location and to measure the reconstruction error of a particular point you figure out which prototype is closest to it and then the reconstruction error is the distance between the data point and the reconstruction and the the the closest prototype okay so the minimizing with respect to the Z vector will figure out which column of W which is which prototype is close as to why and that's the that's the one that produces the lowest reconstruction error and so now the energy function is defined as the minimum of Z where Z is a word of one of