k-means interesting because it has a latent variable in it so the energy function is not directly a function is the minimum of some other more elementary energy function okay so it's the the min over a vector Z of the squared distance between the data point and the this Z vector multiplied by a matrix whose columns are the prototypes of the the k-means model and you constrain this vector to be a one heart vector okay so only one one only one component can be one the other ones have to be 0 and so you have to do this search exhaustively which is