Distance measures

Some of the most relevant measurement techniques

Distance
Formula

Euclidean

d(x,y)=i=1n(xiyi)2d(\mathbf{x}, \mathbf{y}) = \sqrt{ \sum_{i=1}^{n} (x_i - y_i)^2 }

Cosine

cosine_similarity(x,y)=xyxy\text{cosine\_similarity}(\mathbf{x}, \mathbf{y}) = \frac{\mathbf{x} \cdot \mathbf{y}}{\|\mathbf{x}\| \, \|\mathbf{y}\|}

Manhattan

d(x,y)=i=1nxiyid(\mathbf{x}, \mathbf{y}) = \sum_{i=1}^{n} |x_i - y_i|

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