问题
minΣ(||xi-Xci||^2+ λ||ci||),
s.t cii = 0,
where X is a matrix of shape d * n and C is of the shape n * n, xi and ci means a column of X and C separately.
X is known here and based on X we want to find C.
回答1:
Usually with a loss like that you need to vectorize it, instead of working with columns:
loss = X - tf.matmul(X, C)
loss = tf.reduce_sum(tf.square(loss))
reg_loss = tf.reduce_sum(tf.square(C), 0) # L2 loss for each column
reg_loss = tf.reduce_sum(tf.sqrt(reg_loss))
total_loss = loss + lambd * reg_loss
To implement the zero constraint on the diagonal of C, the best way is to add it to the loss with another constant lambd2:
reg_loss2 = tf.trace(tf.square(C))
total_loss = total_loss + lambd2 * reg_loss2
来源：https://stackoverflow.com/questions/38376473/how-do-i-implement-the-optimization-function-in-tensorflow