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Dec 5, 2020
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Geometric Median
Also listed in…
Clustering
geometricMedian(points, P)
[
...geometricMedianIterator(points, {
P,
alpha: 0.5
})
]
paths = points.map(p0 => [
p0,
...geometricMedianIterator(points, {
P,
alpha: .2 / P,
precision: .03,
x: p0[0],
y: p0[1]
})
])
// as a function
geometricMedian = (points, options = {}) => {
for (var m of geometricMedianIterator(points, options));
return m;
}
function* geometricMedianIterator(
points,
{ P = 1, alpha = 1, precision = 1e-6, x = 0, y = 0 } = {}
) {
// starting point
let delta,
i = 0;
if (x === undefined) x = y = 0;
do {
let sx = 0;
let sy = 0;
let s = 0;
for (const p of points) {
const d = [x - p[0], y - p[1]];
const n = norm(d);
if (n) {
const np = pow(n, P - 2);
s += np;
sx += p[0] * np;
sy += p[1] * np;
}
}
yield [x, y];
const x_ = x,
y_ = y;
x += alpha * (sx / s - x);
y += alpha * (sy / s - y);
delta = abs(x - x_) + abs(y - y_);
} while (delta > precision && i++ < 1000);
return yield [x, y];
}
function norm(X) {
return Math.hypot(...X);
}
points = (replay,
Array.from({ length: 50 }, () => [random(), random()])
.map(d => [d[0] - 300, d[1] - 50])
.concat(
Array.from({ length: 30 + 40 * Math.random() }, () => [random(), random()])
))
random = d3.randomNormal(0, width / 20)
d3 = require("d3@6")
height = 500
import { abs, pow, tau } from "@fil/math"
import { slider } from "@jashkenas/inputs"
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