Clustering is the task of grouping observations in such a way that members of the same cluster are more similar to each other and members of different clusters are very different from each other.

Clustering is commonly used to explore a dataset to either identify the underlying patterns in it or to create a group of characteristics. In the case of social networks, they can be clustered to identify communities and to suggest missing connections between people. Here are a few examples:

• In anti-money laundering measures, suspicious activities and individuals can be identified using anomaly detection
• In biology, clustering is used to find groups of genes with similar expression patterns
• In marketing analytics, clustering is used to find segments of similar customers so that different marketing strategies can be applied to different customer segments accordingly

The k-means clustering algorithm is an iterative process of moving the centers of clusters or centroids to the mean position of their constituent points, and reassigning instances to their closest clusters iteratively until there is no significant change in the number of cluster centers possible or number of iterations reached.

The cost function of k-means is determined by the Euclidean distance (square-norm) between the observations belonging to that cluster with its respective centroid value. An intuitive way to understand the equation is, if there is only one cluster (k=1), then the distances between all the observations are compared with its single mean. Whereas, if, number of clusters increases to 2 (k= 2), then two-means are calculated and a few of the observations are assigned to cluster 1 and other observations are assigned to cluster two-based on proximity. Subsequently, distances are calculated in cost functions by applying the same distance measure, but separately to their cluster centers: