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incrpcorrdistmat

Compute a sample Pearson product-moment correlation distance matrix incrementally.

A sample Pearson product-moment correlation distance matrix is an M-by-M matrix whose elements specified by indices j and k are the sample Pearson product-moment correlation distances between the jth and kth data variables. The sample Pearson product-moment correlation distance is defined as

$$d_{x,y} = 1 - r_{x,y} = 1 - \frac{\mathop{\mathrm{cov_n(x,y)}}}{\sigma_x \sigma_y}$$

where r is the sample Pearson product-moment correlation coefficient, cov(x,y) is the sample covariance, and σ corresponds to the sample standard deviation. As r resides on the interval [-1,1], d resides on the interval [0,2].

Installation

npm install @stdlib/stats-incr-pcorrdistmat

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 incrpcorrdistmat = require( '@stdlib/stats-incr-pcorrdistmat' );

incrpcorrdistmat( out[, means] )

Returns an accumulator function which incrementally computes a sample Pearson product-moment correlation distance matrix.

// Create an accumulator for computing a 2-dimensional correlation distance matrix:
var accumulator = incrpcorrdistmat( 2 );

The out argument may be either the order of the correlation distance matrix or a square 2-dimensional ndarray for storing the correlation distance matrix.

var Float64Array = require( '@stdlib/array-float64' );
var ndarray = require( '@stdlib/ndarray-ctor' );

var buffer = new Float64Array( 4 );
var shape = [ 2, 2 ];
var strides = [ 2, 1 ];

// Create a 2-dimensional output correlation distance matrix:
var dist = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );

var accumulator = incrpcorrdistmat( dist );

When means are known, the function supports providing a 1-dimensional ndarray containing mean values.

var Float64Array = require( '@stdlib/array-float64' );
var ndarray = require( '@stdlib/ndarray-ctor' );

var buffer = new Float64Array( 2 );
var shape = [ 2 ];
var strides = [ 1 ];

var means = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );

means.set( 0, 3.0 );
means.set( 1, -5.5 );

var accumulator = incrpcorrdistmat( 2, means );

accumulator( [vector] )

If provided a data vector, the accumulator function returns an updated sample Pearson product-moment distance correlation matrix. If not provided a data vector, the accumulator function returns the current sample Pearson product-moment correlation distance matrix.

var Float64Array = require( '@stdlib/array-float64' );
var ndarray = require( '@stdlib/ndarray-ctor' );

var buffer = new Float64Array( 4 );
var shape = [ 2, 2 ];
var strides = [ 2, 1 ];
var dist = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );

buffer = new Float64Array( 2 );
shape = [ 2 ];
strides = [ 1 ];
var vec = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );

var accumulator = incrpcorrdistmat( dist );

vec.set( 0, 2.0 );
vec.set( 1, 1.0 );

var out = accumulator( vec );
// returns <ndarray>

var bool = ( out === dist );
// returns true

vec.set( 0, 1.0 );
vec.set( 1, -5.0 );

out = accumulator( vec );
// returns <ndarray>

vec.set( 0, 3.0 );
vec.set( 1, 3.14 );

out = accumulator( vec );
// returns <ndarray>

out = accumulator();
// returns <ndarray>

Notes

• Due to limitations inherent in representing numeric values using floating-point format (i.e., the inability to represent numeric values with infinite precision), the correlation distance between perfectly correlated random variables may not be 0 or 2. In fact, the correlation distance is not guaranteed to be strictly on the interval [0,2]. Any computed distance should, however, be within floating-point roundoff error.

Examples

var randu = require( '@stdlib/random-base-randu' );
var ndarray = require( '@stdlib/ndarray-ctor' );
var Float64Array = require( '@stdlib/array-float64' );
var incrpcorrdistmat = require( '@stdlib/stats-incr-pcorrdistmat' );

var dist;
var dxy;
var dyx;
var dx;
var dy;
var i;

// Initialize an accumulator for a 2-dimensional correlation distance matrix:
var accumulator = incrpcorrdistmat( 2 );

// Create a 1-dimensional data vector:
var buffer = new Float64Array( 2 );
var shape = [ 2 ];
var strides = [ 1 ];

var vec = ndarray( 'float64', buffer, shape, strides, 0, 'row-major' );

// For each simulated data vector, update the sample correlation distance matrix...
for ( i = 0; i < 100; i++ ) {
    vec.set( 0, randu()*100.0 );
    vec.set( 1, randu()*100.0 );
    dist = accumulator( vec );

    dx = dist.get( 0, 0 ).toFixed( 4 );
    dy = dist.get( 1, 1 ).toFixed( 4 );
    dxy = dist.get( 0, 1 ).toFixed( 4 );
    dyx = dist.get( 1, 0 ).toFixed( 4 );

    console.log( '[ %d, %d\n  %d, %d ]', dx, dxy, dyx, dy );
}

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See Also

• @stdlib/stats-incr/pcorrdist: compute a sample Pearson product-moment correlation distance.
• @stdlib/stats-incr/pcorrmat: compute a sample Pearson product-moment correlation matrix 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.