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NicklasXYZ 2024-03-19 15:18:07 +01:00
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src/gleam_community/maths/metrics.gleam
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@ -25,14 +25,17 @@
////
//// Metrics: A module offering functions for calculating distances and other types of metrics.
////
//// * **Distances**
//// * **Distance measures**
//// * [`norm`](#norm)
//// * [`manhatten_distance`](#float_manhatten_distance)
//// * [`manhatten_distance`](#manhatten_distance)
//// * [`minkowski_distance`](#minkowski_distance)
//// * [`euclidean_distance`](#euclidean_distance)
//// * [`cosine_similarity`](#cosine_similarity)
//// * **Set & string similarity measures**
//// * [`jaccard_index`](#jaccard_index)
//// * [`sorensen_dice_coefficient`](#sorensen_dice_coefficient)
//// * [`tversky_index`](#tversky_index)
//// * [`overlap_coefficient`](#overlap_coefficient)
//// * **Basic statistical measures**
//// * [`mean`](#mean)
//// * [`median`](#median)
@ -571,7 +574,7 @@ pub fn standard_deviation(arr: List(Float), ddof: Int) -> Result(Float, String)
/// is defined as:
///
/// \\[
/// \text{JI}(X, Y) = \frac{|X \cap Y|}{|X \cup Y|} \in \left[0, 1\right]
/// \frac{|X \cap Y|}{|X \cup Y|} \\; \in \\; \left[0, 1\right]
/// \\]
///
/// where:
@ -621,7 +624,7 @@ pub fn jaccard_index(xset: set.Set(a), yset: set.Set(a)) -> Float {
/// coefficient is defined as:
///
/// \\[
/// \text{DSC}(X, Y) = \frac{2 \times |X \cap Y|}{|X| + |Y|} \in \left[0, 1\right]
/// \frac{2 |X \cap Y|}{|X| + |Y|} \\; \in \\; \left[0, 1\right]
/// \\]
///
/// where:
@ -672,7 +675,7 @@ pub fn sorensen_dice_coefficient(xset: set.Set(a), yset: set.Set(a)) -> Float {
/// measures between sets. The Tversky index is defined as:
///
/// \\[
/// \text{TI}(X, Y) = \frac{|X \cap Y|}{|X \cap Y| + \alpha|X - Y| + \beta|Y - X|}
/// \frac{|X \cap Y|}{|X \cap Y| + \alpha|X - Y| + \beta|Y - X|}
/// \\]
///
/// where:
@ -759,7 +762,7 @@ pub fn tversky_index(
/// smaller of the two sets. It is defined mathematically as:
///
/// \\[
/// \text{OC}(X, Y) = \frac{|X \cap Y|}{\min(|X|, |Y|)} \in \left[0, 1\right]
/// \frac{|X \cap Y|}{\min(|X|, |Y|)} \\; \in \\; \left[0, 1\right]
/// \\]
///
/// where:
@ -816,13 +819,13 @@ pub fn overlap_coefficient(xset: set.Set(a), yset: set.Set(a)) -> Float {
/// Calculate the cosine similarity between two lists (representing vectors):
///
/// \\[
/// \frac{\sum_{i=1}^n x_i \cdot y_i}{\left(\sum_{i=1}^n x_i^2\right)^{\frac{1}{2}} \cdot \left(\sum_{i=1}^n y_i^2\right)^{\frac{1}{2}}}
/// \frac{\sum_{i=1}^n x_i \cdot y_i}{\left(\sum_{i=1}^n x_i^2\right)^{\frac{1}{2}} \cdot \left(\sum_{i=1}^n y_i^2\right)^{\frac{1}{2}}} \\; \in \\; \left[-1, 1\right]
/// \\]
///
/// In the formula, $n$ is the length of the two lists and $x_i, y_i$ are the values in the respective input lists indexed by $i$. The numerator
/// represents the dot product of the two vectors, while the denominator is the product of the magnitudes (Euclidean norms) of the two vectors.
/// The cosine similarity provides a value between -1 and 1, where 1 means the vectors are in the same direction, -1 means they are in exactly
/// opposite directions, and 0 indicates orthogonality.
/// In the formula, $$n$$ is the length of the two lists and $$x_i$$, $$y_i$$ are the values in the respective input lists indexed by $$i$$.
/// The numerator represents the dot product of the two vectors, while the denominator is the product of the magnitudes (Euclidean norms) of
/// the two vectors. The cosine similarity provides a value between -1 and 1, where 1 means the vectors are in the same direction, -1 means
/// they are in exactly opposite directions, and 0 indicates orthogonality.
///
/// <details>
/// <summary>Example:</summary>