As for the understanding of the function of the l2,1 norm-regularization term, different from the sparse requirement of the L1 norm (the sum of the absolute value of the matrix element), the l21 norm also requires a sparse machine learning mathematics.

When we discussed the problem with our tutor today, we talked about the l21 norm. Derivative hope I can explain, I understand its role but I know I did not explain to the teacher clearly, some lost. Make a summary of yourself tonight and hope that I can explain it to someone again the next time someone asks me this question.

First look at the definition of the l21 norm above, note that the original matrix is n row t columns, the square root is the sum of the columns, that is, in the same row, the root is equivalent to a L2 norm, it can be seen that the l21 norm is the sum of the L2 norm of each row of the matrix X .

In the sparse representation model of matrices, what is the role of it as a regularization term ? As mentioned above, it is the sum of the L2 norm of each line, and in minimizing the problem, only the minimum L2 norm of each row is the smallest. And each line norm gets the minimum meaning that the constraint can be minimized when the maximum number of elements in the row is 0 o'clock. And the line as much as possible to take 0 means that the line is sparse.

It can be explained in this way that, unlike the sparse requirements of the L1 norm (the sum of the absolute values of the matrix elements), the l21 norm also requires a sparse line.

(as if I had given the teacher a sparse list today, although the sparse difference between the lines in the problem I encountered was not too great ...) Of course there are L12, the key is to see how the specific definition, we refer to this class collectively as structured sparse. After people ask me questions I must be as clear as possible with others ... ）