Math and numbers are the ultimate in ‘exact science.’ When we work within the confines of mathematics, we can expect absolute precision in our results. In data analysis terms, this can be a real advantage, giving us clear, definite numbers on which to base future decisions. Unfortunately, sometimes the real world being represented by the data is anything but exact. And when it comes to grouping objects based on a somewhat nebulous idea of similarity, traditional statistical tools may fall short.
Cluster analysis is an answer to this problem. With cluster analysis, data analysts can construct data groups (or clusters) based on a range of similarities and differences. The end goal is to distinguish data points in such a way that those within a group are as similar as possible and completely distinct from the data points belonging to separate groups.
Here, we take a closer look at cluster analysis, how to perform one, how to interpret the data, and what potential disadvantages you should be aware of before you get started. But first, let’s define the term itself.
What Is Cluster Analysis?
At its most basic, cluster analysis is a statistical methodology designed to allow analysts to process data by organizing individual objects into groups defined by their similarity or association. Also called segmentation analysis or taxonomy analysis, cluster analysis exists to help identify homogenous groups with a range of items when the grouping is not already known or defined. In other words, cluster analysis is exploratory; data scientists who apply cluster analysis don’t begin with any predefined classes or expectations.
Instead, cluster analysis takes a collection of data items and attempts to organize them based on how closely associated each one is with the others. Visually, this is often represented using a multi-axis graph to more accurately identify which data points are similar and which are not.
One common example of clustering is the arrangement of items within a grocery store—products are classified and grouped based on how similar they are in purpose.
Cluster analysis is an essential aspect of modern artificial intelligence (AI) and data mining, and businesses often rely on clustering to segment customer populations into different marketing or user groups. Cluster analysis may be used in a range of business and non-business applications.
Steps for Making a Cluster Analysis
There are nearly as many ways to cluster data points as there are groups to segment them into. As such, there is no single process that represents the standard mechanism of cluster analysis. The following process, however, is a reliable set of steps you can use when clustering data:
1. Confirm the Metricality of the Data
For effective clustering, your data needs to have actual numerical values. This is because you will need to define the ‘distance’ between data points. So even if you are working with non-metric data (such as people’s names), you still need to define the similarities in a numerical way (such as by saying that individuals with the same name have a distance defined as 0 and those with different names have a distance defined as 1).
2. Select Variables
Selecting the right variables is essential to producing relevant, usable cluster data. Perform exploratory research beforehand so that you have a clear idea of which variables to use.
3. Define Similarities
As with selecting your variables, choosing and defining similarity measures to chart the ‘distances’ between your observations is key to producing a usable cluster analysis. You can define similarities in hundreds of different ways, so be aware of your options as you work with your data.
4. Visualize Pairwise Distances
With the correct variables in place and your similarities fully defined, you can now begin to visualize your cluster analysis data. You can plot individual attributes as well as the pairwise distances on a histogram chart, with your classes represented as columns on the horizontal axis. Peaks within those columns may represent potential segments.
5. Choose a Method and Number of Segments
Again, there are many different methods one may use to cluster data. You may wish to try a variety of approaches until you find one that clearly represents actionable information in a clear and robust way. Cluster analysis is iterative, so be willing to work with the data until it starts to work for you.
6. Interpret the Segments
With your chosen method and number of segments, your next step is to get a clearer idea of the data points themselves and how they relate to one another. Make note of how the segments differ based on your variables. It can be extremely helpful to visualize these clusters using graphing techniques.
7. Perform Ongoing Analysis
With your core data visually represented and your individual data points more fully understood, the final step is to dig down deeper with increasingly robust cluster analysis. This may include subjecting your data to different subsets, distance metrics, segmentation attributes, segmentation methods, or numbers of clusters. By exploring multiple variations, you should be able to see how well your data holds up, how much overlap you have between your clusters, and how similar your segment profiles are across different approaches.
How to Interpret and Measure Clustering
Cluster analysis is based on the assumption that the lower the numerically-represented distance between items, the higher the similarity level—provided that you have a reasonable number of clusters to work with. You can use a silhouette coefficient score to calculate how healthy your clusters are by determining the average silhouette coefficient value of each of the objects in the data set.
Measuring your clusters also heavily depends on the questions you ask regarding your initial data. Important cluster analysis questions include:
- How will you measure the similarity between objects?
- How will similarity variables be weighted?
- Once similarities are established how will classes be formed?
- How will clusters be defined?
- What conclusions can you draw regarding the clusters’ statistical significance?
Advantages and Disadvantages of Cluster Analysis in Sampling
A key application of cluster analysis in cluster sampling. Cluster sampling divides an entire study population into externally homogeneous but internally heterogeneous groups, with each cluster acting as a miniature representation of the whole. The groups must be divided randomly, and then individual groups are randomly selected and every individual in that group is sampled.
For example, cluster sampling allows researchers to study certain types of communities within the country without having to acquire subjects from hundreds or thousands of different locations. Instead, these communities are divided into similar groups and a random sample of communities is assessed. In this case, the randomly-selected subset represents the whole population. Another example might be an airline that chooses to survey all of the passengers on several randomly-selected flights every day to infer conclusions about their passengers as a whole population.
Cluster analysis as a sampling methodology offers some clear advantages over more traditional random or stratified sampling. For one, cluster sampling tends to demand fewer resources and is more cost-effective. For another, cluster analysis may be more feasible while still providing a comprehensive view of an entire population.
That said, there are also certain disadvantages that you should be aware of. Perhaps the biggest drawback is that cluster sampling is prone to higher error rates than many other sampling techniques; the results obtained are not always fully reflective of the population as a whole. Additionally, unconscious biases may seep into this sampling methodology creating biased inferences about the entire population.
Better Analysis with InMoment
If you’re interested in getting a clear picture of the similarities and differences across a data set, then cluster analysis may be the answer. But ensuring that your cluster data accurately represents your sample group and clearly expresses valuable information can be difficult. Understanding cluster analysis and cluster sampling methodologies and how best to interpret the resultant data will provide you with the insight you need to understand the associations between your objects.
InMoment, the leader in people-oriented text analytics, can help. Built on industry-recognized metrics and real-time intelligence, InMoment provides the tools and support you need to find hidden insights in your data. For more information on data gathering and analysis, visit our Learning Hub.