Degeneracy problem in PARAFAC models

Persistent degeneracies can also be caused by poor preprocessing. In such a case, degenerate solutions are observed even for a (too) low number of components. Extracting too many components can also give a degeneracy-like problem because the noise components can be correlated. Some details about degeneracies can be found in Section 6.3. 

A typical sign of a degeneracy is that two of the components become almost identical but with opposite sign or contribution to the model. The contribution of the components almost cancel each other. In PARAFAC each rank-one component can be expressed as the vectorized rank-one array obtained as 

This means that the loading vectors in component r and component p will be almost equal in shape, but negatively correlated. 

An indication of degenerate solutions can thus be obtained by monitoring the correlation between all pairs of components. For three-way PARAFAC, the measure in Equation (5.22) can be calculated as 

Multi-way Analysis With Applications in the Chemical Sciences 

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