Multivariate LOESS

Smoothing over multiple predictor dimensions simultaneously.

Overview

Standard LOESS operates on a single predictor $x$. Setting dimensions > 1 extends the neighbourhood search and local polynomial fit into an $n$-dimensional predictor space, enabling surface smoothing over spatial grids, time–altitude combinations, and similar multi-predictor datasets.

Dimensions	Use Case	Input Shape
1	Time series, 1D signal (default)	x: 1-D array
2	Spatial surface, 2-predictor model	x: n × 2 matrix
3+	High-dimensional regression	x: n × d matrix

Computational cost

Neighbourhood search scales with $d$ dimensions. For dimensions ≥ 3 keep fraction small and consider increasing delta to activate interpolation.

---

1D — Standard (Default)

Single predictor. No configuration required.

const { Loess } = require('fastloess-wasm');

const n = 100;
const x = Float64Array.from({ length: n }, (_, i) => i * 2 * Math.PI / (n - 1));
const y = Float64Array.from(x, (xi, i) => Math.sin(xi) + (((i * 7 + 3) % 17) / 17 - 0.5) * 0.6);

const model = new Loess({ fraction: 0.3 });
const result = model.fit(x, y);
console.log("y[0]:", result.y[0].toFixed(4));

y[0]: 0.0281

---

2D — Spatial Surface

Two predictors (e.g., latitude/longitude, time/altitude). Pass an $n \times 2$ matrix as x.

const { Loess } = require('fastloess-wasm');

const n = 100;
const lat = Float64Array.from({ length: n }, (_, i) => i * 2 * Math.PI / (n - 1));
const lon = Float64Array.from({ length: n }, (_, i) => i * 2 * Math.PI / (n - 1));
const z = Float64Array.from({ length: n }, (_, i) => Math.sin(lat[i]) + Math.cos(lon[i]) + 0.05);
const x2d = Float64Array.from({ length: n * 2 }, (_, k) => k % 2 === 0 ? lat[k >> 1] : lon[k >> 1]);

const model = new Loess({ dimensions: 2, fraction: 0.3 });
const result = model.fit(x2d, z);
console.log("y[0]:", result.y[0].toFixed(4));

y[0]: 1.2204

---

3D and Higher

Three or more predictors. The neighbourhood radius grows in each additional dimension, so a larger fraction (or smaller dataset) is typically needed.

const { Loess } = require('fastloess-wasm');

const n = 100;
const x1 = Float64Array.from({ length: n }, (_, i) => i * 2 * Math.PI / (n - 1));
const x2 = Float64Array.from({ length: n }, (_, i) => i / (n - 1));
const x3 = Float64Array.from({ length: n }, (_, i) => 1 - i / (n - 1));
const y = Float64Array.from({ length: n }, (_, i) => Math.sin(x1[i]) + x2[i] - x3[i] + 0.05);
const x3d = Float64Array.from({ length: n * 3 }, (_, k) => {
    const i = Math.floor(k / 3), d = k % 3;
    return d === 0 ? x1[i] : d === 1 ? x2[i] : x3[i];
});

const model = new Loess({ dimensions: 3, fraction: 0.5 });
const result = model.fit(x3d, y);
console.log("y[0]:", result.y[0].toFixed(4));

y[0]: -0.6708

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Distance Metrics for Multivariate Data

When dimensions > 1 you can also control how inter-point distances are computed.

Metric	Description	When to Use
"normalized"	Each dimension scaled to unit range (default)	Predictors on different scales
"euclidean"	Raw Euclidean distance	Predictors already on same scale
"minkowski:p"	Generalised Minkowski ($L_p$) norm	Custom distance geometry
"weighted"	Per-dimension weighted Euclidean	Domain-specific importance

See API Reference for the full list of options per language.