I am currently reading a scientific paper about clustering of brain signals, which consist on long time series across many channels (each signal is a matrix of C channels by T time samples). In the preprocessing of their datas, the authors normalize each signal matrix by dividing it with its Frobenius norm. My problem is that they don't even say why they do so... is this so obvious that I can't see it?
Any thought?
Thanks!
My educated guess is that they want to compare relative values, not absolute ones, for purposes of clustering. Perhaps they chose the Frobenius norm because it is easy to calculate.
edit: So the Frobenius norm was chosen out of computational considerations. It is easy to compute because it does not necessitate SVD, as required of the spectral norm. Moreover, it is easy to update when expanding or reducing the matrix.
Once you normalize something by its norm, it is obviously going to have a unit norm (i.e., lie on the unit sphere).