp algorithm by default.
BackPropUses the back propogation algorithm to determine the neural network weights.
RProp-Uses the resilient back propogation algorithm without backtracking which can be faster to train and does not require any free parameter values.
RProp+Uses the resilient back propogation algorithm with backtracking.
SagUses the globally convergent algorithm with the learning rate associated with the smallest absolute gradient.
SlrUses the globally convergent algorithm with the learning rate associated with the smallest learning rate.
Linear Output: Specify if you want a linear output.
YesThe activation function would not be applied to your output.
NoThe activation function will be applied to your output.
Activation Function: A differentiable function that is used for smoothing the result of the cross product of the covariate or neurons and the weights.
AutoUses the Logistic function by default.
LogisticUses the logistic function for smoothing.
TanhUses the tangent hyperbolic function for smoothing.
Error Function: A differentiable function that is used for the calculation of the error.
CEUses the sum of squared errors.
SSEUses the cross-entropy.
Hidden Layer: A vector of integers specifying the number of hidden neurons in each layer. If you specify 4, then there are four neurons in the hidden layer. If you need more than one hidden layer, you can specify 4,3. Then the first hidden layer will have 4 neurons and the second hidden layer will have 3 neurons.
Threshold: A numeric value specifying the threshold for the partial derivatives of th error function as stopping criteria.
Num Reps: The number of repetitions for neural network training.
Max Steps: The maximum steps for the training of the neural network. Reaching this maximum leads to a stop of the neural network's training process.
Additional Options: This field is optional. You can specify any additional options for the R software program directly by typing it here.
Help Button: Click on the Help Button to view the help documentation for this template.
Cancel Button: Click on the Cancel Button to discard your changes and exit this menu.
OK Button: Click on the OK Button to save your changes and try to execute the program. Note that you will need to specify the required data in order to complete the analysis and generate outputs. If there are any missing data, then the software will remind you to specify the data and click on Compute Outputs to generate analysis results.


If you click on the Data button, you will see the following dialog box. Here you can specify the data required for this analysis. Data
Search Data: The available data displays all the columns of data that are available for analysis. You can use the search bar to filter this list and to speed up finding the right data to use for analysis. Enter a few characters in the search field and the software will filter and display the filtered data in the Available Data box.
Available Data: The available data box contains the list of data available for analysis. If your workbook does not have any data in tabular format, this box will display "No Data Found". The information displayed in this box includes the row number, whether the data is Numeric (N) or Text (T), and the name of the column variable. Note that the software displays data from all the tables in the current workbook. Even though data within the same table have unique column names, columns across different tables can have similar names. Hence, it is important that you not only specify the column name but also the table name.
Add or View Data: Click on this button either to add more data into your workbook for analysis or to view more details about the data listed in the available data box. When you click on this button, it opens up the Data Editor dialog box where you can import more data into your workbook, or you can switch from the list view to a table view to see the individual data values for each column.
Required Data: The code for the required data specifies what data can be specified for that box. An example code is N: 2-4. If the code starts with an N, then you will need to select only numeric columns. If the code starts with a T, then you can select both numeric and text columns. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, then you need to select a minimum of 2 columns of data and a maximum of 4 columns of data in this box. If the minimum value is 0, then no data is required to be specified for this box.
Select Button: Click on this button to select the data for analysis. Any data you select for the analysis is moved to the right. To select a column, click on the columns in the Available Databox to highlight them and then click on the Select Button. A second method to select the data is to double click on the columns in the list of Available Data. Finally, you can also drag and drop the columns you are interested in by holding down the select columns using your left mouse key and dragging and dropping them in one of the boxes on the right.
Selected Data: If the right amount of data columns has been specified, the list box header will be displayed in the black color. If sufficient data has not been specified, then the list box header will be displayed in the red color. Note that you can double-click on any of the columns in this box to remove them from the box.
View Selection: Click on this button to view the data you have specified for this analysis. The data can be viewed either in the tablular format or you can view a graphical summary of the data selected.


If you click on the Program button, the software will display the program code - an example screenshot is shown in the figure below. Pre-Process Inputs 3
R Program: You can view the R program that will be executed here. This program is usually automatically generated from the options you have specified in the setup earlier. This is the program that will be executed by the R program to generate analysis outputs. If you like, you can edit this program.
Auto Mode: If the radio button is selected as Auto, then the software will automatically update this code based on any changes you make in the input dialog box. We recommend that you use this option to generate the R program so that all your input settings are used to generate analysis results.
Manual Mode: If you use the Manual option, then you will be allowed to edit the R program before the program is executed. Make sure that you specify a syntactically correct program; otherwise, the R program may report errors.


If you click on the Verify button, the software will perform some checks on the data you have entered. A sample screenshot of the data is shown in this figure. Pre-Process Inputs 4
Verify Checks: The objective of this analysis as well as any checks that are performed are listed in this dialog box. For example, the software may check if you have correctly specified the input options and if you have specified the data correctly for analysis.
Check Status: The results of the analysis checks are listed here. If the checks are passed, then they are shown as a green-colored checkmark. If the verification checks fail, then they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange color exclamation mark and finally, any checks that are required to be performed by the user are shown as blue info icons.


Click on Compute Outputs to generate the outputs from this analysis. A sample screenshot of the worksheet is shown below. Neural Network Example
Notes Section: The analysis results section a summary of the inputs used to build the neural network model. Next, it displays a summary of the training - threshold reached and the number of steps taken for model convergence. Finally, the weights of the neural network model are displayed.
Graph Section: The first graph shows the neural network model that was used, and the second graph shows a histogram of the residuals. The prediction column shows the model predictions using the developed neural network model. Finally, the conclusions at the bottom show the mean square errors for the training data set and test data set (if available).


Here are a few notes regarding this analysis:
  • For the best performance of the neural network model, the input predictors need to be numeric and normalized. The normalization is automatically done by Sigma Magic software but make sure to transform all input variables to numeric before using this template.
  • If you want to review the R program that was used to generate this output, go to the %TMP%/Sigma Magic/ folder and look for the file smRScript.R after you execute the program. Note that this folder also contains other files such as error or warning output, text, and graphical output from running R. However, these files are stored in a temporary location and are not persistent between sessions.


Following examples can be found in the Examples folder within the software.
  • Use the Neural Network method to estimate the number of gears in a car given the rest of the features (Neural 1.xlsm).


For more information on this topic, please refer to the following articles. Do note that if any external links are mentioned below, they are for reference purposes only.