Distance

Utility functions for normalized distance between arrays with numba decorators.

def hamming(...)

def hamming(u: npt.NDArray, v: npt.NDArray) -> np.float64:

The function to calculate the normalized Hamming distance between two points.

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

Parameters:

• u (npt.NDArray): Coordinates of the first point.
• v (npt.NDArray): Coordinates of the second point.

Returns:

• Distance (float) between the two points.

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def euclidean(...)

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

Function to calculate the normalized Euclidean distance between two points.

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

Parameters:

• u (npt.NDArray): Coordinates of the first point.
• v (npt.NDArray): Coordinates of the second point.

Returns:

• Distance (float) between the two points.

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def cityblock(...)

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

Function to calculate the normalized Manhattan distance between two points.

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

Parameters:

• u (npt.NDArray): Coordinates of the first point.
• v (npt.NDArray): Coordinates of the second point.

Returns:

• Distance (float) between the two points.

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def minkowski(...)

def minkowski(u: npt.NDArray[np.float64], v: npt.NDArray[np.float64], p: float = 2.0):

Function to calculate the normalized Minkowski distance between two points.

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

Parameters:

• u (npt.NDArray): Coordinates of the first point.
• v (npt.NDArray): Coordinates of the second point.
• p float: The p parameter defines the type of distance to be calculated:
  • 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:

• Distance (float) between the two points.

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def compute_metric_distance(...)

def compute_metric_distance(
    u: npt.NDArray[np.float64],
    v: npt.NDArray[np.float64],
    metric: int,
    p: np.float64 = 2.0
) -> np.float64:

Function to calculate the distance between two points by the chosen metric.

Parameters:

• u (npt.NDArray): Coordinates of the first point.
• v (npt.NDArray): Coordinates of the second point.
• metric (int): Distance metric to be used. Available options: [0 (Euclidean), 1 (Manhattan), 2 (Minkowski)]
• p (float): Parameter for the Minkowski distance (used only if metric is "minkowski").

Returns:

• Distance (double) between the two points with the selected metric.

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def min_distance_to_class_vectors(...)

def min_distance_to_class_vectors(
    x_class: npt.NDArray,
    vector_x: npt.NDArray,
    metric: int,
    p: float = 2.0
) -> float:

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

Parameters:

• x_class (npt.NDArray): Array containing the class vectors to be compared with the input vector. Expected shape: (n_samples, n_features).
• vector_x (npt.NDArray): 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)]
• p (float): Parameter for the Minkowski distance (used only if metric is "minkowski").

Returns:

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

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def get_metric_code(...)

def get_metric_code(metric: str) -> int:

Returns the numeric code associated with a distance metric.

Parameters:

• metric (str): Name of the metric. Can be "euclidean", "manhattan", "minkowski" or "hamming".

Raises

• ValueError: If the metric provided is not supported

Returns:

• int: Numeric code corresponding to the metric.

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