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Locally-weighted polynomial regression via the LOWESS algorithm.
To use in Observable,
lowess = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-lowess@umd/browser.js' )To vendor stdlib functionality and avoid installing dependency trees for Node.js, you can use the UMD server build:
var lowess = require( 'path/to/vendor/umd/stats-lowess/index.js' )To include the bundle in a webpage,
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-lowess@umd/browser.js"></script>If no recognized module system is present, access bundle contents via the global scope:
<script type="text/javascript">
(function () {
window.lowess;
})();
</script>For input arrays and/or typed arrays x and y, the function returns an object holding the ordered input values x and smoothed values for y.
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
numberspecifying 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:
numberof 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
numberwhich may be used to reduce the number of computations. Default: 1/100th of the range ofx. - sorted:
booleanindicating if the input arrayxis 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.
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.
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.
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.
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
]
}
*/<!DOCTYPE html>
<html lang="en">
<body>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randn@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/plot-ctor@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-lowess@umd/browser.js"></script>
<script type="text/javascript">
(function () {
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' );
})();
</script>
</body>
</html>- 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, William S. 1981. "Lowess: A program for smoothing scatterplots by robust locally weighted regression." American Statistician 35 (1): 54–55. doi:10.2307/2683591.
This package is part of 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, see the main project repository.
See LICENSE.
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