Maximal Marginal Relevance (MMR)

MMR builds the final keyphrase set iteratively. In each step, it selects the candidate that maximizes the MMR score, which is a linear combination of relevance and novelty. The algorithm starts with the most relevant phrase and then penalizes subsequent candidates based on their maximum similarity to the already chosen set, ensuring broad topical coverage.

The λ (lambda) parameter, typically ranging from 0 to 1, controls the trade-off between relevance and diversity.

• λ=1: Pure relevance ranking; the algorithm ignores redundancy and selects the top-scoring candidates.
• λ=0: Maximal diversity; the algorithm aggressively penalizes similarity, potentially selecting less relevant but unique phrases.
• λ=0.5 to 0.7: A common balanced range for keyphrase extraction, ensuring the selected terms are both salient and distinct.

The penalty term in MMR relies on a pairwise similarity function between candidate phrases. The choice of this metric critically shapes the final output.

• Cosine Similarity on TF-IDF vectors: A classic, sparse representation that penalizes lexical overlap.
• Cosine Similarity on Embeddings: Using models like BERT or Sentence-BERT captures semantic redundancy, penalizing synonyms and paraphrases.
• Jaccard Similarity: A simple token-overlap coefficient useful for penalizing exact word repetition.

MMR is a re-ranking framework, not a standalone extraction method. It requires an initial relevance score for each candidate phrase. This score can come from any upstream method:

• TF-IDF or BM25 for statistical salience.
• TextRank for graph-based centrality.
• Embedding similarity (e.g., cosine similarity between the phrase embedding and the document embedding). MMR then adjusts these raw relevance scores by subtracting the redundancy penalty.

For a candidate phrase c and the set of already selected phrases S, the penalty is calculated as max_{s in S} sim(c, s). This means a candidate is penalized based on its similarity to the single most similar already-selected phrase. This max-based penalty aggressively prevents near-duplicate keyphrases from entering the final set, promoting a high-level topical diversity rather than a clustered set of related terms.

A graph-based ranking algorithm that builds a word or phrase co-occurrence network and applies PageRank to identify the most salient keyphrases.

• Mechanism: Vertices are lexical units; edges represent co-occurrence within a sliding window.
• Redundancy Handling: Unlike MMR, TextRank relies on graph centrality rather than explicit diversity penalties.
• Use Case: Unsupervised extraction of present keyphrases without external corpora.

An embedding-based approach that ranks candidate phrases by the cosine similarity between their sentence embeddings and the document embedding.

• Semantic Core: Uses Sentence-BERT or similar models to capture topical alignment.
• MMR Variant: EmbedRank++ applies MMR to the ranked list to penalize redundancy among selected phrases.
• Advantage: Captures semantic similarity beyond exact lexical overlap.

A robust data fusion method that combines ranked lists by summing the reciprocal of the rank positions assigned to each candidate.

• Formula: RRF_score(d) = Σ 1/(k + rank_i(d)) where k is a constant (typically 60).
• Relationship to MMR: Often used to merge the output of multiple extraction algorithms before applying MMR re-ranking.
• Strength: Outperforms linear combination when rank distributions are disparate.

An evaluation metric computing the harmonic mean of precision and recall for the top-K predicted keyphrases against a gold-standard set.

• Precision@K: Correct predictions in top-K / K.
• Recall@K: Correct predictions in top-K / total gold keyphrases.
• MMR Context: MMR optimizes for this metric by ensuring the top-K set is both relevant and diverse.

The process of assigning a numerical weight to each candidate phrase based on features like frequency, position, and semantic similarity.

• Features: TF-IDF, first occurrence offset, POS tag patterns, embedding similarity.
• Pre-MMR Step: Candidate scoring establishes the initial relevance ranking that MMR then re-orders for diversity.
• Supervised Variants: Models like BERT-KPE learn to score candidates directly from labeled data.

Two orthogonal scoring dimensions used in unsupervised keyphrase extraction.

• Phraseness: Measures how linguistically well-formed a candidate is (e.g., noun phrase chunking).
• Informativeness: Measures how well a phrase captures the document's topical content.
• MMR Integration: MMR primarily operates on the informativeness dimension, ensuring selected phrases cover distinct aspects of the document.