distance

Utility functions for distance between arrays with numba decorators.

Module: aisp.utils.distance
Import: from aisp.utils import distance

Functions

hamming

@njit([(types.boolean[:], types.boolean[:])], cache=True)
def hamming(u: npt.NDArray[np.bool_], v: npt.NDArray[np.bool_]) -> float64:
    ...

Calculate the Hamming distance between two points.

$$\frac{(x_1 \neq y_1) + (x_2 \neq y_2) + \cdots + (x_n \neq y_n)}{n}$$

Parameters

Name	Type	Default	Description
u	npt.NDArray[np.bool_]	-	Coordinates of the first point.
v	npt.NDArray[np.bool_]	-	Coordinates of the second point.

Returns

Type	Description
float64	Hamming distance between two points.

---

euclidean

@njit()
def euclidean(u: npt.NDArray[np.float64], v: npt.NDArray[np.float64]) -> float64:
    ...

Calculate the Euclidean distance between two points.

$$\sqrt{(X_{1} - X_{1})^2 + (Y_{2} - Y_{2})^2 + \cdots + (Y_{n} - Y_{n})^2}$$

Parameters

Name	Type	Default	Description
u	npt.NDArray[float64]	-	Coordinates of the first point.
v	npt.NDArray[float64]	-	Coordinates of the second point.

Returns

Type	Description
float64	Euclidean distance between two points.

---

cityblock

@njit()
def cityblock(u: npt.NDArray[float64], v: npt.NDArray[float64]) -> float64:
    ...

Calculate the Manhattan distance between two points.

$$|X_{1} - Y_{1}| + |X_{2} - Y_{2}| + \cdots + |X_{n} - Y_{n}|$$

Parameters

Name	Type	Default	Description
u	npt.NDArray[float64]	-	Coordinates of the first point.
v	npt.NDArray[float64]	-	Coordinates of the second point.

Returns

Type	Description
float64	Manhattan distance between two points.

---

minkowski

@njit()
def minkowski(
    u: npt.NDArray[float64],
    v: npt.NDArray[float64],
    p: float = 2.0
) -> float64:
    ...

Calculate the Minkowski distance between two points.

$$(|X_{1} - Y_{1}|^p + |X_{2} - Y_{2}|^p + \cdots + |X_{n} - Y_{n}|^p)^\frac{1}{p}|$$

Parameters

Name	Type	Default	Description
u	npt.NDArray[float64]	-	Coordinates of the first point.
v	npt.NDArray[float64]	-	Coordinates of the second point.
p	float	2.0	The p parameter defines the type of distance to be calculated.

Parameter p

• p = 1: Manhattan distance - sum of absolute differences.
• p = 2: Euclidean distance - sum of squared differences (square root).
• p > 2: Minkowski distance with an increasing penalty as p increases.

Returns

Type	Description
float64	Minkowski distance between two points.

---

compute_metric_distance

@njit([(types.float64[:], types.float64[:], types.int32, types.float64)], cache=True)
def compute_metric_distance(
    u: npt.NDArray[float64],
    v: npt.NDArray[float64],
    metric: int,
    p: float = 2.0
) -> float64:
    ...

Calculate the distance between two points by the chosen metric.

Parameters

Name	Type	Default	Description
u	npt.NDArray[float64]	-	Coordinates of the first point.
v	npt.NDArray[float64]	-	Coordinates of the second point.
metric	int	-	Distance metric to be used. Available options: 0 (Euclidean), 1 (Manhattan), 2 (Minkowski)
p	float	2.0	The p parameter defines the type of distance to be calculated.

Returns

Type	Description
float64	Distance between the two points with the selected metric.

---

min_distance_to_class_vectors

@njit([(types.float64[:, :], types.float64[:], types.int32, types.float64)], cache=True)
def min_distance_to_class_vectors(
    x_class: npt.NDArray[float64],
    vector_x: npt.NDArray[float64],
    metric: int,
    p: float = 2.0,
) -> float:
    ...

Calculate the minimum distance between an input vector and the vectors of a class.

Parameters

Name	Type	Default	Description
x_class	npt.NDArray[float64]	-	Array containing the class vectors to be compared with the input vector. Expected shape: (n_samples, n_features).
vector_x	npt.NDArray[float64]	-	Vector to be compared with the class vectors. Expected shape: (n_features,).
metric	int	-	Distance metric to be used. Available options: 0 ("euclidean"), 1 ("manhattan"), 2 ("minkowski") or ("hamming")
p	float	2.0	Parameter for the Minkowski distance (used only if metric is "minkowski").

Returns

Type	Description
float	The minimum distance calculated between the input vector and the class vectors. Returns -1.0 if the input dimensions are incompatible.

---

get_metric_code

def get_metric_code(metric: str) -> int:
    ...

Get the numeric code associated with a distance metric.

Parameters

Name	Type	Default	Description
metric	str	-	Name of the metric. Can be "euclidean", "manhattan", "minkowski" or "hamming".

Returns

Type	Description
int	Numeric code corresponding to the metric.

Raises

Exception	Description
ValueError	If the metric provided is not supported.