基于tf-idf的稀疏检索

Sparse Retrieval with tf-idf

A collection has $N = 4$ documents and a term occurs in $\text{df} = 1$ of them. Compute $\text{idf} = \log_{10}(N/\text{df})$, rounding to three decimals.

A term appears 1 times in a document. Compute its tf as $1 + \log_{10}(\text{count})$, rounding to three decimals.

A one-word document contains exactly the query's single term, with everything else zero. What cosine does the tf-idf scoring assign, and why?

A user queries two terms. How does the inverted index make scoring efficient?

In BM25, what do the parameters $k$ and $b$ control, and what happens at the extremes?