基于word-frequency与document-frequency的文本相似度度量方法咨询

Great question! Let's walk through this based on your existing workflow and the similarity requirements you've laid out.

First, let's align on what you're working with:

• You've preprocessed your corpus: tokenization → stopword removal → stemming
• You have two key metrics:
  • word-frequency: Total occurrences of a word across all documents
  • document-frequency: Number of documents that contain the word
• Your goal: Score similarity between a new text and your existing corpus, with rules like:
  • "hunters love foxes" → high similarity (all words exist in your corpus)
  • "deer are funny" → 0 similarity (none/key words don't exist in your corpus)

1. Strict Vocabulary Match + Weighted Importance (Perfect for Your Example) #

This formula enforces the "0 similarity if any word is new" rule, while weighting words by their importance in your existing corpus:

Similarity = (sum(weight(w) for w in preprocessed_new_text)) / len(preprocessed_new_text)

Where weight(w) is defined as:

• If w does NOT exist in your corpus's vocabulary (post-preprocessing): weight(w) = 0 → and if any word has weight 0, the entire similarity score becomes 0 (you can add a check for this upfront to optimize)
• If w DOES exist:

  weight(w) = (word_freq(w) / total_words_in_corpus) * log(total_documents / doc_freq(w))
  

Breakdown of the Weight Formula: #

• word_freq(w) / total_words_in_corpus: Measures how common the word is across your entire corpus (more frequent words get a base boost)
• log(total_documents / doc_freq(w)): Acts like a simplified IDF (Inverse Document Frequency) — it penalizes words that appear in almost every document (since they're less distinctive) and boosts words that are more unique to subsets of your corpus
• Multiplying these two gives a balanced weight that accounts for both prevalence and uniqueness

How It Fits Your Examples: #

• For "hunters love foxes": After preprocessing, all words exist in your corpus. The weighted sum will be positive, and dividing by the number of words gives a high similarity score (you can normalize this to 0-1 if needed)
• For "deer are funny": At least one preprocessed word (e.g., "deer") isn't in your corpus, so the score drops to 0 immediately

2. Partial Match Variant (If You Want Flexibility) #

If you ever need to allow partial matches (instead of a hard 0 score when a new word is present), adjust the formula to only sum weights for words that exist in your corpus:

Similarity = (sum(weight(w) for w in preprocessed_new_text if w in corpus_vocabulary)) / len(preprocessed_new_text)

This way, a text with some new words will get a lower (but non-zero) score proportional to how many of its words are familiar to your corpus.

• Consistent Preprocessing: Make sure you apply the exact same tokenization, stopword removal, and stemming logic to new texts as you did to your original corpus — mismatched preprocessing will lead to false "new word" flags
• Normalization: If you want scores to fall neatly between 0 and 1, divide the final similarity value by the maximum possible weight sum (e.g., the sum of weights for the most impactful words in your corpus)
• Tuning: Feel free to adjust the weight formula to fit your priorities. For example, if you care more about word frequency than uniqueness, you can drop the log term entirely, or weight the frequency component more heavily.

内容的提问来源于stack exchange，提问作者bodacydo