Mastering cluster analysis: Techniques and applications

Researchers in certain fields will often find they have a large collection of data that needs to be sorted in some way. They need to find out how individual data points relate to one another.

As a simple example, imagine a large list of countries. We could cluster them into their respective continents, or we could cluster them by language spoken. These clusters could be created by hand relatively easily. But, as the data to be clustered becomes more complex or abstract, we would need to use more advanced methods to handle it. Cluster analysis is what we’d use.

This article will explore cluster analysis and show you how to master this useful technique.

Cluster analysis is a powerful statistical method used to uncover hidden patterns and structures in large or complex datasets. When similar data points are grouped together, it opens up a number of possibilities for analysis:

• Simplifying large datasets

• Identifying natural groupings

• Identifying relationships between variables

• Detecting outliers or anomalies

As an unsupervised learning algorithm, cluster analysis is applied in diverse fields like customer segmentation in marketing and gene expression analysis in biology. It doesn’t require any prior knowledge of the number of clusters or assumptions about relationships within the data.

Let’s take a closer look at how cluster analysis can be used in various industries to give you a clearer picture of how useful this method can be.

Exploratory data analysis

Cluster analysis is beneficial as a way to discover hidden patterns that would otherwise go unnoticed when first examining data. It groups similar data points together so that analysts can quickly identify natural segments or distinct categories.

In the process, you can uncover unexpected relationships or outliers, allowing for better insights into the distribution of data. From here, you can generate more informed hypotheses.

Market segmentation

Marketing teams rely heavily on concepts like buyer personas. Who is buying your products? Is it one specific type of person or multiple types of people?

Cluster analysis uses variables such as demographics, purchasing habits, and preferences to group customers in a way that enhances personalization efforts. By identifying distinct segments, your business can tailor marketing strategies to meet each group’s specific needs. This leads to more targeted communication and boosts customer satisfaction and loyalty.

Recommendation engines

Marketers can also use cluster analysis to drive product recommendations. An analysis of your company’s product line highlights products that fit well together. A customer who buys one of these may be interested in buying another.

You can also perform cluster analysis on customers’ purchasing habits. This will reveal customers who have similar tastes, enabling you to recommend products to customers who are likely to purchase them.

Resource allocation

Using resources efficiently can be challenging for large businesses. Cluster analysis helps here as it enables you to group entities with similar resource requirements or performance characteristics.

When you identify areas with similar production needs, you can manage inventory and supply chains more effectively. The public sector can use this approach to group regions or projects with similar resource requirements and ensure resources are distributed more equitably.

Detecting anomalies

Cluster analysis also enables you to discover anomalies that don’t fit well anywhere. In many industries, this means nothing. In some industries, it can be vital information.

For example, financial institutions can flag transactions well outside a person’s usual purchase patterns as fraudulent. In cybersecurity, network traffic well outside of the norm could indicate that an attack is underway.

Cluster analysis can be a powerful statistical method, but it’s not the right solution for every task. Sometimes, it may even provide unusable results.

Like any technique in an analyst’s arsenal, the key is to know its strengths and weaknesses. Below are the pros and cons of cluster analysis:

Pros of cluster analysis

• Pattern discovery: cluster analysis reveals hidden patterns and structures in data.

• Data organization: grouping similar data points simplifies large datasets.

• Unsupervised learning: doesn’t require labeled data.

• Versatility: the analysis is applicable across various fields (such as marketing and biology).

• Outlier detection: it helps identify anomalies in datasets, including fraud.

Cons of cluster analysis

• Subjectivity: choosing the number of clusters can be arbitrary.

• Sensitivity: results can vary depending on the algorithms and parameters you choose.

• Scalability issues: some methods struggle with high-dimensional data.

• Interpretation challenges: clusters may not always have clear meanings.

• Assumes structure: cluster analysis assumes data has inherent groupings, which may not always be true.

There are many families of clustering algorithms. Each approach provides a unique set of benefits and tradeoffs. Selecting the correct approach is one of the most important factors in getting meaningful results.

Here are some of the most common approaches:

Partitioning algorithms

This type of clustering divides data into non-overlapping subsets. Typically, it starts with an initial clustering. The next step is iterating over it. During each iteration, the elements are repositioned to improve the quality of the results.

The most common of these algorithms is known as “k-means clustering.”

With partitioning algorithms, you generally need to tell them how many clusters to divide the data into.

Hierarchy algorithms

As the name implies, this kind of algorithm divides the data into hierarchical clusters. There are two approaches to this:

1. Starting with a single large cluster and working down to more discrete ones

2. Starting with each individual element and working up to group them together

AGNES and DIANA are the most common of these algorithms. With these, you’ll end up with one large cluster at the top and individual elements at the bottom. You can then choose the most useful clustering in the middle.

Density-based algorithms

To understand how these algorithms work, imagine you have a large cloud of data. Some elements are densely packed together, and some are positioned more sparsely. These algorithms identify the elements that are closely clustered together.

The most common density-based algorithm is called DBSCAN.

A benefit of density-based algorithms is that they automatically determine the number of clusters. This method is also great at identifying outliers in the data.

Grid-based algorithms

This family of algorithms is useful when you’re dealing with very large datasets. Rather than working on the data itself, grid-based algorithms divide the data space into a grid-like structure. The clustering is then performed on the grid, and the data is placed in the cluster for the grid it’s in. This allows large datasets to be processed efficiently.

Common algorithms in this family include STING and CLIQUE.

Model-based algorithms

These algorithms look at the data and try to find the parameters of the distributions that best fit the data. They are useful for data generated from a mix of probability distributions and are highly accurate when the data’s underlying mathematical formula fits this use case.

The Gaussian mixture models are common examples of model-based algorithms.

Although some clustering algorithms attempt to distribute the data into a logical number of clusters automatically, others require you to decide that parameter on your own. Selecting the wrong number can result in data that’s not very granular or, worse, completely useless.

Here are some approaches for choosing a cluster number wisely:

Hierarchical clustering dendrogram

The hierarchical clustering method can be useful even when it doesn’t provide you with perfect clusters. The set of clusters that most closely matches your data can give you a starting point for the number of clusters to use in other algorithms.

Elbow method

This works in a similar way to the hierarchical clustering method in that you’re trying to add more clusters until doing so doesn’t result in cleaner data. However, instead of using one of the hierarchical algorithms, the elbow method works by measuring the compactness of the clusters.

Silhouette analysis

The silhouette analysis method works well when you can measure how well a data point fits into a cluster. As you add more clusters, the data should fit better. However, the reverse will be true if you add too many. The ideal number of clusters is the one with the highest average cluster score.

Gap statistic

This method randomly assigns data points to a number of clusters and calculates how well they fit. This becomes a baseline.

When the actual clustering algorithm is applied to that number of clusters, the score is compared to random chance. The number of clusters that performs best against random chance is considered the best choice.

Let’s look at how researchers and analysts understand the results of their analysis.

Cluster visualization techniques

Visualizing the results of cluster analysis can be very helpful in understanding the underlying data. There are several methods that you can use:

• Scatter plots: these display data points in two or three dimensions. The clusters are represented as point clouds, with each cluster getting a different color.

• Heatmaps: these use color-coding to represent similarities between data points, revealing patterns across large datasets.

• Dendrograms: these tree-like structures show the results of hierarchical clustering methods. Broader clusters are at the top and split into more discrete clusters as the chart moves downward.

Dimensionality reduction techniques

Often, the data you’re working on won’t fit well into two or three dimensions. This is a problem because your vision can only work in those spaces.

Dimensionality reduction techniques, such as principal component analysis (PCA) and t-SNE, can reduce that high-dimensional data without destroying important relationships. This makes it possible to visualize even complex data with relatively simple charts.

Cluster analysis is performed with software tools. You can use numerous libraries for common data analysis languages (such as R and Python) to perform cluster analysis. We’ll provide a high-level overview of the process here—your data team can handle the specifics.

Here’s an example of using cluster analysis to segment customer data.

• Prepare the data: gather data about your customers (for example, their income and spending scores). Format it in a way that your algorithms can read.

• Pre-process the data: the data needs to be normalized before it can be used to ensure everything is on the same scale. Some clustering algorithms are more sensitive to this than others.

• Choose the number of clusters: some algorithms determine the number of clusters for you. Otherwise, you’ll need to use the elbow method, silhouette analysis, or one of the other methods previously discussed.

• Apply clustering: this part is simple. With your data processed and cleaned and your parameters decided, the computer will do the heavy lifting and apply the clustering.

• Visualize the results: the most common way to visualize the results is to have the software generate a scatter plot. Each cluster is a different color, so it’s easy to see how the data points relate to one another.

• Interpret the results: with the data generated, you can take the center of each cluster to get the average profile for customers in that segment.

There’s a lot that can go wrong with this type of analysis. Following these tips will help you avoid common pitfalls.

• Choose the number of clusters intelligently: the elbow method or silhouette analysis are good choices if you don’t know which to try. Experiment with different values to see which provides the best results.

• Pre-process the data: don’t forget to normalize the data before processing it. Also, look for any outliers that might be noise in the dataset and remove them for the best results. For high-dimensional data, consider dimensionality reduction.

• Validate the results: clustering algorithms can be tricky. The best one depends a lot on the underlying data. Use cross-validation and compare multiple algorithms and cluster sizes to get the best results. It’s best to use this approach when you’re first learning how the algorithms work.

• Update and refine regularly: when new data arrives, it might not fit neatly into the same number of clusters. Reevaluate and refine your processes when adding new data to ensure you’re always getting the best results.

It can take a while to learn what the algorithms do and how they process your data. It’s worth taking the time to try all of them on various datasets so you’ll be better prepared to pick the best option for your current task.