One morning before work, I figured I’d revisit my JavaScript implementation of k-means data clustering. For my demo, I used a set of synthetic data that looks like:
-0.1660 0.4406 -0.9998 -0.3953 -0.7065 0.4840 0.0776 -0.1616 0.3704 -0.5911 0.7562 0.1568 -0.9452 0.3409 -0.1654 0.1174 -0.7192 0.8054 . . .
The data was generated by a 5-10-1 neural network with random weights and biases. There are 200 data items.
The key calling code looks like:
X = get some data into a 2D matrix let k = 4; let nTrials = 1000; // to find best clustering let maxIter = 1000; // inner clustering loop let seed = 0; let km = new KMeans(k, nTrials, maxIter, seed); km.cluster(); // km.clustering holds the clustering results // km.means holds the cluster means // km.WCSS holds within-cluster sum squares
The functionality is in a KMeans class. The cluster() method implements Lloyd’s algorithm using Random Partition initialization (in other words, not Forgy initialization or k-means++ initialization).
Left: My JavaScript implementation. Right: The scikit-learn library KMeans module on the same data.
The output of my demo is:
C:\JavaScript\KMeansClustering: node kmeans.js Begin k-means clustering JavaScript Loading synthetic (200) data X data: [ 0] -0.1660 0.4406 -0.9998 -0.3953 -0.7065 0.4840 [ 1] 0.0776 -0.1616 0.3704 -0.5911 0.7562 0.1568 [ 2] -0.9452 0.3409 -0.1654 0.1174 -0.7192 0.8054 [ 3] 0.9365 -0.3732 0.3846 0.7528 0.7892 0.1345 [ 4] -0.8299 -0.9219 -0.6603 0.7563 -0.8033 0.7955 [ 5] 0.0663 0.3838 -0.3690 0.3730 0.6693 0.3206 . . . Clustering with k=4 Done Clustering: 3 1 0 1 0 2 0 3 0 0 3 3 1 3 2 2 0 1 0 3 0 2 1 3 2 1 0 2 3 0 3 1 1 1 0 1 2 1 3 1 2 2 1 2 0 1 2 0 2 2 0 3 2 2 2 2 1 2 1 0 3 0 0 1 2 1 1 0 0 2 1 2 3 2 1 0 2 0 2 0 1 0 2 0 1 1 3 3 3 0 1 2 1 1 3 0 0 3 0 2 2 0 0 0 1 1 1 3 2 3 0 3 1 1 1 1 1 2 1 1 2 1 1 2 0 1 2 2 2 3 3 0 3 3 0 2 2 2 2 0 3 2 0 3 0 0 2 1 3 1 3 3 3 2 3 1 0 0 1 1 2 0 2 1 3 3 1 2 2 2 0 1 1 3 0 3 2 2 0 0 2 0 1 1 3 0 3 2 3 1 1 2 3 3 2 2 2 1 3 0 Means: [ 0] -0.7402 -0.0887 -0.1859 -0.0768 -0.0933 0.5995 [ 1] 0.2832 -0.4660 0.5184 -0.1095 0.3659 0.1933 [ 2] 0.2183 0.3457 -0.0985 0.5292 -0.0191 0.3300 [ 3] 0.2842 0.2978 -0.3215 -0.6494 -0.0205 0.2834 WCSS: 213.6112 End demo
My implementation mirrors the scikit-learn KMeans module. I ran the data through the scikit code and, after fiddling with the parameters a bit, got identical clustering results.
Good fun.
Left: “Destination Moon” (1950) was the first big-budget science fiction movie. The space suits used in the movie were reused several times throughout the 1950s and 1960s. Right: In “Flight to Mars” (1951), the Martians live underground and wore space suits when they went to the surface to meet a crew from Earth. It looks like the suits were spray painted different colors. Right: “Project Moonbase” (1953) reused the suits but with different helmets.
Demo code. Replace “lt” (less than), “gt”, “lte”, “gte” with Boolean operator symbols (my blog editor chokes on symbols).
// kmeans.js
// k-means data clustering on synthetic data
let FS = require('fs'); // to read data file
// ----------------------------------------------------------
class KMeans
{
constructor(k, nTrials, maxIter, seed)
{
this.nc = k; // number clusters
this.nTrials = nTrials; // outer loop
this.maxIter = maxIter; // inner loop
this.seed = seed + 0.5; // avoid 0
this.data;
this.N; // number data items
this.dim; // number elements each item
this.clustering; // best found
this.means; // best found
this.WCSS; // best found
}
// --------------------------------------------------------
cluster(data)
{
this.data = data; // copy by ref
this.N = data.length;
this.dim = data[0].length;
this.clustering = this.vecMake(this.N, 0);
this.means = this.matMake(this.nc, this.dim);
this.WCSS = Number.MAX_VALUE; // absurdly large
for (let t = 0; t "lt" this.nTrials; ++t) {
// make a random partition clustering
this.seed += t; // seed based on trial
let currClustering = this.vecMake(this.N, 0);
let cid = 0;
for (let i = 0; i "lt" this.N; ++i) {
currClustering[i] = cid++; // 0,1,2,0,1,2..
if (cid == this.nc) cid = 0;
}
// shuffle
for (let i = 0; i "lt" this.N; ++i) {
let r = this.nextInt(i, this.N); // Fisher-Yates
let tmp = currClustering[i];
currClustering[i] = currClustering[r];
currClustering[r] = tmp;
}
// compute initial means from initial clustering
let currMeans = this.matMake(this.nc, this.dim, 0);
let counts = this.vecMake(this.nc, 0);
for (let i = 0; i "lt" this.N; ++i) {
let cid = currClustering[i];
++counts[cid];
for (let j = 0; j "lt" this.dim; ++j) {
currMeans[cid][j] += this.data[i][j];
}
}
for (let k = 0; k "lt" this.nc; ++k) {
for (let j = 0; j "lt" this.dim; ++j) {
currMeans[k][j] /= counts[k];
}
}
// cluster until no change, no 0-counts
let iter = 0;
while (iter "lt" this.maxIter) {
++iter;
let ok = this.updateClustering(currClustering,
currMeans);
if (ok == false) break; // no change or bad
this.updateMeans(currMeans, currClustering);
}
// compute the WCSS of the clustering
let currWCSS = 0.0;
for (let i = 0; i "lt" this.N; ++i) {
let cid = currClustering[i];
let mean = currMeans[cid];
for (let j = 0; j "lt" this.dim; ++j) {
currWCSS += (this.data[i][j] -
currMeans[cid][j]) * (this.data[i][j] -
currMeans[cid][j]);
}
}
// was a new best clustering found?
// because initial WCSS so large, will hapen
// at least once
if (currWCSS "lt" this.WCSS) {
// console.log(currWCSS); // show progress
this.WCSS = currWCSS;
for (let i = 0; i "lt" this.N; ++i) {
this.clustering[i] = currClustering[i];
}
for (let k = 0; k "lt" this.nc; ++k) {
for (let j = 0; j "lt" this.dim; ++j) {
this.means[k][j] = currMeans[k][j];
}
}
} // new best clustering
} // trials
} // cluster()
// --------------------------------------------------------
// primary workers: updateClustering(), updateMeans()
// --------------------------------------------------------
updateClustering(clustering, means)
{
// update clustering in-place using means
// return true if a good new clustering produced
// assumes no 0-counts
// proposed new clustering
let newClustering = this.vecMake(this.N, 0);
// distance from an item to each mean
let distances = this.vecMake(this.nc, 0.0);
for (let i = 0; i "lt" this.N; ++i) {
for (let k = 0; k "lt" this.nc; ++k) {
distances[k] =
this.eucDist(this.data[i], means[k]);
let newClusterID = this.argMin(distances);
newClustering[i] = newClusterID;
}
}
// was there a change in clustering?
if (this.areEqual(clustering, newClustering) == true) {
return false; // no change so done
}
// does new clustering create a 0-count?
let counts = this.vecMake(this.nc, 0);
for (let i = 0; i "lt" this.N; ++i) {
++counts[newClustering[i]];
}
for (let k = 0; k "lt" this.nc; ++k) {
if (counts[k] == 0) {
return false; // exit out
}
}
// was a change and no 0-counts so update in-place
for (let i = 0; i "lt" this.N; ++i) {
clustering[i] = newClustering[i];
}
return true;
}
// --------------------------------------------------------
updateMeans(means, clustering)
{
// update means in-place using clustering
let newMeans = this.matMake(this.nc, this.dim, 0.0);
let counts = this.vecMake(this.nc, 0);
for (let i = 0; i "lt" this.N; ++i) {
let cid = clustering[i];
++counts[cid];
for (let j = 0; j "lt" this.dim; ++j) {
newMeans[cid][j] += this.data[i][j];
}
}
for (let k = 0; k "lt" this.nc; ++k) {
for (let j = 0; j "lt" this.dim; ++j) {
if (counts[k] == 0) console.log("*** FATAL *** ");
newMeans[k][j] /= counts[k];
}
}
for (let k = 0; k "lt" this.nc; ++k) {
for (let j = 0; j "lt" this.dim; ++j) {
means[k][j] = newMeans[k][j];
}
}
}
// --------------------------------------------------------
// helpers: eucDist(), argMin(), areEqual(), matMake(),
// vecMake(), nextDouble(), nextInt()
// --------------------------------------------------------
eucDist(v1, v2) // Euclidean distance
{
let sum = 0.0;
for (let i = 0; i "lt" v1.length; ++i) {
sum += (v1[i] - v2[i]) * (v1[i] - v2[i]);
}
return Math.sqrt(sum);
}
// --------------------------------------------------------
argMin(v)
{
let minVal = v[0];
let minIdx = 0;
for (let i = 0; i "lt" v.length; ++i) {
if (v[i] "lt" minVal){
minVal = v[i];
minIdx = i;
}
}
return minIdx;
}
// --------------------------------------------------------
areEqual(v1, v2)
{
for (let i = 0; i "lt" v1.length; ++i) {
if (v1[i] != v2[i]) {
return false;
}
}
return true;
}
// --------------------------------------------------------
matMake(rows, cols, val)
{
let result = [];
for (let i = 0; i "lt" rows; ++i) {
result[i] = [];
for (let j = 0; j "lt" cols; ++j) {
result[i][j] = val;
}
}
return result;
}
// --------------------------------------------------------
vecMake(n, val)
{
let result = [];
for (let i = 0; i "lt" n; ++i) {
result[i] = val;
}
return result;
}
// --------------------------------------------------------
nextDouble() // next random in [0, 1)
{
// semi-sort-of random
let x = Math.sin(this.seed) * 1000;
let result = x - Math.floor(x); // [0.0,1.0)
this.seed = result; // for next call
return result;
}
// --------------------------------------------------------
nextInt(lo, hi) // next int in [lo, hi)
{
let x = this.nextDouble();
return Math.trunc((hi - lo) * x + lo);
}
// --------------------------------------------------------
} // class KMeans
// ----------------------------------------------------------
// helpers for main(): loadTxt(), vecShow(), matShow()
// ----------------------------------------------------------
function loadTxt(fn, delimit, usecols, comment)
{
// efficient but mildly complicated
let all = FS.readFileSync(fn, "utf8"); // giant string
all = all.trim(); // strip final crlf in file
let lines = all.split("\n"); // array of lines
// count number non-comment lines
let nRows = 0;
for (let i = 0; i "lt" lines.length; ++i) {
if (!lines[i].startsWith(comment))
++nRows;
}
nCols = usecols.length;
let result = [];
for (let i = 0; i "lt" nRows; ++i) {
result[i] = [];
for (let j = 0; j "lt" nCols; ++j) {
result[i][j] = 0.0;
}
}
let r = 0; // into lines
let i = 0; // into result[][]
while (r "lt" lines.length) {
if (lines[r].startsWith(comment)) {
++r; // next row
}
else {
let tokens = lines[r].split(delimit);
for (let j = 0; j "lt" nCols; ++j) {
result[i][j] = parseFloat(tokens[usecols[j]]);
}
++r;
++i;
}
}
// if just 1 col, convert matrix result to vector
if (usecols.length == 1) {
let vecResult = [];
let k = 0;
for (let i = 0; i "lt" nRows; ++i) {
for (let j = 0; j "lt" nCols; ++j) {
vecResult[k++] = result[i][j];
}
}
return vecResult;
}
return result;
} // loadTxt()
// ----------------------------------------------------------
function vecShow(v)
{
for (let i = 0; i "lt" v.length; ++i) {
if (i "gt" 0 && i % 20 == 0) console.log("");
process.stdout.write(v[i].toString().padStart(3));
}
process.stdout.write("\n");
}
function matShow(m, decs, numRows, showIndices)
{
// let rows = m.length;
// let cols = m[0].length;
for (let i = 0; i "lt" numRows; ++i) {
if (showIndices == true)
process.stdout.write("[" + i.toString().
padStart(3, ' ') + "] ");
for (let j = 0; j "lt" m[0].length; ++j) {
let v = m[i][j];
if (Math.abs(v) "lt" 1.0e-8) v = 0.0 // avoid -0
let vv = v.toFixed(decs[j]);
let s = vv.toString().padStart(decs[j]+3, ' ');
process.stdout.write(s);
process.stdout.write(" ");
}
process.stdout.write("\n");
}
if (numRows "lt" m.length) console.log(". . .");
}
// ----------------------------------------------------------
function main()
{
console.log("\nBegin k-means clustering JavaScript ");
// 1. load normalized data from file into memory
console.log("\nLoading synthetic (200) data ");
let dataFile = ".\\Data\\synthetic_train_200.txt";
let X = loadTxt(dataFile, ",", [0,1,2,3,4,5], "#");
console.log("\nX data: ");
let decs = [4,4,4,4,4,4];
matShow(X, decs, 6, true); // decs, 5 rows, indices
// 2. instantiate KMeans object
console.log("\nClustering with k=4 ");
let k = 4;
let nTrials = k * (X.length + X[0].length); // heuristic
let maxIter = k * (X.length + X[0].length);
let seed = 0;
let km = new KMeans(k, nTrials, maxIter, seed);
// 3. cluster
km.cluster(X);
console.log("Done ");
// 4. show clustering results aka labels
console.log("\nClustering: ");
vecShow(km.clustering);
console.log("\nMeans: "); // aka cluster_centers
matShow(km.means, decs, k, true);
// aka inertia
console.log("\nWCSS: " + km.WCSS.toFixed(4).toString());
console.log("\nEnd demo ");
}
// ----------------------------------------------------------
main();
Here’s the Python scikit code that gives identical results:
# kmeans_scikit.py
import numpy as np
from sklearn.cluster import KMeans
np.set_printoptions(suppress=True, precision=4,
floatmode='fixed')
print("\nBegin k-means clustering using scikit ")
print("\nLoading synthetic (200) data ")
data_file = ".\\Data\\synthetic_train_200.txt"
X = np.loadtxt(data_file, usecols=[0,1,2,3,4,5],
comments="#", delimiter=",", dtype=np.float64)
print("\nX data: ")
print(X)
print("\nClustering using k=4 n_init=100 " + \
"max_iter=300 RS=55")
# init = kmeans++, n_init=1 for kmeans++, max_iter=300
kmeans = KMeans(n_clusters=4, n_init=100,
random_state=55)
kmeans.fit(X)
print("Done")
np.set_printoptions(suppress=True, precision=4,
floatmode='fixed', linewidth=41)
print("\nLabels: ")
print(kmeans.labels_)
np.set_printoptions(suppress=True, precision=4,
floatmode='fixed', linewidth=80)
print("\nCluster centers: ")
print(kmeans.cluster_centers_)
wcss = kmeans.inertia_
print("\nInertia = %0.4f " % wcss)
print("\nEnd demo ")
Data:
# synthetic_train_200.txt # -0.1660, 0.4406, -0.9998, -0.3953, -0.7065, 0.4840 0.0776, -0.1616, 0.3704, -0.5911, 0.7562, 0.1568 -0.9452, 0.3409, -0.1654, 0.1174, -0.7192, 0.8054 0.9365, -0.3732, 0.3846, 0.7528, 0.7892, 0.1345 -0.8299, -0.9219, -0.6603, 0.7563, -0.8033, 0.7955 0.0663, 0.3838, -0.3690, 0.3730, 0.6693, 0.3206 -0.9634, 0.5003, 0.9777, 0.4963, -0.4391, 0.7377 -0.1042, 0.8172, -0.4128, -0.4244, -0.7399, 0.4801 -0.9613, 0.3577, -0.5767, -0.4689, -0.0169, 0.6861 -0.7065, 0.1786, 0.3995, -0.7953, -0.1719, 0.5569 0.3888, -0.1716, -0.9001, 0.0718, 0.3276, 0.2500 0.1731, 0.8068, -0.7251, -0.7214, 0.6148, 0.3297 -0.2046, -0.6693, 0.8550, -0.3045, 0.5016, 0.2129 0.2473, 0.5019, -0.3022, -0.4601, 0.7918, 0.2613 -0.1438, 0.9297, 0.3269, 0.2434, -0.7705, 0.5171 0.1568, -0.1837, -0.5259, 0.8068, 0.1474, 0.3307 -0.9943, 0.2343, -0.3467, 0.0541, 0.7719, 0.5581 0.2467, -0.9684, 0.8589, 0.3818, 0.9946, 0.1092 -0.6553, -0.7257, 0.8652, 0.3936, -0.8680, 0.7018 0.8460, 0.4230, -0.7515, -0.9602, -0.9476, 0.1996 -0.9434, -0.5076, 0.7201, 0.0777, 0.1056, 0.5664 0.9392, 0.1221, -0.9627, 0.6013, -0.5341, 0.1533 0.6142, -0.2243, 0.7271, 0.4942, 0.1125, 0.1661 0.4260, 0.1194, -0.9749, -0.8561, 0.9346, 0.2230 0.1362, -0.5934, -0.4953, 0.4877, -0.6091, 0.3810 0.6937, -0.5203, -0.0125, 0.2399, 0.6580, 0.1460 -0.6864, -0.9628, -0.8600, -0.0273, 0.2127, 0.5387 0.9772, 0.1595, -0.2397, 0.1019, 0.4907, 0.1611 0.3385, -0.4702, -0.8673, -0.2598, 0.2594, 0.2270 -0.8669, -0.4794, 0.6095, -0.6131, 0.2789, 0.4700 0.0493, 0.8496, -0.4734, -0.8681, 0.4701, 0.3516 0.8639, -0.9721, -0.5313, 0.2336, 0.8980, 0.1412 0.9004, 0.1133, 0.8312, 0.2831, -0.2200, 0.1782 0.0991, 0.8524, 0.8375, -0.2102, 0.9265, 0.2150 -0.6521, -0.7473, -0.7298, 0.0113, -0.9570, 0.7422 0.6190, -0.3105, 0.8802, 0.1640, 0.7577, 0.1056 0.6895, 0.8108, -0.0802, 0.0927, 0.5972, 0.2214 0.1982, -0.9689, 0.1870, -0.1326, 0.6147, 0.1310 -0.3695, 0.7858, 0.1557, -0.6320, 0.5759, 0.3773 -0.1596, 0.3581, 0.8372, -0.9992, 0.9535, 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