Add Euclidean Distance algorithm.

trekhleb · trekhleb · commit 610f16fe209d · 2020-12-19T19:21:32.000+01:00
diff --git a/README.md b/README.md
@@ -78,6 +78,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Fast Powering](src/algorithms/math/fast-powering)
   * `B` [Horner's method](src/algorithms/math/horner-method) - polynomial evaluation
   * `B` [Matrices](src/algorithms/math/matrix) - matrices and basic matrix operations (multiplication, transposition, etc.)
+  * `B` [Euclidean Distance](src/algorithms/math/euclidean-distance) - distance between two points/vectors/matrices
   * `A` [Integer Partition](src/algorithms/math/integer-partition)
   * `A` [Square Root](src/algorithms/math/square-root) - Newton's method
   * `A` [Liu Hui π Algorithm](src/algorithms/math/liu-hui) - approximate π calculations based on N-gons
diff --git a/src/algorithms/math/euclidean-distance/README.md b/src/algorithms/math/euclidean-distance/README.md
@@ -0,0 +1,36 @@
+# Euclidean Distance
+
+In mathematics, the **Euclidean distance** between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance.
+
+![Euclidean distance between two points](https://upload.wikimedia.org/wikipedia/commons/5/55/Euclidean_distance_2d.svg)
+
+## Distance formulas
+
+### One dimension
+
+The distance between any two points on the real line is the absolute value of the numerical difference of their coordinates
+
+![One dimension formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/7d75418dbec9482dbcb70f9063ad66e9cf7b5db9)
+
+### Two dimensions
+
+![Two dimensions formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c0157084fd89f5f3d462efeedc47d3d7aa0b773)
+
+### Higher dimensions
+
+In three dimensions, for points given by their Cartesian coordinates, the distance is
+
+![Three dimensions formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1d13a40a7b203b455ae6d4be8b3cce898bda625)
+
+Example: the distance between the two points `(8,2,6)` and `(3,5,7)`:
+
+![3-dimension example](https://www.mathsisfun.com/algebra/images/dist-2-points-3d.svg)
+
+In general, for points given by Cartesian coordinates in `n`-dimensional Euclidean space, the distance is
+
+![n-dimensional formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0ef4fe055b2a51b4cca43a05e5d1cd93f758dcc)
+
+## References
+
+- [Euclidean Distance on MathIsFun](https://www.mathsisfun.com/algebra/distance-2-points.html)
+- [Euclidean Distance on Wikipedia](https://en.wikipedia.org/wiki/Euclidean_distance)
diff --git a/src/algorithms/math/euclidean-distance/__tests__/euclideanDistance.test.js b/src/algorithms/math/euclidean-distance/__tests__/euclideanDistance.test.js
@@ -0,0 +1,23 @@
+import euclideanDistance from '../euclideanDistance';
+
+describe('euclideanDistance', () => {
+  it('should calculate euclidean distance between vectors', () => {
+    expect(euclideanDistance([[1]], [[2]])).toEqual(1);
+    expect(euclideanDistance([[2]], [[1]])).toEqual(1);
+    expect(euclideanDistance([[5, 8]], [[7, 3]])).toEqual(5.39);
+    expect(euclideanDistance([[5], [8]], [[7], [3]])).toEqual(5.39);
+    expect(euclideanDistance([[8, 2, 6]], [[3, 5, 7]])).toEqual(5.92);
+    expect(euclideanDistance([[8], [2], [6]], [[3], [5], [7]])).toEqual(5.92);
+    expect(euclideanDistance([[[8]], [[2]], [[6]]], [[[3]], [[5]], [[7]]])).toEqual(5.92);
+  });
+
+  it('should throw an error in case if two matrices are of different shapes', () => {
+    expect(() => euclideanDistance([[1]], [[[2]]])).toThrowError(
+      'Matrices have different dimensions',
+    );
+
+    expect(() => euclideanDistance([[1]], [[2, 3]])).toThrowError(
+      'Matrices have different shapes',
+    );
+  });
+});
diff --git a/src/algorithms/math/euclidean-distance/euclideanDistance.js b/src/algorithms/math/euclidean-distance/euclideanDistance.js
@@ -0,0 +1,28 @@
+/**
+ * @typedef {import('../matrix/Matrix.js').Matrix} Matrix
+ */
+
+import * as mtrx from '../matrix/Matrix';
+
+/**
+ * Calculates the euclidean distance between 2 matrices.
+ *
+ * @param {Matrix} a
+ * @param {Matrix} b
+ * @returns {number}
+ * @trows {Error}
+ */
+const euclideanDistance = (a, b) => {
+  mtrx.validateSameShape(a, b);
+
+  let squaresTotal = 0;
+
+  mtrx.walk(a, (indices, aCellValue) => {
+    const bCellValue = mtrx.getCellAtIndex(b, indices);
+    squaresTotal += (aCellValue - bCellValue) ** 2;
+  });
+
+  return Number(Math.sqrt(squaresTotal).toFixed(2));
+};
+
+export default euclideanDistance;
diff --git a/src/algorithms/math/matrix/Matrix.js b/src/algorithms/math/matrix/Matrix.js
@@ -58,7 +58,7 @@ const validate2D = (m) => {
  * @param {Matrix} b
  * @trows {Error}
  */
-const validateSameShape = (a, b) => {
+export const validateSameShape = (a, b) => {
   validateType(a);
   validateType(b);
 
@@ -177,7 +177,7 @@ export const t = (m) => {
  * @param {Matrix} m
  * @param {function(indices: CellIndices, c: Cell)} visit
  */
-const walk = (m, visit) => {
+export const walk = (m, visit) => {
   /**
    * Traverses the matrix recursively.
    *
@@ -208,7 +208,7 @@ const walk = (m, visit) => {
  * @param {CellIndices} cellIndices - Array of cell indices
  * @return {Cell}
  */
-const getCellAtIndex = (m, cellIndices) => {
+export const getCellAtIndex = (m, cellIndices) => {
   // We start from the row at specific index.
   let cell = m[cellIndices[0]];
   // Going deeper into the next dimensions but not to the last one to preserve
@@ -227,7 +227,7 @@ const getCellAtIndex = (m, cellIndices) => {
  * @param {CellIndices} cellIndices - Array of cell indices
  * @param {Cell} cellValue - New cell value
  */
-const updateCellAtIndex = (m, cellIndices, cellValue) => {
+export const updateCellAtIndex = (m, cellIndices, cellValue) => {
   // We start from the row at specific index.
   let cell = m[cellIndices[0]];
   // Going deeper into the next dimensions but not to the last one to preserve
diff --git a/src/algorithms/ml/knn/__test__/knn.test.js b/src/algorithms/ml/knn/__test__/knn.test.js
@@ -25,7 +25,7 @@ describe('kNN', () => {
     const inconsistent = () => {
       kNN([[1, 1]], [1], [1]);
     };
-    expect(inconsistent).toThrowError('Inconsistent vector lengths');
+    expect(inconsistent).toThrowError('Matrices have different shapes');
   });
 
   it('should find the nearest neighbour', () => {
diff --git a/src/algorithms/ml/knn/kNN.js b/src/algorithms/ml/knn/kNN.js
@@ -1,23 +1,3 @@
-/**
- * Calculates calculate the euclidean distance between 2 vectors.
- *
- * @param {number[]} x1
- * @param {number[]} x2
- * @returns {number}
- */
-function euclideanDistance(x1, x2) {
-  // Checking for errors.
-  if (x1.length !== x2.length) {
-    throw new Error('Inconsistent vector lengths');
-  }
-  // Calculate the euclidean distance between 2 vectors and return.
-  let squaresTotal = 0;
-  for (let i = 0; i < x1.length; i += 1) {
-    squaresTotal += (x1[i] - x2[i]) ** 2;
-  }
-  return Number(Math.sqrt(squaresTotal).toFixed(2));
-}
-
 /**
  * Classifies the point in space based on k-nearest neighbors algorithm.
  *
@@ -27,6 +7,9 @@ function euclideanDistance(x1, x2) {
  * @param {number} k - number of nearest neighbors which will be taken into account (preferably odd)
  * @return {number} - the class of the point
  */
+
+import euclideanDistance from '../../math/euclidean-distance/euclideanDistance';
+
 export default function kNN(
   dataSet,
   labels,
@@ -42,7 +25,7 @@ export default function kNN(
   const distances = [];
   for (let i = 0; i < dataSet.length; i += 1) {
     distances.push({
-      dist: euclideanDistance(dataSet[i], toClassify),
+      dist: euclideanDistance([dataSet[i]], [toClassify]),
       label: labels[i],
     });
   }
