Help Manual


Sigma Magic Help Version 15

Discriminant Analysis


Discriminant analysis is a statistical analysis to determine whether a set of variables is effective in predicting category membership. For example, if you have two groups of data (say fake banknotes and original banknotes). For each group, we collect some characteristic data such as length, width, thickness, the color of ink, markings on the note, etc., and use this information to determine whether we can correctly assign future members to one of these two groups. Discriminant analysis is used when groups are known up-front (unlike in cluster analysis). The inputs to this analysis could be either continuous or binary independent variables (called predictors), and the output is group membership into two or more groups. If we have a good model, then this model can be used to predict group membership from data on independent variables.

Linear discriminant analysis is not just a dimension reduction tool but also a robust classification method. It specifically does not require any normality assumption for the data points, so it is pretty robust and works well independent of the type of data that is fed into the model. It can be used for classification, dimension reduction, and data visualization. When tackling real-world problems, LDA is often the first and benchmarking method before other more complicated analyses are employed.

This functionality is provided by the R software using the function lda within the MASS package. Note that this functionality requires that RScript software be installed on your computer and linked to the Sigma Magic software within the options menu. Discriminant Analysis worksheet can be added to your active workbook by clicking on Analytics and then selecting Discriminant Analysis.


Click on Analysis Setup to open the menu options for this tool. A sample screenshot of the menu is shown below.
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: Moments or Max. Likelihood. You can use one of these two methods to determine your analysis results.
MomentsUse the method of moments for the estimation of parameters.
Max. LikelihoodUse maximum likelihood estimates for the estimation of parameters.
Prediction: Specify the algorithm to determine predictions. This method determines how the parameter estimation is handled.
AutoUses the Plug-In method as the default.
Plug-InTHe usual unbiased parameter estimates are used and assumed to be correct.
DebiasedAn unbiased estimator of the log posterior probabilities is used for this analysis.
PredictiveTHe parameter estimates are integrated out using prior estimates.
Dimension: Specify the dimension of the space to be used for predictions. Only the dimensions specified are returned in the analysis results.
Tolerance: Specify the tolerance to decide if a matrix is singular. The software will reject variables and linear combinations of unit-variance variables whose variance is less than tol^2.
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 tool.
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 update the results on the worksheet. A sample screenshot of the worksheet is shown below.
LDA Example
Notes Section: The notes section provides a summary of the input data, and the analysis results section shows the name of the response variable along with the names of the input variables. The group means are shown along with the coefficients of the linear discriminants. The prediction column contains the prediction of the group based on the selected model. In this example, the cylinders column is used as an output variable, and cars with 8 cylinders (LD1 is closer to +5) are discriminated against vs. cars with 4 cylinders LD1 is closer to -5). If you want to make predictions on newer input variables to determine what is the most likely cylinder category you would have, you can enter the values for the remaining parameters in the inputs column and leave the cylinder column blank; when you run the outputs, the prediction of the cylinder will be shown in the prediction column (using these linear discriminators).
Graph Section: The graph section shows a chart for linear discriminant analysis and a confusion matrix, which shows how well the model works. The graph visualizes the data into two discriminant coordinates found by LDA. In this two-dimensional space, the classes can be well-separated.


Here are a few pointers regarding this analysis:
  • This analysis requires that the R software needs to be installed on your computer. Further, you will need to provide a link to the RScript executable file under Sigma Magic Options so that the software can use the R software to generate analysis results.


Following examples can be found in the Examples folder.
  • For the data given in the file, perform the discriminant analysis for predicting the gear based on other variable inputs. (Discriminant Analysis 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.