Storify k-nearest-neighbors

content/snippets/js/s/k-nearest-neighbors.md

@@ -1,17 +1,26 @@
 ---
-title: K-nearest neighbors
-type: snippet
+title: Classify data using the K-nearest neighbors algorithm in JavaScript
+shortTitle: K-nearest neighbors
+type: story
 language: javascript
 tags: [algorithm,array]
 cover: building-blocks
-dateModified: 2021-10-13
+excerpt: Implement the K-nearest neighbors algorithm in JavaScript to classify a data point relative to a labelled data set.
+dateModified: 2024-05-12
 ---
 
-Classifies a data point relative to a labelled data set, using the [k-nearest neighbors](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm) algorithm.
+## Definition
 
-- Use `Array.prototype.map()` to map the `data` to objects. Each object contains the euclidean distance of the element from `point`, calculated using `Math.hypot()`, `Object.keys()` and its `label`.
-- Use `Array.prototype.sort()` and `Array.prototype.slice()` to get the `k` nearest neighbors of `point`.
-- Use `Array.prototype.reduce()` in combination with `Object.keys()` and `Array.prototype.indexOf()` to find the most frequent `label` among them.
+The [K-nearest neighbors](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm) algorithm is a **simple, instance-based learning algorithm** used for classification and regression tasks. It classifies a data point based on the majority class of its `k` nearest neighbors in a feature space.
+
+## Implementation
+
+This implementation classifies a data point relative to a labelled data set, using the K-nearest neighbors algorithm. The `data` is expected to be an array of objects, where each object represents a data point with its features. The `labels` are an array of the corresponding classes for each data point.
+
+1. Use `Array.prototype.map()` to map the `data` to objects. Each object contains the [**Euclidean distance**](/js/s/euclidean-distance) of the element from `point`, calculated using `Math.hypot()`, `Object.keys()` and its `label`.
+2. Use `Array.prototype.sort()` and `Array.prototype.slice()` to get the `k` **nearest neighbors** of `point`.
+3. Use `Array.prototype.reduce()` in combination with `Object.keys()` and `Array.prototype.indexOf()` to find the **most frequent** `label` among them.
+4. Return the most frequent `label` as the **classification** of `point`.
 
 ```js
 const kNearestNeighbors = (data, labels, point, k = 3) => {
@@ -49,3 +58,7 @@ const labels = [0, 1, 1, 0];
 kNearestNeighbors(data, labels, [1, 2], 2); // 1
 kNearestNeighbors(data, labels, [1, 0], 2); // 0
 ```
+
+## Complexity
+
+The **time complexity** of this algorithm is `O(n)` for each classification, where `n` is the number of data points. The **space complexity** is `O(n)` as well, since we are storing the distances and labels for each data point. The algorithm is **non-parametric**, meaning it does not make any assumptions about the underlying data distribution. It is also **lazy**, as it does not require a training phase, making it suitable for online learning scenarios.