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Metrics

moll.metrics.cosine 

cosine(u: ArrayLike, v: ArrayLike) -> Array

Computes the cosine similarity between two vectors: $$ \cos \widehat{\bf u, \bf v} = \dfrac{\bf u \cdot \bf v}{\norm{\bf u} \cdot \norm{\bf v}}, $$ this formula follows from the dot product expression: $$ \bf u \cdot \bf v = \norm{\bf u} \cdot \norm{\bf v} \cdot \cos \widehat{\bf u, \bf v}. $$

Examples:

>>> cosine([1, 0], [1, 0])
Array(1., dtype=float32)

>>> cosine([1, 0], [0, 1])
Array(0., dtype=float32)

>>> cosine([1, 0], [-1, 0])
Array(-1., dtype=float32)

moll.metrics.euclidean 

euclidean(u: ArrayLike, v: ArrayLike) -> Array

Computes the Euclidean distance (L2-norm) \(||x - y||_2\) between two vectors.

Examples:

>>> euclidean([1, 2, 3], [1, 2, 3])
Array(0., dtype=float32)

>>> euclidean([1, 2, 3], [1, 2, 4])
Array(1., dtype=float32)

>>> euclidean([1, 2, 3], [4, 5, 6])
Array(5.196152, dtype=float32)

moll.metrics.manhattan 

manhattan(u: ArrayLike, v: ArrayLike) -> Array

Computes the Manhattan distance between two vectors.

Examples:

>>> manhattan([1, 2, 3], [1, 2, 3])
Array(0., dtype=float32)

>>> manhattan([1, 2, 3], [1, 2, 4])
Array(1., dtype=float32)

>>> manhattan([1, 2, 3], [4, 5, 6])
Array(9., dtype=float32)

moll.metrics.mismatches 

mismatches(u: ArrayLike, v: ArrayLike) -> Array

Computes the L0-norm distance between two vectors.

Examples:

>>> mismatches([1, 2, 3], [1, 2, 3])
Array(0., dtype=float32)

>>> mismatches([1, 2, 3], [1, 2, -3])
Array(1., dtype=float32)

>>> mismatches([1, 2, 3], [4, 5, 6])
Array(3., dtype=float32)

moll.metrics.negative_cosine 

negative_cosine(u: ArrayLike, v: ArrayLike) -> Array

Computes the cosine distance between two vectors.

Examples:

>>> negative_cosine([1, 0], [1, 0])
Array(-1., dtype=float32)

>>> negative_cosine([1, 0], [0, 1])
Array(-0., dtype=float32)

>>> negative_cosine([1, 0], [-1, 0])
Array(1., dtype=float32)

moll.metrics.one_minus_tanimoto 

one_minus_tanimoto(u: ArrayLike, v: ArrayLike) -> Array

Computes the Tanimoto distance between two vectors.

Examples:

>>> one_minus_tanimoto([1, 1], [1, 0])
Array(0.5, dtype=float32)

>>> one_minus_tanimoto([1, 1], [0, 0])
Array(1., dtype=float32)

moll.metrics.tanimoto 

tanimoto(u: ArrayLike, v: ArrayLike) -> Array

Computes the Tanimoto coefficient between two vectors.

Examples:

>>> tanimoto([1, 1], [1, 0])
Array(0.5, dtype=float32)

>>> tanimoto([1, 1], [0, 0])
Array(0., dtype=float32)