Ward's method is a popular hierarchical clustering algorithm used to group similar data points into clusters. It is a bottom-up approach where each data point starts as its own cluster and is merged with other clusters based on the proximity of the data points. The goal of Ward's method is to minimize the sum of squared differences within each cluster.
The process of Ward's method can be broken down into the following steps:
Calculate the distance between all pairs of data points: This can be done using a variety of distance metrics such as Euclidean distance, Manhattan distance, or cosine similarity.
Initialize each data point as its own cluster: In the first iteration of the algorithm, each data point is considered its own cluster.
Merge the two closest clusters: In each subsequent iteration of the algorithm, the two closest clusters are merged into a single cluster. The distance between two clusters can be calculated using several methods such as the minimum distance between any two data points in the two clusters, the maximum distance, or the average distance.
Calculate the within-cluster sum of squares (WSS): After each merge, the WSS is calculated to determine the quality of the clustering. The WSS is the sum of squared differences between each data point in a cluster and the centroid of that cluster. The goal of the algorithm is to minimize the total WSS across all clusters.
Repeat steps 3 and 4 until all data points are in a single cluster: The algorithm continues to merge the closest clusters until all data points are part of a single cluster.
Ward's method is known for its ability to create compact and spherical clusters. It tends to produce clusters of roughly equal sizes and can be effective in identifying clusters with varying densities. However, it can be computationally expensive and may not be suitable for large data sets.
Overall, Ward's method is a powerful tool for exploratory data analysis and can be used in a variety of applications such as customer segmentation, image clustering, and bioinformatics.