you compute the square error so in this case the C cost function here is just a square error between the data points and the multiplication of a matrix by latent vector okay this is like a means except we don't constrain this vector to be one of K and there's a problem with this if you just use this without anything else if Z has the same dimension as Y your bigger or even slightly smaller there's always going to be a wire that's going to reconstruct ie it is always going to be a Z that is going to perfectly