Clustering is a machine learning technique that involves grouping data points together. In theory, data points that are in the same group should have similar characteristics or properties, while data points in different groups should have distinct characteristics. Among clustering algorithms, K-Means and Hierarchical Clustering are among the most used. In this text, we will explore these two methods in detail.
K-Means Clustering
K-Means is a clustering method that aims to partition n observations into k clusters, where each observation belongs to the cluster with the closest mean. This method is particularly computationally efficient and easy to implement, making it one of the most popular clustering algorithms.
How K-Means works
The K-Means algorithm follows a simple approach to classify a given set of data through a certain number of clusters (assumed to be k clusters). The process consists of the following steps:
- Initialization: Choosing k random points as cluster centers (centroids).
- Assignment: Assign each data point to the nearest centroid, forming k clusters.
- Update: Recalculate the centroids to be the center (average) of all data points assigned to the cluster.
- Repetition: Repeat steps 2 and 3 until the centroids do not change significantly, which indicates convergence of the algorithm.
K-Means Challenges
Despite its simplicity and efficiency, K-Means faces some challenges:
- Choosing the k number of clusters can be difficult and may require methods such as the elbow method or silhouette analysis to determine the optimal number of clusters.
- The algorithm is sensitive to the initialization of centroids and can converge to local minima. This can be partially mitigated with methods like K-Means++ for smarter initialization of centroids.
- K-Means assumes that clusters are spherical and of similar size, which may not be the case for all datasets.
Hierarchical Clustering
In contrast to K-Means, hierarchical clustering does not require prior specification of the number of clusters. Instead, it creates a tree of clusters called a dendrogram, which allows you to visualize the structure of the data and determine the number of clusters by analyzing the dendrogram.
How Hierarchical Clustering works
There are two types of hierarchical clustering: agglomerative (bottom-up) and divisive (top-down). The agglomerative method is the most common and works as follows:
- Start by treating each data point as an individual cluster.
- Find the two closest clusters and combine them into a single cluster.
- Repeat step 2 until all data points are in a single cluster.
The result is a tree that reflects the structure of the data.
Distance Measurement in Hierarchical Clustering
A crucial part of hierarchical clustering is choosing a distance metric to determine the proximity between clusters. Some of the most common metrics include:
- Euclidean Distance
- Distance from Manhattan
- Maximum Distance
- Distance from Mahalanobis
In addition, it is necessary to define how to measure the distance between sets of data points (clusters). Some approaches include the simple link method (smallest distance between points from different clusters), full link (largest distance between points from different clusters) and average link (average distance between all pairs of points from different clusters).
Advantages and Disadvantages of Hierarchical Clustering
Hierarchical clustering has several advantages and disadvantages:
- Advantages:
- It is not necessary to specify the number of clusters beforehand.
- The dendrogram produced is very informative and shows the structure of the data.
- May be more suitable for certain types of structural data.
- Disadvantages:
- Computationally more intensive than K-Means, especially for large data sets.
- Difficult to apply whenWe don't have a large amount of data.
- Once a data point is assigned to one cluster, it cannot be moved to another.
Conclusion
K-Means and Hierarchical Clustering clustering algorithms are powerful tools for unsupervised data analysis. K-Means is suitable for large data sets and where you have an idea of the number of clusters. Hierarchical clustering is useful when the data structure is unknown and a visual representation is desired through the dendrogram. The choice between the two methods will depend on the specific characteristics of the data set and the objectives of the analysis.
