Cosine Distance

    • useful in spaces that have dimensions
      • Euclidian spaces
      • Discrete euclidian spaces (i.e vectors of integers, vector of bools)
      • …
    • Points are thought as directions
    • No distinction between a vector and a multiple of it

    The Cosine Distance between two points is the angle that the vectors to these points make

    • The angle will be between 0∘0^{\circ} and 180∘180^{\circ} regardless of how many dimensions the space has
    dcos(a⃗,b⃗)=arcos(a⃗⋅b⃗∥a⃗∥2⋅∥b⃗∥2)=arcos(∑i=1nai⋅bi∥a⃗∥2⋅∥b⃗∥2)d_{cos}(\vec a, \vec b) = arcos \left ( \frac{\vec a \cdot \vec b}{\| \vec a \|_2 \cdot \| \vec b \|_2} \right ) = arcos \left ( \frac{\sum_{i=1}^na_i \cdot b_i}{\| \vec a \|_2 \cdot \| \vec b \|_2} \right )

    • Category

    • Mathematics

    • Tags

    • Data Minig
      ETH

    • Created

    • 8. January 2016

    • Modified

    • 3. June 2023