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k_means_cluster.js
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k_means_cluster.js
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import euclideanDistance from "./euclidean_distance";
import makeMatrix from "./make_matrix";
import sample from "./sample";
/**
* @typedef {Object} kMeansReturn
* @property {Array<number>} labels The labels.
* @property {Array<Array<number>>} centroids The cluster centroids.
*/
/**
* Perform k-means clustering.
*
* @param {Array<Array<number>>} points N-dimensional coordinates of points to be clustered.
* @param {number} numCluster How many clusters to create.
* @param {Function} randomSource An optional entropy source that generates uniform values in [0, 1).
* @return {kMeansReturn} Labels (same length as data) and centroids (same length as numCluster).
* @throws {Error} If any centroids wind up friendless (i.e., without associated points).
*
* @example
* kMeansCluster([[0.0, 0.5], [1.0, 0.5]], 2); // => {labels: [0, 1], centroids: [[0.0, 0.5], [1.0 0.5]]}
*/
function kMeansCluster(points, numCluster, randomSource = Math.random) {
let oldCentroids = null;
let newCentroids = sample(points, numCluster, randomSource);
let labels = null;
let change = Number.MAX_VALUE;
while (change !== 0) {
labels = labelPoints(points, newCentroids);
oldCentroids = newCentroids;
newCentroids = calculateCentroids(points, labels, numCluster);
change = calculateChange(newCentroids, oldCentroids);
}
return {
labels: labels,
centroids: newCentroids
};
}
/**
* Label each point according to which centroid it is closest to.
*
* @private
* @param {Array<Array<number>>} points Array of XY coordinates.
* @param {Array<Array<number>>} centroids Current centroids.
* @return {Array<number>} Group labels.
*/
function labelPoints(points, centroids) {
return points.map((p) => {
let minDist = Number.MAX_VALUE;
let label = -1;
for (let i = 0; i < centroids.length; i++) {
const dist = euclideanDistance(p, centroids[i]);
if (dist < minDist) {
minDist = dist;
label = i;
}
}
return label;
});
}
/**
* Calculate centroids for points given labels.
*
* @private
* @param {Array<Array<number>>} points Array of XY coordinates.
* @param {Array<number>} labels Which groups points belong to.
* @param {number} numCluster Number of clusters being created.
* @return {Array<Array<number>>} Centroid for each group.
* @throws {Error} If any centroids wind up friendless (i.e., without associated points).
*/
function calculateCentroids(points, labels, numCluster) {
// Initialize accumulators.
const dimension = points[0].length;
const centroids = makeMatrix(numCluster, dimension);
const counts = Array(numCluster).fill(0);
// Add points to centroids' accumulators and count points per centroid.
const numPoints = points.length;
for (let i = 0; i < numPoints; i++) {
const point = points[i];
const label = labels[i];
const current = centroids[label];
for (let j = 0; j < dimension; j++) {
current[j] += point[j];
}
counts[label] += 1;
}
// Rescale centroids, checking for any that have no points.
for (let i = 0; i < numCluster; i++) {
if (counts[i] === 0) {
throw new Error(`Centroid ${i} has no friends`);
}
const centroid = centroids[i];
for (let j = 0; j < dimension; j++) {
centroid[j] /= counts[i];
}
}
return centroids;
}
/**
* Calculate the difference between old centroids and new centroids.
*
* @private
* @param {Array<Array<number>>} left One list of centroids.
* @param {Array<Array<number>>} right Another list of centroids.
* @return {number} Distance between centroids.
*/
function calculateChange(left, right) {
let total = 0;
for (let i = 0; i < left.length; i++) {
total += euclideanDistance(left[i], right[i]);
}
return total;
}
export default kMeansCluster;