Partitioning clustering algorithms iteratively define k cluster centers and assign cluster membership (or the probability of group membership) to cases based on distances between the case and the cluster. Agglomerative clustering algorithms also create clusters based on distances, starting with each individual belonging to a separate cluster and the grouping clusters two by two. The k-nearest neighbors algorithm also uses distance measures.
Consider only one attribute, for instance the height of individuals. The distance of someone measuring 180 cm and someone measuring 170 cm will be 10 on this sole dimension considering the algebraic difference between the two measures as our distance metric. Things get a little more complicated when we add more attributes, such as weight (we will not consider variable scaling here). Let's say the first individual is clearly overweight (90 kg), and the second has a normal weight (80 kg). Considering only the sum of the difference between...
