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Maximal Marginal Relevance

Calculate Maximal Marginal Relevance (MMR) between candidate keywords and the document.

MMR considers the similarity of keywords/keyphrases with the document, along with the similarity of already selected keywords and keyphrases. This results in a selection of keywords that maximize their within diversity with respect to the document.

Parameters:

Name Type Description Default
doc_embedding ndarray

The document embeddings

required
word_embeddings ndarray

The embeddings of the selected candidate keywords/phrases

required
words List[str]

The selected candidate keywords/keyphrases

required
top_n int

The number of keywords/keyhprases to return

5
diversity float

How diverse the select keywords/keyphrases are. Values between 0 and 1 with 0 being not diverse at all and 1 being most diverse.

0.8

Returns:

Type Description
List[Tuple[str, float]]

The selected keywords/keyphrases with their distances

Source code in keybert\_mmr.py
def mmr(
    doc_embedding: np.ndarray,
    word_embeddings: np.ndarray,
    words: List[str],
    top_n: int = 5,
    diversity: float = 0.8,
) -> List[Tuple[str, float]]:
    """Calculate Maximal Marginal Relevance (MMR)
    between candidate keywords and the document.


    MMR considers the similarity of keywords/keyphrases with the
    document, along with the similarity of already selected
    keywords and keyphrases. This results in a selection of keywords
    that maximize their within diversity with respect to the document.

    Arguments:
        doc_embedding: The document embeddings
        word_embeddings: The embeddings of the selected candidate keywords/phrases
        words: The selected candidate keywords/keyphrases
        top_n: The number of keywords/keyhprases to return
        diversity: How diverse the select keywords/keyphrases are.
                   Values between 0 and 1 with 0 being not diverse at all
                   and 1 being most diverse.

    Returns:
         List[Tuple[str, float]]: The selected keywords/keyphrases with their distances

    """

    # Extract similarity within words, and between words and the document
    word_doc_similarity = cosine_similarity(word_embeddings, doc_embedding)
    word_similarity = cosine_similarity(word_embeddings)

    # Initialize candidates and already choose best keyword/keyphras
    keywords_idx = [np.argmax(word_doc_similarity)]
    candidates_idx = [i for i in range(len(words)) if i != keywords_idx[0]]

    for _ in range(min(top_n - 1, len(words) - 1)):
        # Extract similarities within candidates and
        # between candidates and selected keywords/phrases
        candidate_similarities = word_doc_similarity[candidates_idx, :]
        target_similarities = np.max(
            word_similarity[candidates_idx][:, keywords_idx], axis=1
        )

        # Calculate MMR
        mmr = (
            1 - diversity
        ) * candidate_similarities - diversity * target_similarities.reshape(-1, 1)
        mmr_idx = candidates_idx[np.argmax(mmr)]

        # Update keywords & candidates
        keywords_idx.append(mmr_idx)
        candidates_idx.remove(mmr_idx)

    # Extract and sort keywords in descending similarity
    keywords = [
        (words[idx], round(float(word_doc_similarity.reshape(1, -1)[0][idx]), 4))
        for idx in keywords_idx
    ]
    keywords = sorted(keywords, key=itemgetter(1), reverse=True)
    return keywords
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