Distance metrics¶
Common distance functions.
euclidean
¶

numpy_ml.utils.distance_metrics.
euclidean
(x, y)[source]¶ Compute the Euclidean (L2) distance between two real vectors
Notes
The Euclidean distance between two vectors x and y is
\[d(\mathbf{x}, \mathbf{y}) = \sqrt{ \sum_i (x_i  y_i)^2 }\]Parameters: x,y ( ndarray
s of shape (N,)) – The two vectors to compute the distance betweenReturns: d (float) – The L2 distance between x and y.
chebyshev
¶

numpy_ml.utils.distance_metrics.
chebyshev
(x, y)[source]¶ Compute the Chebyshev (\(L_\infty\)) distance between two real vectors
Notes
The Chebyshev distance between two vectors x and y is
\[d(\mathbf{x}, \mathbf{y}) = \max_i x_i  y_i\]Parameters: x,y ( ndarray
s of shape (N,)) – The two vectors to compute the distance betweenReturns: d (float) – The Chebyshev distance between x and y.
hamming
¶

numpy_ml.utils.distance_metrics.
hamming
(x, y)[source]¶ Compute the Hamming distance between two integervalued vectors.
Notes
The Hamming distance between two vectors x and y is
\[d(\mathbf{x}, \mathbf{y}) = \frac{1}{N} \sum_i \mathbb{1}_{x_i \neq y_i}\]Parameters: x,y ( ndarray
s of shape (N,)) – The two vectors to compute the distance between. Both vectors should be integervalued.Returns: d (float) – The Hamming distance between x and y.
manhattan
¶

numpy_ml.utils.distance_metrics.
manhattan
(x, y)[source]¶ Compute the Manhattan (L1) distance between two real vectors
Notes
The Manhattan distance between two vectors x and y is
\[d(\mathbf{x}, \mathbf{y}) = \sum_i x_i  y_i\]Parameters: x,y ( ndarray
s of shape (N,)) – The two vectors to compute the distance betweenReturns: d (float) – The L1 distance between x and y.
minkowski
¶

numpy_ml.utils.distance_metrics.
minkowski
(x, y, p)[source]¶ Compute the Minkowskip distance between two real vectors.
Notes
The Minkowskip distance between two vectors x and y is
\[d(\mathbf{x}, \mathbf{y}) = \left( \sum_i x_i  y_i^p \right)^{1/p}\]Parameters:  x,y (
ndarray
s of shape (N,)) – The two vectors to compute the distance between  p (float > 1) – The parameter of the distance function. When p = 1, this is the L1 distance, and when p=2, this is the L2 distance. For p < 1, Minkowskip does not satisfy the triangle inequality and hence is not a valid distance metric.
Returns: d (float) – The Minkowskip distance between x and y.
 x,y (