In clustering, what is the term for the point where the mean distance between data examples and their centroid stabilizes?

The concept of the "Elbow Point" refers to a specific point in a graph that displays the relationship between the number of clusters and the sum of squared distances between data points and the centroids of the clusters. As more clusters are added, the mean distances generally decrease, but at a certain point, adding more clusters yields diminishing returns; the decrease in distance stabilizes and forms an elbow shape in the graph. This point signals an optimal number of clusters for the data, as beyond this point, the additional clusters do not significantly reduce the mean distance.

In clustering analysis, identifying the Elbow Point helps practitioners to decide how many clusters to use without overfitting the model or increasing complexity unnecessarily. This makes it critical to the clustering process, ensuring that the model remains interpretable and efficient while capturing the underlying structure of the data.

The other terms, while relevant in clustering, do not specifically describe this phenomenon. "Saturation Point" could refer to a similar concept but is not widely used in clustering contexts. "Centroid Stability" is a more general term that could pertain to how consistently centroids represent their respective clusters over time, while "Clustering Threshold" might imply parameters set during clustering but does not capture the concept of stabil