Neighbourhood space

The Babel function (also known as cumulative coherence) measures the maximum total coherence between a fixed atom and a collection of other atoms in a dictionary.

Definition and formulation

The Babel function of a dictionary $𝑨$ with normalized columns is a real-valued function that is defined as

$\mu (p)=\underset{|\lambda |=p}{max}\{\underset{j\notin \lambda }{max}\{\sum _{i\in \lambda }|{𝒂}_i^{𝑻}{𝒂}_j|\}\}$

where ${𝒂}_k$ are the columns (atoms) of the dictionary $𝑨$

References

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