Clustering for data analysis

Álvaro Muñoz

GAMCO R&D&I Dept.

Clustering methods, or grouping, are a fundamental part of the data analysis process, as they allow an automatic segmentation of the information from which valuable conclusions can be drawn. 

Due to their importance, they have been widely studied, hence there are hundreds of algorithms and different ways to classify them.(1). One way would be to divide them into two groups, those that only address the task of grouping, and those that also include certain advantages in the visualization and understanding of the information.

In this article you will understand what clustering is, how it works and how this method can be of great help for the data analysis.

What is clustering? 

The clustering is a process in which different objects with similar characteristics are grouped into groups called clusters. It is usual not to know the output of the objects to be grouped, so it will be carried out by means of unsupervised training.

This task may seem simple when you have a very small number of characteristics, but the truth is that as you have a larger number of variables, the possible relationships between each object become more complex and difficult to analyze.

How clustering works

It is not a problem with a direct solution, so it requires an iterative process that will vary according to the clustering algorithm.

To group objects together, similar samples must first be found. Measuring this similarity of the samples is done with a similarity function, which is usually a distance function between the feature vectors that make up the sample.

Once the similarity measure is established, the process of clustering depends on the type of algorithm. The most common ones are classified into hierarchical, centroid-based, distribution-based and density-based clustering.

One of the best-known algorithms is that of k-meansbased on centroid. The operation is simple, each cluster will be defined with a prototype object that may or may not be a member of the data set, and will be the centroid of the group. Once the number of clusters is defined, the problem is to find these centroids such that the square of the distances from the group to the prototype object are minimized. An iterative process is carried out where samples are assigned to the clusters and the centroids are updated until the assignments stop changing.

what is clustering
Movement of the centroids during the K-means process

Cluster analysis

Two types of utilities that can be given to the grouping of the data samples can be highlighted:

  • Cluster analysis: where segmentation of unstructured data allows for better analysis and understanding of the data.
  • Automatic classification in the field of Machine Learning.

Focusing on this first utility, cluster analysis can be performed through segmentation. But there are also clustering methods that provide a number of additional advantages to extract even more information from the data.

These methods can make it possible to visualize high-dimensional data in low-dimensional (typically 2D) maps by performing a smooth, nonlinear mapping of both spaces. This property is known as dimensionality reduction and allows preserving information about the distribution of the input data and observing the relationships of variables in different maps. 

In this way, different samples can be compared and moved on these maps to observe the smooth change in their characteristics.

This feature of some clustering methods is very important in most clustering applications and leads to a deeper and easier to understand analysis of the data.

This is best seen with an example. In the following image you can see how these 2D maps look like once the information has been organized with the clustering algorithm. Where each cell characterizes the group of individuals that fall into it and their variables are represented through the different maps.

cluster analysis
2D maps obtained through clustering methods for medical data of individuals.

These maps show medical variables such as weight, height, body mass index, cholesterol and fat percentage. 

Thus, once the algorithm has been applied, conclusions can be drawn such as that individuals with a high weight (more than 100 kg), short stature (less than 162 cm) have a body mass index, a high cholesterol level and a high percentage of fat, so they could be considered as a high risk group. 

This is a very small example, in a real case it would be possible to know the medical history of the patients and a greater number of variables to obtain better and more valuable conclusions. 

If, for example, we wanted to know which variables influence the occurrence of an infarction, we could add variables such as the number of infarctions suffered or the type of infarction. Applying the clustering algorithm would help to find different groups of individuals and the characteristics that differentiate them.

Not only that, knowing which are the variables on which we can act, known as levers, thanks to the maps we could know what value they should have to move the behavior to where we want. Knowing also how the rest of the variables would be changed.

Other analyses that these maps allow would be to know the variables that differ the most or are most similar in close groups, seeing their gradual change.

Applications

The segmentation of samples according to their properties can be used in any application where you want to relate unclassified samples or want to analyze unstructured data in depth. Some of the applications include:

  • Market and customer segmentation: for different objectives, such as offering better products and knowing the best potential customers. 
  • Disease identification in medicine: In medicine, clustering methods are a powerful tool for understanding experimental data and identifying relationships. For example, studies can be found that use these techniques for breast cancer detection.(2)
  • Face identification in biometrics: Despite the success achieved in face detection and recognition in the last decade, the analysis of facial attributes is still a trending problem. Clustering allows the discovery of new features automatically.
  • Search recommenders: to provide personalized suggestions about products, services and information. Where users with similar characteristics are related to make recommendations. Examples of recommendation engines include Amazon or Youtube,
  • Spam filters: By analyzing the different sections of an email (subject, sender, content, ...) it is possible to detect similarities between unwanted emails and thus be able to detect them effectively.

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  1. Xu, D., Tian, Y. A Comprehensive Survey of Clustering Algorithms. Ann. Data. Sci. 2, 165-193 (2015). https://doi.org/10.1007/s40745-015-0040-1
  2. Dubey, A. K., Gupta, U., & Jain, S. (2016). Analysis of k-means clustering approach on the breast cancer Wisconsin dataset. International journal of computer assisted radiology and surgery, 11(11), 2033-2047. https://doi.org/10.1007/s11548-016-1437-9
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