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Overview

The distance matrix functions are fundamental utilities for calculating distances between points and centroids in clustering algorithms. These functions form the basis for both crisp and fuzzy C-means clustering.

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getDistanceMatrix

Calculates the distance matrix between each point and each centroid. 
getDistanceMatrix(points: Point[], centroids: Point[]): number[][]

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Parameters

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points
Point[]
required
Array of points to calculate distances from. Each point should have x and y coordinates.
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centroids
Point[]
required
Array of centroids to calculate distances to. Each centroid should have x and y coordinates.

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Returns

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distanceMatrix
number[][]
A matrix of distances where each element [i][j] is the distance between the i-th centroid and the j-th point. Returns an empty array if either points or centroids is empty.

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Example

import { getDistanceMatrix } from 'fuzzy-cmeans';

const points = [
  { x: 1, y: 2 },
  { x: 3, y: 4 },
  { x: 5, y: 6 }
];

const centroids = [
  { x: 2, y: 3 },
  { x: 4, y: 5 }
];

const distanceMatrix = getDistanceMatrix(points, centroids);
// Returns: [[distance(c1,p1), distance(c1,p2), distance(c1,p3)],
//           [distance(c2,p1), distance(c2,p2), distance(c2,p3)]]

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euclidianDistance

Calculates the Euclidean distance between two points. 
euclidianDistance(pointA: Point, pointB: Point): number

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Parameters

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pointA
Point
required
First point with x and y coordinates.
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pointB
Point
required
Second point with x and y coordinates.

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Returns

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distance
number
The Euclidean distance between the two points, calculated as √((x₁ - x₂)² + (y₁ - y₂)²).

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Example

import { euclidianDistance } from 'fuzzy-cmeans';

const pointA = { x: 0, y: 0 };
const pointB = { x: 3, y: 4 };

const distance = euclidianDistance(pointA, pointB);
// Returns: 5 (since √(3² + 4²) = √25 = 5)
The Euclidean distance formula is used extensively throughout the clustering algorithms. It represents the straight-line distance between two points in 2D space.

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Mathematical Formula

The Euclidean distance is calculated using the formula: 
d(A, B) = √((xₐ - xᵦ)² + (yₐ - yᵦ)²)
Where:
  • A and B are two points in 2D space
  • xₐ, yₐ are the coordinates of point A
  • xᵦ, yᵦ are the coordinates of point B

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