# Squared Error Function

(Redirected from squared error)
• Given a set of observations (x1, x2, …, xn), where each observation is a d-dimensional real vector, k-means clustering aims to partition the n observations into k (≤ n) sets S = {S1S2, …, Sk} so as to minimize the within-cluster sum of squares (WCSS). In other words, its objective is to find: $\underset{\mathbf{S}} {\operatorname{arg\,min}} \sum_{i=1}^{k} \sum_{\mathbf x \in S_i} \left\| \mathbf x - \boldsymbol\mu_i \right\|^2$ where μi is the mean of points in Si.