Consider a centroid-based clustering algorithm with the following objective function: J(,U)=i=1Nk=1Kuikmd2(xi,k),suchthat0uik1 where d2(xi,k) is the distance of sample xi to cluster centroid k,uik is the membership value of sample xi in cluster with centroid k in the range [0,1], and m is a scalar with m>1. 1. (1 point) Discuss whether we need to include the constraint k=1Kuik=1. Explain why or why not? 1. (1 point) Propose a term to be added onto J(,U) to ensure that the membership value for each sample xi is close to 1 for at least one of the cluster groups k, while leaving outliers with low membership values