stdlib-js / stats-incr-mapcorr

Compute a moving sample absolute Pearson product-moment correlation coefficient incrementally.

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incrmapcorr

Compute a moving sample absolute Pearson product-moment correlation coefficient incrementally.

The Pearson product-moment correlation coefficient between random variables X and Y is defined as

$$\rho_{X,Y} = \frac{\mathop{\mathrm{cov}}(X,Y)}{\sigma_X \sigma_Y}$$

where the numerator is the covariance and the denominator is the product of the respective standard deviations.

For a sample of size W, the sample Pearson product-moment correlation coefficient is defined as

$$r = \frac{\displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}$$

The sample absolute Pearson product-moment correlation coefficient is thus defined as the absolute value of the sample Pearson product-moment correlation coefficient.

Installation

npm install @stdlib/stats-incr-mapcorr

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md 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

var incrmapcorr = require( '@stdlib/stats-incr-mapcorr' );

incrmapcorr( window[, mx, my] )

Returns an accumulator function which incrementally computes a moving sample absolute Pearson product-moment correlation coefficient. The window parameter defines the number of values over which to compute the moving sample absolute Pearson product-moment correlation coefficient.

var accumulator = incrmapcorr( 3 );

If means are already known, provide mx and my arguments.

var accumulator = incrmapcorr( 3, 5.0, -3.14 );

accumulator( [x, y] )

If provided input values x and y, the accumulator function returns an updated accumulated value. If not provided input values x and y, the accumulator function returns the current accumulated value.

var accumulator = incrmapcorr( 3 );

var ar = accumulator();
// returns null

// Fill the window...
ar = accumulator( 2.0, 1.0 ); // [(2.0, 1.0)]
// returns 0.0

ar = accumulator( -5.0, 3.14 ); // [(2.0, 1.0), (-5.0, 3.14)]
// returns ~1.0

ar = accumulator( 3.0, -1.0 ); // [(2.0, 1.0), (-5.0, 3.14), (3.0, -1.0)]
// returns ~0.925

// Window begins sliding...
ar = accumulator( 5.0, -9.5 ); // [(-5.0, 3.14), (3.0, -1.0), (5.0, -9.5)]
// returns ~0.863

ar = accumulator( -5.0, 1.5 ); // [(3.0, -1.0), (5.0, -9.5), (-5.0, 1.5)]
// returns ~0.803

ar = accumulator();
// returns ~0.803

Notes

• Input values are not type checked. If provided NaN or a value which, when used in computations, results in NaN, the accumulated value is NaN for at least W-1 future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.
• As W (x,y) pairs are needed to fill the window buffer, the first W-1 returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.
• In comparison to the sample Pearson product-moment correlation coefficient, the sample absolute Pearson product-moment correlation coefficient is useful when only concerned with the strength of the correlation and not the direction.

Examples

var randu = require( '@stdlib/random-base-randu' );
var incrmapcorr = require( '@stdlib/stats-incr-mapcorr' );

var accumulator;
var x;
var y;
var i;

// Initialize an accumulator:
accumulator = incrmapcorr( 5 );

// For each simulated datum, update the moving sample absolute correlation coefficient...
for ( i = 0; i < 100; i++ ) {
    x = randu() * 100.0;
    y = randu() * 100.0;
    accumulator( x, y );
}
console.log( accumulator() );

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See Also

• @stdlib/stats-incr/apcorr: compute a sample absolute Pearson product-moment correlation coefficient.
• @stdlib/stats-incr/mpcorr: compute a moving sample Pearson product-moment correlation coefficient incrementally.
• @stdlib/stats-incr/mpcorr2: compute a moving squared sample Pearson product-moment correlation coefficient incrementally.

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Notice

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.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.