Which clustering algorithm starts with all data examples in a single cluster and splits them?

The appropriate choice for the clustering algorithm that begins with all data examples in a single cluster and then proceeds to split them is hierarchical derivative clustering. This particular type of clustering is based on a hierarchical structure that allows for the division of a dataset into increasingly smaller clusters. It typically starts with a single cluster that encompasses all data points and then iteratively splits the clusters based on a defined criterion, often involving distance measures or similarity metrics.

Hierarchical clustering creates a tree-like structure, also known as a dendrogram, where each data point or cluster can be combined or further divided based on their characteristics. This process continues until each data point is in its own individual cluster or until a stopping criterion is met. The key aspect of this algorithm is its divisive nature, differentiating it from other clustering methods that may operate differently, such as with predefined numbers of clusters or aggregation methods.

Other clustering algorithms listed have distinct methodologies: K-means clustering typically starts by randomly initializing a set number of clusters and updates them based on data points' assignments. Affinity propagation uses a message-passing approach to simultaneously update cluster assignments without starting with an initial number of clusters. Gaussian mixture models assume that data are generated from a mixture of several Gaussian distributions, which introduces probabilistic assignments