README.md (6226B)
1 <!-- 2 3 @license Apache-2.0 4 5 Copyright (c) 2018 The Stdlib Authors. 6 7 Licensed under the Apache License, Version 2.0 (the "License"); 8 you may not use this file except in compliance with the License. 9 You may obtain a copy of the License at 10 11 http://www.apache.org/licenses/LICENSE-2.0 12 13 Unless required by applicable law or agreed to in writing, software 14 distributed under the License is distributed on an "AS IS" BASIS, 15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 16 See the License for the specific language governing permissions and 17 limitations under the License. 18 19 --> 20 21 # incrmapcorr 22 23 > Compute a moving sample absolute [Pearson product-moment correlation coefficient][pearson-correlation] incrementally. 24 25 <section class="intro"> 26 27 The [Pearson product-moment correlation coefficient][pearson-correlation] between random variables `X` and `Y` is defined as 28 29 <!-- <equation class="equation" label="eq:pearson_correlation_coefficient" align="center" raw="\rho_{X,Y} = \frac{\operatorname{cov}(X,Y)}{\sigma_X \sigma_Y}" alt="Equation for the Pearson product-moment correlation coefficient."> --> 30 31 <div class="equation" align="center" data-raw-text="\rho_{X,Y} = \frac{\operatorname{cov}(X,Y)}{\sigma_X \sigma_Y}" data-equation="eq:pearson_correlation_coefficient"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@e7c0cbc398c5e64614baf47cf5c6259b93c0ffce/lib/node_modules/@stdlib/stats/incr/mapcorr/docs/img/equation_pearson_correlation_coefficient.svg" alt="Equation for the Pearson product-moment correlation coefficient."> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 where the numerator is the [covariance][covariance] and the denominator is the product of the respective standard deviations. 39 40 For a sample of size `W`, the sample [Pearson product-moment correlation coefficient][pearson-correlation] is defined as 41 42 <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> --> 43 44 <div class="equation" align="center" data-raw-text="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient"> 45 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@e7c0cbc398c5e64614baf47cf5c6259b93c0ffce/lib/node_modules/@stdlib/stats/incr/mapcorr/docs/img/equation_sample_pearson_correlation_coefficient.svg" alt="Equation for the sample Pearson product-moment correlation coefficient."> 46 <br> 47 </div> 48 49 <!-- </equation> --> 50 51 The sample **absolute** [Pearson product-moment correlation coefficient][pearson-correlation] is thus defined as the absolute value of the sample [Pearson product-moment correlation coefficient][pearson-correlation]. 52 53 </section> 54 55 <!-- /.intro --> 56 57 <section class="usage"> 58 59 ## Usage 60 61 ```javascript 62 var incrmapcorr = require( '@stdlib/stats/incr/mapcorr' ); 63 ``` 64 65 #### incrmapcorr( window\[, mx, my] ) 66 67 Returns an accumulator `function` which incrementally computes a moving sample absolute [Pearson product-moment correlation coefficient][pearson-correlation]. The `window` parameter defines the number of values over which to compute the moving sample absolute [Pearson product-moment correlation coefficient][pearson-correlation]. 68 69 ```javascript 70 var accumulator = incrmapcorr( 3 ); 71 ``` 72 73 If means are already known, provide `mx` and `my` arguments. 74 75 ```javascript 76 var accumulator = incrmapcorr( 3, 5.0, -3.14 ); 77 ``` 78 79 #### accumulator( \[x, y] ) 80 81 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. 82 83 ```javascript 84 var accumulator = incrmapcorr( 3 ); 85 86 var ar = accumulator(); 87 // returns null 88 89 // Fill the window... 90 ar = accumulator( 2.0, 1.0 ); // [(2.0, 1.0)] 91 // returns 0.0 92 93 ar = accumulator( -5.0, 3.14 ); // [(2.0, 1.0), (-5.0, 3.14)] 94 // returns ~1.0 95 96 ar = accumulator( 3.0, -1.0 ); // [(2.0, 1.0), (-5.0, 3.14), (3.0, -1.0)] 97 // returns ~0.925 98 99 // Window begins sliding... 100 ar = accumulator( 5.0, -9.5 ); // [(-5.0, 3.14), (3.0, -1.0), (5.0, -9.5)] 101 // returns ~0.863 102 103 ar = accumulator( -5.0, 1.5 ); // [(3.0, -1.0), (5.0, -9.5), (-5.0, 1.5)] 104 // returns ~0.803 105 106 ar = accumulator(); 107 // returns ~0.803 108 ``` 109 110 </section> 111 112 <!-- /.usage --> 113 114 <section class="notes"> 115 116 ## Notes 117 118 - 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. 119 - 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. 120 - In comparison to the sample [Pearson product-moment correlation coefficient][pearson-correlation], the sample absolute [Pearson product-moment correlation coefficient][pearson-correlation] is useful when only concerned with the strength of the correlation and not the direction. 121 122 </section> 123 124 <!-- /.notes --> 125 126 <section class="examples"> 127 128 ## Examples 129 130 <!-- eslint no-undef: "error" --> 131 132 ```javascript 133 var randu = require( '@stdlib/random/base/randu' ); 134 var incrmapcorr = require( '@stdlib/stats/incr/mapcorr' ); 135 136 var accumulator; 137 var x; 138 var y; 139 var i; 140 141 // Initialize an accumulator: 142 accumulator = incrmapcorr( 5 ); 143 144 // For each simulated datum, update the moving sample absolute correlation coefficient... 145 for ( i = 0; i < 100; i++ ) { 146 x = randu() * 100.0; 147 y = randu() * 100.0; 148 accumulator( x, y ); 149 } 150 console.log( accumulator() ); 151 ``` 152 153 </section> 154 155 <!-- /.examples --> 156 157 <section class="links"> 158 159 [pearson-correlation]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient 160 161 [covariance]: https://en.wikipedia.org/wiki/Covariance 162 163 </section> 164 165 <!-- /.links -->