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Sigma Magic Help Version 18

Hierarchical Clusters Analysis

Overview

This analysis can determine a dendrogram that builds the hierarchy from the bottom up. The algorithm puts each data point in its cluster or one of the randomly determined clusters. Then, the closest two clusters are identified and then combined into one cluster. The above process is repeated until all the data points are combined into a single cluster. The tree can then be pruned to display which data points belong within a cluster.

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

Inputs

Click on Analysis Setup to open the menu options for this tool. A sample screenshot of the menu is shown below.
menu 1
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Algorithm: Specify the agglomeration method to be used.
OptionDescription
AutoUses Ward's minimum variance method as the default.
AverageAims for clusters between the single and complete link methods.
CentroidAims for clusters between the single and complete link methods.
CompleteThe complete linkage method finds similar clusters.
McquittyAims for clusters between the single and complete link methods.
MedianAims for clusters between the single and complete link methods.
SingleThe single linkage method adopts friends-of-friends clustering strategy.
WardWard's minimum variance method aims at finding compact spherical clusters.
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Num Clusters: Specify the number of clusters to display in the final dendrogram.
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Distance Metric: Specify the formula used to determine the distance between observations. Available distance measures are:
OptionDescription
AutoUses the Euclidean distance as the default metric.
BinaryVectors are regarded as binary bits (non-zero elements are treated as 1, and zero elements are treated as 0).
CanberraIs a numerical measure of the distance between pairs of points and is a weighted version of L1 distance. It can be used to compare ranked lists.
EuclideanSquare of the distance between two vectors.
ManhattanAbsolute distance between two vectors.
MaximumUses the maximum distance between two components as the metric.
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Standardize: This specifies if the input observations should be standardized so that each variable has a similar variance structure.
OptionDescription
AutoUses the standardization as the default method.
YesPerforms standardization of data prior to analysis.
NoDoes not perform any standardization of data before analysis.
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Additional Options: This field is optional. By typing it here, you can specify any additional options for the R software program.
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Help Button: Click on the Help Button to view the help documentation for this tool.
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Cancel Button: Click on the Cancel Button to discard your changes and exit this menu.
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OK Button: Click on the OK Button to save your changes and try to execute the program. You must specify the required data to complete the analysis and generate outputs. If there are any missing data, the software will remind you to specify the data and click on Compute Outputs to generate analysis results.

Data

You will see the following dialog box if you click the Data button. Here, you can specify the data required for this analysis. Data
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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 speed up finding the right data 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.
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Available Data: The available data box contains the list of data available for analysis. If your workbook has no 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, you must specify the column name and the table name.
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Add or View Data: Click on this button to add more data to 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 the Data Editor dialog box, where you can import more data into your workbook. You can also switch from the list view to a table view to see the individual data values for each column.
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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, you must select only numeric columns. If the code begins with a T, you can select 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, you must select a minimum of 2 columns of data and a maximum of 4 columns in this box. If the minimum value is 0, then no data is required to be specified for this box.
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Select Button: Click on this button to select the data for analysis. Any data you choose 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 choose the data is to double-click on the columns in the list of Available Data. Finally, you can 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.
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Selected Data: The list box header will be displayed in black if the right number of data columns is specified. If sufficient data is not specified, the list box header will be displayed in red. Note that you can double-click on any of the columns in this box to remove them from the box.
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View Selection: Click on this button to view the data specified for this analysis. The data can be viewed in a tabular format or a graphical summary of the selected data.

Verify

If you click the Verify button, the software will perform some checks on the data you entered. A sample screenshot of the data is shown in this figure. Pre-Process Inputs 4
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Verify Checks: The software checks if you have correctly specified the input options and if you have specified the data correctly for analysis.
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Check Status: The results of the analysis checks are listed here. If the checks are passed, they are shown as a green checkmark. If the verification checks fail, they are shown as a red cross. If the verification checks result in a warning, they are shown in the orange exclamation mark. Finally, any checks that are required to be performed by the user are shown as blue info icons.
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Overall Status: The overall status of all the checks for the given analysis is shown here. The overall status check shows a green thumps-up sign if everything is okay and a red thumps-down sign if any checks have not passed. Note that you cannot proceed with generating analysis results for some analyses if the overall status is not okay.

Outputs

Click on Compute Outputs to update the results on the worksheet. A sample screenshot of the worksheet is shown below.
Hierarchical Outputs
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Notes Section: The notes section summarizes the input data, and the analysis results section shows the call used to analyze the data.
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Graph Section: The graph section shows the cluster dendrogram and the red boxes highlighting the cluster groups. In this example, rows 4 and 6 are "similar" since they belong to the same cluster. Similarly, rows 1 and 2 are "similar," and 5 and 7 are "similar."

Notes

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 are available so the software can use the R software to generate analysis results.

Examples

The following examples are in the Examples folder.
  • Determine the hierarchical cluster analysis for the data given in the file. (Hierarchical 1.xlsx)

References

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.

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