= Cumulative coherence
{title2=$\mu_1(k)=\max_i\max_{|S|=k,\ i\notin S}\sum_{j\in S}|\langle a_i,a_j\rangle|$}
= L1 coherence
{c}
{synonym}
For unit <Euclidean norm> columns, cumulative coherence measures the largest sum of $k$ correlations with one other column. Its domain is $0\le k\le N-1$, with $\mu_1(0)=0$ by the empty-sum convention. It is nondecreasing, $\mu_1(1)=\mu$ for $N\ge2$, and $\mu_1(k)\le k\mu$, where $\mu$ is the <mutual coherence>. Keeping a sum of actual correlations can be substantially sharper than replacing each summand by the largest one.
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