Blind signal separation (BSS) is a powerful tool to open-up complex signals into component sources that are often interpretable. However, BSS methods are generally unsupervised, therefore the assignment of class membership from the elements of the mixing matrix may be sub-optimal. This paper proposes a three-stage approach using Fisher information metric to define a natural metric for the data, from which a Euclidean approximation can then be used to drive BSS. Results with synthetic data models of real-world high-dimensional data show that the classification accuracy of the method is good for challenging problems, while retaining interpretability.