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where <math>\| \cdot \|</math> is a norm and <math>\varepsilon</math> the recurrence threshold. An alternative, more formal expression is using the [[Heaviside step function]] <math>R(i,j)=\Theta(\varepsilon - D_{i,j})</math>
with <math>D_{i,j} = \| \vec{x}(i)- \vec{x}(j) \|</math> the norm of distance vector between <math>\vec{x}(i)</math> and <math>\vec{x}(j)</math>.
Alternative recurrence definitions consider different distances <math>D_{i,j}</math>, e.g., [[angular distance]], [[fuzzy set|fuzzy distance]], or [[Levenshtein distance|edit distance]]<ref name="marwan2023">{{cite journal
| author1=N. Marwan | author2=K. H. Kraemer
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