Matrix norm in TensorFlow
python, tensorflow
Solution
So the Frobenius norm is a sum over a `nxm` matrix, but `tf.norm` allows to process several vectors and matrices in batch.
To better understand, imagine you have a rank 3 tensor:
`t = [[[2], [4], [6]], [[8], [10], [12]], [[14], [16], [18]]]`
It can be seen as several matrices aligned over one direction, but the function can't figure by itself which one. It could be either a batch of the following matrices:
`[2, 4, 6] , [8 ,10, 12], [14, 16, 18]`
or
`[2 8 14], [4, 10, 16], [6, 12, 18]`
So basically `axis` tells which directions you want to consider when doing the summation in the Frobenius norm.
In your case, any of `[1,2]` or `[-2,-1]` would do the trick.
Problem
I need to compute the Frobenius norm in order to achieve this formula using the TensorFlow framework: where `w` is a matrix with 50 rows and 100 columns. I tried to write something, but I don't understand how to fill out the `axis` argument. ``` tf.pow( tf.norm(x, ord='fro', axis=?), 2 ) ``` According to the TensorFlow docs I have to use a 2-tuple (or a 2-list) because it determines the axies in tensor over which to compute a matrix norm, but I simply need a plain Frobenius norm. In `SciPy`, for example, I can do it without specify any axis. So, what should I use as `axis` to emulate the `SciPy` function?