Cluster analysis is a technique for finding groups of similar objects in a data set. It is also known as unsupervised learning, since it does not require any labels or predefined categories for the data. Cluster analysis can be used for various purposes, such as exploratory data analysis, customer segmentation, anomaly detection, image segmentation, and more.
In this article, we will introduce some basic concepts and methods of cluster analysis, and show how to apply them in Python using the scikit-learn library. We will also discuss some challenges and limitations of cluster analysis, and provide some tips for choosing the best clustering algorithm for your data.
What is a cluster?
A cluster is a group of objects that are similar to each other within the group, and dissimilar to the objects in other groups. The similarity and dissimilarity can be measured by various metrics, such as Euclidean distance, cosine similarity, Jaccard index, etc. The choice of the metric depends on the type and scale of the data, and the domain knowledge of the problem.
There are different types of clusters, depending on the shape and structure of the data. Some common types are:
- Centroid-based clusters: These clusters have a central point that represents the mean or median of the objects in the group. For example, k-means clustering is a centroid-based algorithm that partitions the data into k groups based on the distance to the nearest centroid.
- Density-based clusters: These clusters have a high density of objects in the group, and a low density of objects between the groups. For example, DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based algorithm that identifies clusters based on the number of neighbors within a given radius.
- Hierarchical clusters: These clusters have a tree-like structure that shows the nested relationships between the groups. For example, agglomerative hierarchical clustering is an algorithm that starts with each object as a single cluster, and then merges the closest pairs of clusters until a single cluster remains.
- Distribution-based clusters: These clusters have a probabilistic model that describes how the objects in the group are generated. For example, Gaussian mixture models (GMMs) are a distribution-based algorithm that assumes that each cluster follows a multivariate normal distribution.
How to perform cluster analysis?
The general steps for performing cluster analysis are:
1. Define the objective and scope of the analysis. What is the goal of clustering? What are the expected outcomes? How will the results be used or evaluated?
2. Preprocess and explore the data. What are the features and variables of the data? How are they distributed and correlated? Do they need any transformation or scaling? Are there any outliers or missing values?
3. Choose a clustering algorithm and parameters. What type of clusters are suitable for the data? What are the assumptions and requirements of the algorithm? How many clusters are needed? How to measure the similarity or dissimilarity between the objects?
4. Apply the clustering algorithm and obtain the results. How to assign each object to a cluster? How to interpret and visualize the clusters? How to validate and compare the results?
5. Analyze and report the findings. What are the characteristics and profiles of each cluster? What are the insights and implications of the clustering? How to communicate and present the results to stakeholders?
Example: Cluster analysis in Python
To illustrate how to perform cluster analysis in Python, we will use a sample data set from scikit-learn called make_blobs. This data set contains 200 synthetic observations with two features (x1 and x2) that form three clusters.
First, we import some libraries and load the data set: