@stdlib/stats-lowess

Locally-weighted polynomial regression via the LOWESS algorithm.

https://github.com/stdlib-js/stats-lowess

Science Score: 57.0%

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Keywords

javascript local locally loess lowess math mathematics node node-js nodejs regression smoother smoothing statistics stats stdlib weighted weights

Last synced: 4 months ago · JSON representation ·

Repository

Locally-weighted polynomial regression via the LOWESS algorithm.

Basic Info

Host: GitHub
Owner: stdlib-js
License: apache-2.0
Language: JavaScript
Default Branch: main
Homepage: https://github.com/stdlib-js/stdlib
Size: 1.5 MB

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Stars: 7
Watchers: 3
Forks: 0
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javascript local locally loess lowess math mathematics node node-js nodejs regression smoother smoothing statistics stats stdlib weighted weights

Created over 4 years ago · Last pushed 6 months ago

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Readme Changelog Contributing License Code of conduct Citation Security

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

LOWESS

Locally-weighted polynomial regression via the LOWESS algorithm.

## Installation ```bash npm install @stdlib/stats-lowess ``` Alternatively, - To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]). - If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions). - For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]). The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships. To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

## Usage ```javascript var lowess = require( '@stdlib/stats-lowess' ); ``` #### lowess( x, y\[, opts] ) For [input arrays][mdn-array] and/or [typed arrays][mdn-typed-array] `x` and `y`, the function returns an object holding the ordered input values `x` and smoothed values for `y`. ```javascript var x = [ 4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25 ]; var y = [ 2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46, 26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68, 32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85 ]; var out = lowess( x, y ); /* returns { 'x': [ 4, 4, 7, 7, ..., 24, 24, 24, 25 ], 'y': [ ~4.857, ~4.857, ~13.1037, ~13.1037, ..., ~79.102, ~79.102, ~79.102, ~84.825 ] } */ ``` The function accepts the following `options`: - **f**: positive `number` specifying the smoothing span, i.e., the proportion of points which influence smoothing at each value. Larger values correspond to more smoothing. Default: `2/3`. - **nsteps**: `number` of iterations in the robust fit (fewer iterations translates to faster function execution). If set to zero, the nonrobust fit is returned. Default: `3`. - **delta**: nonnegative `number` which may be used to reduce the number of computations. Default: 1/100th of the range of `x`. - **sorted**: `boolean` indicating if the input array `x` is sorted. Default: `false`. By default, smoothing at each value is determined by `2/3` of all other points. To choose a different smoothing span, set the `f` option. ```javascript var x = [ 4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25 ]; var y = [ 2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46, 26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68, 32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85 ]; var out = lowess( x, y, { 'f': 0.2 }); /* returns { 'x': [ 4, 4, 7, ..., 24, 24, 25 ], 'y': [ ~6.03, ~6.03, ~12.68, ..., ~82.575, ~82.575, ~93.028 ] } */ ``` By default, three iterations of locally weighted regression fits are calculated after the initial fit. To set a different number of iterations for the robust fit, set the `nsteps` option. ```javascript var x = [ 4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25 ]; var y = [ 2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46, 26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68, 32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85 ]; var out = lowess( x, y, { 'nsteps': 20 }); /* returns { 'x': [ 4, ..., 25 ], 'y': [ ~4.857, ..., ~84.825 ] } */ ``` To save computations, set the `delta` option. For cases where one has a large number of (x,y)-pairs, carrying out regression calculations for all points is not likely to be necessary. By default, `delta` is set to 1/100th of the range of the values in `x`. In this case, if the values in `x` were uniformly scattered over the entire range, the locally weighted regression would be calculated at approximately 100 points. On the other hand, for small data sets with less than 100 observations, one can safely set the option to zero so calculations are made for each data point. ```javascript var x = [ 4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25 ]; var y = [ 2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46, 26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68, 32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85 ]; var out = lowess( x, y, { 'delta': 0.0 }); /* returns { 'x': [ 4, ..., 25 ], 'y': [ ~4.857, ..., ~84.825 ] } */ ``` If the elements of `x` are sorted in ascending order, set the `sorted` option to `true`. ```javascript var x = [ 4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25 ]; var y = [ 2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46, 26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68, 32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85 ]; var out = lowess( x, y, { 'sorted': true }); /* returns { 'x': [ 4, ..., 25 ], 'y': [ ~4.857, ..., ~84.825 ] } */ ```

## Examples ```javascript var randn = require( '@stdlib/random-base-randn' ); var Float64Array = require( '@stdlib/array-float64' ); var plot = require( '@stdlib/plot-ctor' ); var lowess = require( '@stdlib/stats-lowess' ); var x; var y; var i; // Create some data... x = new Float64Array( 100 ); y = new Float64Array( x.length ); for ( i = 0; i < x.length; i++ ) { x[ i ] = i; y[ i ] = ( 0.5*i ) + ( 10.0*randn() ); } var opts = { 'delta': 0 }; var out = lowess( x, y, opts ); var h = plot( [ x, out.x ], [ y, out.y ] ); h.lineStyle = [ 'none', '-' ]; h.symbols = [ 'closed-circle', 'none' ]; h.view( 'stdout' ); ```

## References - Cleveland, William S. 1979. "Robust Locally and Smoothing Weighted Regression Scatterplots." _Journal of the American Statistical Association_ 74 (368): 829–36. doi:[10.1080/01621459.1979.10481038][@cleveland:1979]. - Cleveland, William S. 1981. "Lowess: A program for smoothing scatterplots by robust locally weighted regression." _American Statistician_ 35 (1): 54–55. doi:[10.2307/2683591][@cleveland:1981].

* * * ## Notice This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more. For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib]. #### Community [![Chat][chat-image]][chat-url] --- ## License See [LICENSE][stdlib-license]. ## Copyright Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].

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Standard library for JavaScript.

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message: >-
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type: software

authors:
  - name: The Stdlib Authors
    url: https://github.com/stdlib-js/stdlib/graphs/contributors

repository-code: https://github.com/stdlib-js/stdlib
url: https://stdlib.io

abstract: |
  Standard library for JavaScript and Node.js.

keywords:
  - JavaScript
  - Node.js
  - TypeScript
  - standard library
  - scientific computing
  - numerical computing
  - statistical computing

license: Apache-2.0 AND BSL-1.0

date-released: 2016

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npmjs.org: @stdlib/stats-lowess

Locally-weighted polynomial regression via the LOWESS algorithm.

Homepage: https://stdlib.io
License: Apache-2.0
Latest release: 0.2.2
published over 1 year ago

Versions: 10
Dependent Packages: 4
Dependent Repositories: 3
Downloads: 651 Last month

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Forks count: 15.4%

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planeshifter rreusser stdlib-bot kgryte

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@stdlib/assert-is-positive-number ^0.0.x
@stdlib/assert-is-typed-array-like ^0.0.x
@stdlib/math-base-special-abs ^0.0.x
@stdlib/math-base-special-floor ^0.0.x
@stdlib/math-base-special-max ^0.0.x
@stdlib/math-base-special-min ^0.0.x
@stdlib/math-base-special-pow ^0.0.x
@stdlib/math-base-special-sqrt ^0.0.x
@stdlib/stats-base-range ^0.0.x
@stdlib/string-format ^0.0.x
@stdlib/types ^0.0.x

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@stdlib/stats-lowess

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