Vector Space Model

Vector Space Model

The VSM represents documents and queries as vectors in a high-dimensional term space. Each dimension corresponds to a term; weights are typically TF-IDF. Similarity is computed via cosine similarity.

Cosine Similarity

$\text{sim}(q,d)=\frac{\vec{q}\cdot \vec{d}}{|\vec{q}|\cdot |\vec{d}|}=\frac{{\sum }_i{q}_i\cdot d_i}{\sqrt{{\sum }_i{q}_i^2}\cdot \sqrt{{\sum }_i{d}_i^2}}$

Properties:

• Handles partial matching (unlike Boolean retrieval)
• Length normalization via cosine
• Foundation extended by BM25 and Dense Retrieval (learned dense vectors)

Appears In

• IR-L02 - IR Fundamentals, IR-L03 - Retrieval Models