Which metric measures the distance between a data point and its cluster centroid?

The metric that specifically measures the distance between a data point and its cluster centroid is the Euclidean distance. This measure calculates the straight-line distance between two points in a multi-dimensional space, making it very relevant in clustering algorithms, such as K-means. When performing clustering, the algorithm uses Euclidean distance to determine how close a data point is to the centroid of a cluster. Each point is assigned to the cluster whose centroid is closest to it, which is primarily based on this distance calculation.

While within-cluster sum of squares (WCSS) is an important metric in clustering, it does not measure the distance of an individual point to the centroid. Instead, WCSS aggregates the squared distances of all points within a cluster from the cluster’s centroid, providing insight into the compactness of a cluster but not the specific distance of a single data point.

Variance and standard deviation, on the other hand, are statistical measures of spread or dispersion within a dataset but do not specifically relate to the distance from a point to a cluster centroid. They are more focused on the distribution of values within a set rather than the relationship between data points and centroids in clustering contexts.