A similarity metric estimates how alike two represented items are. For vector representations, the dot product provides a first quantitative measure: similar vectors tend to produce larger values, while dissimilar or perpendicular vectors produce values near zero. Vectors pointing in opposite directions produce negative dot products. section 2.5.6
For vectors a and b, a·b = aᵀb = aₓbₓ + aᵧbᵧ = ||a|| ||b|| cos(θ). The result reflects how much one vector lies along the other: aligned directions increase the score, perpendicular directions remove directional agreement, and opposite directions reverse it. section 2.5.6
Document retrieval
Represent each document with a descriptor vector whose dimensions correspond to vocabulary terms and whose values record word frequencies. A query can then be compared with archive documents using vector dot products, allowing documents to be ranked by estimated similarity. Sparse storage keeps only the word–frequency pairs for terms that occur. section 4.1
A small comparison
The feature vectors for documents d5 and d6 have dot product 1 × 0 + 0 × 1 = 0, matching their lack of common words of interest. The vectors for d3 and d4 have a higher dot product, matching their greater overlap. section 2.5.6
