Cluster

Cluster Analysis is about exploring and identifying natural groupings in a set of data points. In FastStats we are interested in taking a selection of records (say customers) and automatically detecting groups with similar characteristics. We can use these groups or clusters to better visualize our customer population and segment them for marketing purposes.

For example we could look at customers who bought holidays in a particular year and we might find that they can be grouped into 5 distinct clusters based on their age, income, location etc. This would be a valuable insight in itself and we could further use this knowledge to market different offers / brands to each of the clusters.

Create a cluster¶

Clustering is based upon analysis of a selection of records by certain characteristics using variables and grouping them together.

1. Create a selection of records to analyse.
2. Drag the Cluster tool on to the selection.
3. Decide upon the variables you wish to use as part of the analysis and drag them on to the Dimensions tab of the Cluster window.
4. Determine the number of Clusters to generate and other options using the Cluster Settings window. See Cluster settings.

5. Click on the Build button.

   

To see the detail of the Cluster analysis, look at each of the three tabs on the Cluster tool:

• Dimension results
• Chart results
• Log results

A Cluster Model can be generated through a wizard to present the clusters as categories in a virtual variable. See Create a cluster model.

Cluster settings¶

There are a number of options that can be changed in the Cluster Settings to determine the number, size and calculations used in the creation of clusters.

Click on the button to reveal the following window:

Basic options¶

Number of Clusters¶

A figure that defines the number of clusters required to be found.

Use Multi-Stage Clustering¶

This allows for Hierarchical Clustering:

• Divisive Clustering – start by treating all points as if they are part of a single large cluster, then divide the cluster into smaller and smaller clusters. This can be achieved by making the First Stage Number of Clusters figure smaller than the Number of Clusters figure.
• Agglomerative Clustering – start by treating each point as a separate cluster, and then group them into bigger and bigger clusters. This can be achieved by making the First Stage Number of Clusters figure larger than the Number of Clusters figure.

Minimum Cluster Size¶

This determines the minimum number of points in a cluster as the tool works through the Multi-Stage clustering process.

Maximum Cluster Size¶

This determines the maximum number of points in a cluster as the tool works through the Multi-Stage clustering process.

Advanced options¶

Maximum Number of Iterations¶

This figure is the maximum number of runs through the cluster analysis before the final results are shown. This figure many not be reached if it is determined the clusters are stable after less runs.

Euclidean¶

In mathematics, the Euclidean distance or Euclidean metric is the "straight line" distance between two points that one would measure with a ruler, and is given by the Pythagorean formula.

City Block¶

This is a form of geometry in which the usual metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their coordinates. Also know as Manhattan Distance, whose name alludes to the grid layout of most streets on the island of Manhattan, which causes the shortest path a car could take between two points in the borough.

Medioid¶

This is the middle point of a cluster and focuses on an actual point in the data.

Frequency¶

This uses the point with the highest number of records to set the initial cluster centre. Other cluster centres are selected by the next highest but distant from the other initial centres, with consideration taken to ensure that the centres are not too close together.

Random¶

This uses random starting points to set the initial cluster centres.

Dimension results¶

The Dimensions tab displays a summary line for each variable used in the analysis. It is then possible to drill down into the results for each category of that variable.

Not all options may be on display. to show further display information, right click on one of the headings and select Column Chooser...from the pop up menu. When the column Chooser appears, tick the options to display and click OK.

Variable display options¶

• Reference - the actual name of the variable
• Description- displays the name assigned to that particular variable
• Mean Index - gives the average index across all the clusters showing the influence of this variable on the clusters
• Weight - can be applied to a variable to reflect its importance in creating the clusters
• Use in Clustering - if ticked the variable will be used in creating the clusters. If not, the variable will not influence the creation of the clusters but will be used to describe them afterwards
• Type - of variable in use
• Omit Unclassified - if ticked will not use this category in the calculation. It should only be unticked if the unclassified category has a special or real meaning
• Cardinality - displays the number of categories in the variable

Category display options¶

• Description - displays the name assigned to that particular variable category
• Base - figure displays the total number of records in this category
• Base Histogram - shows graphically the relative number of records in a category
• Stacked Clusters - shows graphically the relative size of each cluster within each category and overall
• Cluster N Penetration - displays a histogram with an Index value shown centred around 100. Histogram bars to the left of the 100 centre line show under representation. Histogram bars to the right of the centre line show over representation.
• Cluster N - is the number of records in the cluster in this category
• Cluster N Index - is the ratio of the Cluster N and Base figure percentages multiplied by 100
• Cluster N Significance - displays a figure which is the standardised measure of how confident we can be that the result presented is a true characteristic of the data and not a quirk of the data sample used. For each category, the Z-Score measures the number of standard deviations the result is away from the expected result of the category.
• Cluster N Histogram - graphically displays the figures in Cluster N
• Cluster N Base - shows a histogram comparison of the Base and Cluster volume figures

Chart results¶

The Chart tab on the Cluster tool allows you to display a Scatter Plot graph. The graph will show how points for any two dimensions are assigned to the clusters.

Use the Rows and Columns drop downs to select which variables you would like displayed.

Mouse over a point to see a tool tip of the actual make-up of each point. The colour indicates the cluster with the highest figure if more than one cluster is associated with a point.

Log results¶

The Log tab on the Cluster tool allows you to view the Cluster Evolution. Each run displays the actions and figures as the clusters are calculated based upon the Cluster Settings.

Using the default options in the above example i.e. number of clusters 4, City Block, Medioid and Frequency, the cluster tool will use a technique called K-Means to detect a fixed number of clusters from a set of data points.

In this example, 4 centres will be located based upon the highest value points represented. the K-Means technique will allocate each point to its nearest cluster centre. Once this has been done, the midpoint of each cluster (in this case Medioid) is calculated and used as the new centre of the cluster. The process repeats itself to now reallocate the points to the nearest new cluster centre. This will continue until no points are reallocated to a different cluster centre or the maximum number of iterations has been met.

Create a cluster model¶

This generates a variable which assigns records to one of the clusters created.

1. When the cluster has been created, click the button on the icon bar to create a Cluster Model.

Follow the wizard steps; once the wizard has been completed, the virtual variable created will be displayed in the Others folder by default, unless you specify another folder in the File Explorer.