1Cademy - ROUGE-L Metric

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Definition

ROUGE-L Metric

ROUGE-L is an automatic summary/text-similarity metric that scores how closely a candidate text X reproduces a reference text Y using the length of their longest common subsequence (LCS). Let $m=|Y|$ , $n=|X|$ , and $\mathrm{LCS}(X,Y)$ be the length of the longest sequence of tokens that appears in both X and Y in the same relative order (not necessarily contiguous). ROUGE-L defines recall $R_{\mathrm{lcs}}=\dfrac{\mathrm{LCS}(X,Y)}{m}$ , precision $P_{\mathrm{lcs}}=\dfrac{\mathrm{LCS}(X,Y)}{n}$ , and the F-measure $F_{\mathrm{lcs}}=\dfrac{(1+\beta^{2}),R_{\mathrm{lcs}},P_{\mathrm{lcs}}}{R_{\mathrm{lcs}}+\beta^{2},P_{\mathrm{lcs}}}$ , where $\beta$ weights recall relative to precision. Because LCS only requires in-order token agreement, ROUGE-L rewards sentence-level structural overlap between two texts even when matched words are not adjacent, which is why it is reported alongside lexical overlap baselines (e.g., TF-IDF cosine, n-gram Jaccard) when comparing a rewritten draft to its original.