# Solving Scale and Permutation indeterminacies in Blind Source Separation

Many papers using blind source separation algorithms solve the inherent scale and permutation indeterminacies of the estimated mixing matrix using an "optimal method", however this method is never explained. How does this work?

What i know in implementations of BSS (e.g jade) is that they first normalise the input data (to variance = 1) and then order the data according to scale. So this is unique and will produce consistent output ordering for the same input data (will add references shortly).

Have in mind however that this is just a consistent heuristic (any consistent heuristic will do) as BSS methods by definition are clue-less about scaling and permutation of the inputs.

References of permutation problem for jade:

The following heuristic is described in the comments section of the matlab version of jade:

% Usage:
%   * If X is an nxT data matrix (n sensors, T samples) then
%     B=jadeR(X) is a nxn separating matrix such that S=B*X is an nxT
%     matrix of estimated source signals.
%   * If B=jadeR(X,m), then B has size mxn so that only m sources are
%     extracted.  This is done by restricting the operation of jadeR
%     to the m first principal components.
%   * Also, the rows of B are ordered such that the columns of pinv(B)
%     are in order of decreasing norm; this has the effect that the
%     most energetically significant' components appear first in the
%     rows of S=B*X.
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