# An In\-Depth Guide to Clustering Algorithms for Machine Learning

- Canonical: https://33rdsquare.com/an-introduction-to-clustering-and-different-methods-of-clustering/
- Published: 2024-09-03
- Author: Jordan Brown
- Categories: [Artificial Intelligence & Machine Learning & ChatGPT](https://33rdsquare.com/category/tech/ai/)

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Clustering is one of the most widely used unsupervised machine learning techniques. It involves automatically discovering natural grouping in data, where objects in the same cluster are similar and objects in different clusters are dissimilar. Clustering has applications across many domains, from customer segmentation in business to identifying cell types in biology.

In this comprehensive guide, we‘ll dive deep into clustering and the different algorithms used to perform it. You‘ll gain an understanding of what clustering is, the types of clustering, how popular algorithms like k-means and hierarchical clustering work, and considerations to keep in mind when applying clustering to real-world problems. Finally, we‘ll look at some of the latest developments in clustering techniques as of 2024.

## What is Clustering?

Clustering is the task of dividing a set of objects into groups, called clusters, so that objects within a cluster are similar to one another and dissimilar to objects in other clusters. Clustering is considered an unsupervised learning problem because the groups are not pre-defined – the algorithm automatically discovers the grouping from the data itself.

For example, a retailer may want to group its customers based on their purchase history. A clustering algorithm could find that the customers fall into five distinct segments: budget conscious, impulse buyers, brand loyal, coupon clippers, and big spenders. The retailer could then tailor marketing strategies for each segment.

There are two main types of clustering:

- Hard clustering: Each object belongs to only one cluster. An example is grouping shoppers as either "deal seekers" or "quality seekers". A shopper can‘t belong to both groups.
- Soft (fuzzy) clustering: Objects can belong to more than one cluster, with a probability or degree of membership in each cluster. For example, a document may be 70% about sports and 30% about health. Soft clustering is more flexible but also more complex.

## Overview of Clustering Algorithms

There are over 100 published clustering algorithms, but most fall into a few main categories:

### Connectivity Models

Connectivity models, like hierarchical clustering, group objects based on the distance between them. Objects that are close are successively combined into clusters. There are two main approaches:

- Agglomerative (bottom-up): Each object starts as its own cluster and close clusters are merged as you move up the hierarchy.
- Divisive (top-down): All objects start in one cluster which is recursively split as you move down the hierarchy.

### Centroid Models

Centroid models, like k-means, represent each cluster by a single mean vector. Objects get assigned to the cluster with the closest centroid. The number of clusters, k, must be specified up front. These algorithms iteratively refine the clusters to find a stable configuration.

### Distribution Models

Distribution models assume the data was generated from a mixture of underlying probability distributions, like Gaussians. The goal is to find the parameters and mixing coefficients of these distributions. A popular distribution model is the expectation-maximization (EM) algorithm.

### Density Models

Density models search for regions of high density separated by regions of low density. Density-based spatial clustering of applications with noise (DBSCAN) and ordering points to identify the clustering structure (OPTICS) are two well-known density-based algorithms. They excel at finding clusters of arbitrary shape.

Now let‘s take a closer look at two of the most widely used clustering methods: k-means and hierarchical clustering.

## K-Means Clustering

K-means is the most popular partitional clustering algorithm. It divides n objects into k clusters, where each object belongs to the cluster with the nearest mean (centroid). The k-means algorithm follows these steps:

1. Specify the number of clusters k.
2. Initialize k centroids randomly.
3. Assign each object to its closest centroid based on the Euclidean distance between the object and centroid.
4. Re-compute the centroids as the mean of all objects in a cluster.
5. Repeat steps 3-4 until the cluster assignments stop changing or a maximum number of iterations is reached.

The goal of k-means is to minimize the within-cluster variance, also known as the sum of squared errors. It does this by iteratively refining the cluster assignments and centroids. However, k-means can get stuck in local minima, so it‘s often run multiple times with different random initializations.

One major limitation of k-means is that you need to specify the number of clusters k in advance. If k is not known a priori, various techniques can be used to determine it, like the elbow method, silhouette analysis, or gap statistic. Another limitation is that k-means favors spherical clusters of equal size and density, which may not match the true shape of groups in the data.

## Hierarchical Clustering

Hierarchical clustering builds a hierarchy of clusters where each node is a cluster consisting of the clusters of its daughter nodes. Strategies for hierarchical clustering generally fall into two types:

- Agglomerative: This is a "bottom-up" approach where each object starts in its own cluster, and pairs of clusters are merged moving up the hierarchy.
- Divisive: This is a "top-down" approach where all objects start in one cluster, and splits are performed recursively moving down the hierarchy.

Agglomerative clustering is the more common of the two. It starts with n clusters (one for each object) and iteratively merges the closest clusters until there is just a single cluster. The results are usually presented in a dendrogram, which is a tree diagram that shows the merging of clusters and the distances at which the merges took place.

To decide which clusters to merge, a distance measure between sets of observations is required. This is done by using a linkage criteria, which determines the distance between sets of observations as a function of the pairwise distances between observations. The common linkage criteria are:

- Single linkage: The shortest distance between objects in the two clusters.
- Complete linkage: The longest distance between objects in the two clusters.
- Average linkage: The average distance between all objects in the two clusters.
- Ward‘s method: The sum of squared differences within all clusters (minimizes variance).

Hierarchical clustering has the advantage that you don‘t need to specify the number of clusters up front. You can choose a cutoff point in the dendrogram to create the desired number of groups. It can also find clusters of arbitrary shape and is less sensitive to outliers compared to k-means.

The disadvantages are that it‘s computationally intensive (O(n^3)) and cannot handle large datasets well. The greedy nature of the algorithm means that merges/splits cannot be undone, even if later steps show they were a poor choice. It also struggles with clusters of very different sizes.

## Comparing K-Means and Hierarchical Clustering

K-means and hierarchical clustering are both widely used, but they have some key differences:

- K-means requires specifying the number of clusters k in advance, while hierarchical clustering does not.
- K-means is more computationally efficient and can handle larger datasets than hierarchical clustering.
- K-means tends to produce spherical clusters of similar size, while hierarchical clustering can find clusters of arbitrary shape and size.
- K-means is sensitive to the initial placement of centroids and can get stuck in local minima, while hierarchical clustering is deterministic and will always produce the same clusters.
- K-means provides a single partitioning of the data, while hierarchical clustering provides an entire hierarchy which allows varying the number of clusters by cutting the dendrogram at different levels.

In practice, the choice between k-means and hierarchical clustering depends on the size and shape of the data, whether you know k in advance, and the computational resources available. It‘s common to run both methods and compare the results.

## Considerations in Clustering

While clustering algorithms are powerful tools, there are several considerations to keep in mind when applying them:

- Outliers and noise can greatly impact the results, especially for methods like k-means that are based on minimizing squared errors. Outlier detection and removal may be necessary.
- The choice of distance measure, like Euclidean vs Manhattan distance, can change the shape and composition of clusters. The best distance measure depends on the data and problem domain.
- Clusters should be validated using external information, like class labels or business knowledge, to assess their meaningfulness and usefulness. Clustering is exploratory, so the results should be interpreted carefully.
- Scaling and normalizing variables before clustering is important so that variables with larger values don‘t dominate the distance calculations. Standardization (mean=0, variance=1) is a common approach.
- Clustering high-dimensional data is challenging due to the curse of dimensionality. Dimensionality reduction techniques like PCA can be used to preprocess the data before clustering.

## Latest Developments in Clustering (2024)

Clustering remains an active area of machine learning research. Some of the latest developments as of 2024 include:

- Deep clustering methods that learn feature representations and cluster assignments simultaneously using deep neural networks. These methods can handle complex data like images and sequences. Examples include deep embedded clustering (DEC) and variational deep embedding (VaDE).
- Kernel-based methods that transform the data to a high-dimensional space to make clusters more separable. Kernel k-means and spectral clustering are popular algorithms in this category.
- Ensemble clustering methods that combine multiple partitionings of the data to obtain a more robust clustering. Examples are consensus clustering, clusterfusion, and hypergraph partitioning.
- Streaming clustering methods that can process data in a single pass and update clusters incrementally. This is useful for clustering massive or evolving datasets. Representative algorithms include CluStream, DenStream, and StreamKM++.
- Subspace and correlation clustering methods that can find clusters in different subspaces of high-dimensional data. These methods don‘t require objects to be close in all dimensions, only in relevant subspaces. Examples are CLIQUE, SUBCLU, and ORCLUS.

## Conclusion

Clustering is a core technique in unsupervised machine learning for finding groups of similar objects in data. There is a spectrum of clustering algorithms, from simple methods like k-means to more advanced methods like distribution and density-based models. Hierarchical clustering is another popular approach that builds a tree of clusters.

When using clustering in practice, it‘s important to carefully preprocess your data, choose an appropriate algorithm and distance measure, and validate the results. With the rapid pace of research, new and improved clustering techniques are constantly emerging to handle more complex types of data.

Whether you‘re a beginner or an experienced practitioner, we hope this guide has clarified the key concepts and algorithms in clustering. For further learning, we recommend experimenting with clustering on real datasets and staying up to date with the latest research in this exciting field.

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Source: [An In\-Depth Guide to Clustering Algorithms for Machine Learning](https://33rdsquare.com/an-introduction-to-clustering-and-different-methods-of-clustering/)