C＃中两个数组的相关性
有两个double值数组，我想计算相关系数（单个double值，就像MS Excel中的CORREL函数一样）。 C＃中有一些简单的单行解决方案吗？
我已经发现了名为Meta Numerics的数学库。 根据这个问题 ，它应该做的工作。 这是Meta Numerics相关方法的文档，我没有得到。
可以请某人为我提供简单的代码片段或示例如何使用该库？
注意：最后，我被迫使用一种自定义实现。 但是，如果有人在阅读这个问题时知道好的，有文档记录的C＃数学库/框架，请不要犹豫，并在回答中发布一个链接。
您可以将值放在相同索引的单独列表中，并使用简单的Zip 。
var fitResult = new FitResult(); var values1 = new List(); var values2 = new List (); var correls = values1.Zip(values2, (v1, v2) => fitResult.CorrelationCoefficient(v1, v2));
第二种方法是编写自己的自定义实现（我的速度并未优化）：
public double ComputeCoeff(double[] values1, double[] values2) { if(values1.Length != values2.Length) throw new ArgumentException("values must be the same length"); var avg1 = values1.Average(); var avg2 = values2.Average(); var sum1 = values1.Zip(values2, (x1, y1) => (x1 - avg1) * (y1 - avg2)).Sum(); var sumSqr1 = values1.Sum(x => Math.Pow((x - avg1), 2.0)); var sumSqr2 = values2.Sum(y => Math.Pow((y - avg2), 2.0)); var result = sum1 / Math.Sqrt(sumSqr1 * sumSqr2); return result; }
用法：
var values1 = new List { 3, 2, 4, 5 ,6 }; var values2 = new List { 9, 7, 12 ,15, 17 }; var result = ComputeCoeff(values1.ToArray(), values2.ToArray()); // 0.997054485501581 Debug.Assert(result.ToString("F6") == "0.997054");
另一种方法是直接使用Excel函数：
var values1 = new List { 3, 2, 4, 5 ,6 }; var values2 = new List { 9, 7, 12 ,15, 17 }; // Make sure to add a reference to Microsoft.Office.Interop.Excel.dll // and use the namespace var application = new Application(); var worksheetFunction = application.WorksheetFunction; var result = worksheetFunction.Correl(values1.ToArray(), values2.ToArray()); Console.Write(result); // 0.997054485501581
Math.NET Numerics是一个记录良好的数学库，包含Correlation类。 它计算了Pearson和Spearman排名相关性： http ： //numerics.mathdotnet.com/api/MathNet.Numerics.Statistics/Correlation.htm
该库可在非常自由的MIT / X11许可下使用。 用它来计算相关系数就像下面这样简单：
using MathNet.Numerics.Statistics; ... correlation = Correlation.Pearson(arrayOfValues1, arrayOfValues2);
祝好运！
为了计算Pearson乘积矩相关系数
http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient
你可以使用这个简单的代码：
public static Double Correlation(Double[] Xs, Double[] Ys) { Double sumX = 0; Double sumX2 = 0; Double sumY = 0; Double sumY2 = 0; Double sumXY = 0; int n = Xs.Length < Ys.Length ? Xs.Length : Ys.Length; for (int i = 0; i < n; ++i) { Double x = Xs[i]; Double y = Ys[i]; sumX += x; sumX2 += x * x; sumY += y; sumY2 += y * y; sumXY += x * y; } Double stdX = Math.Sqrt(sumX2 / n - sumX * sumX / n / n); Double stdY = Math.Sqrt(sumY2 / n - sumY * sumY / n / n); Double covariance = (sumXY / n - sumX * sumY / n / n); return covariance / stdX / stdY; }
如果您不想使用第三方库，可以使用此post中的方法（在此处发布代码进行备份）。
double[] array1 = { 3, 2, 4, 5, 6 }; double[] array2 = { 9, 7, 12, 15, 17 }; double correl = Correlation(array1, array2); public double Correlation(double array1, double array2) { double[] array_xy = new double[array1.Length]; double[] array_xp2 = new double[array1.Length]; double[] array_yp2 = new double[array1.Length]; for (int i = 0; i < array1.Length; i++) array_xy[i] = array1[i] * array2[i]; for (int i = 0; i < array1.Length; i++) array_xp2[i] = Math.Pow(array1[i], 2.0); for (int i = 0; i < array1.Length; i++) array_yp2[i] = Math.Pow(array2[i], 2.0); double sum_x = 0; double sum_y = 0; foreach (double n in array1) sum_x += n; foreach (double n in array2) sum_y += n; double sum_xy = 0; foreach (double n in array_xy) sum_xy += n; double sum_xpow2 = 0; foreach (double n in array_xp2) sum_xpow2 += n; double sum_ypow2 = 0; foreach (double n in array_yp2) sum_ypow2 += n; double Ex2 = Math.Pow(sum_x, 2.00); double Ey2 = Math.Pow(sum_y, 2.00); return (array1.Length * sum_xy - sum_x * sum_y) / Math.Sqrt((array1.Length * sum_xpow2 - Ex2) * (array1.Length * sum_ypow2 - Ey2)); }
在我的测试中，上面的@Dmitry Bychenko和@ keyboardP的代码发布导致与我做过的一些手动测试通常具有与Microsoft Excel相同的相关性，并且不需要任何外部库。
例如，运行一次（底部列出的此运行数据）：
@Dmitry Bychenko：-0.00418479432051121
@keyboardP：______- 0.00418479432051131
MS Excel：_________- 0.004184794
这是一个测试工具：
using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace TestCorrel { class Program { static void Main(string[] args) { Random rand = new Random(DateTime.Now.Millisecond); List x = new List (); List y = new List (); for (int i = 0; i < 100; i++) { x.Add(rand.Next(1000) * rand.NextDouble()); y.Add(rand.Next(1000) * rand.NextDouble()); Console.WriteLine(x[i] + "," + y[i]); } Console.WriteLine("Correl1: " + Correl1(x, y)); Console.WriteLine("Correl2: " + Correl2(x, y)); } public static double Correl1(List x, List y) { //https://stackoverflow.com/questions/17447817/correlation-of-two-arrays-in-c-sharp if (x.Count != y.Count) return (double.NaN); //throw new ArgumentException("values must be the same length"); double sumX = 0; double sumX2 = 0; double sumY = 0; double sumY2 = 0; double sumXY = 0; int n = x.Count < y.Count ? x.Count : y.Count; for (int i = 0; i < n; ++i) { Double xval = x[i]; Double yval = y[i]; sumX += xval; sumX2 += xval * xval; sumY += yval; sumY2 += yval * yval; sumXY += xval * yval; } Double stdX = Math.Sqrt(sumX2 / n - sumX * sumX / n / n); Double stdY = Math.Sqrt(sumY2 / n - sumY * sumY / n / n); Double covariance = (sumXY / n - sumX * sumY / n / n); return covariance / stdX / stdY; } public static double Correl2(List x, List y) { double[] array_xy = new double[x.Count]; double[] array_xp2 = new double[x.Count]; double[] array_yp2 = new double[x.Count]; for (int i = 0; i < x.Count; i++) array_xy[i] = x[i] * y[i]; for (int i = 0; i < x.Count; i++) array_xp2[i] = Math.Pow(x[i], 2.0); for (int i = 0; i < x.Count; i++) array_yp2[i] = Math.Pow(y[i], 2.0); double sum_x = 0; double sum_y = 0; foreach (double n in x) sum_x += n; foreach (double n in y) sum_y += n; double sum_xy = 0; foreach (double n in array_xy) sum_xy += n; double sum_xpow2 = 0; foreach (double n in array_xp2) sum_xpow2 += n; double sum_ypow2 = 0; foreach (double n in array_yp2) sum_ypow2 += n; double Ex2 = Math.Pow(sum_x, 2.00); double Ey2 = Math.Pow(sum_y, 2.00); double Correl = (x.Count * sum_xy - sum_x * sum_y) / Math.Sqrt((x.Count * sum_xpow2 - Ex2) * (x.Count * sum_ypow2 - Ey2)); return (Correl); } } }
以上示例数字的数据：
287.688269702572,225.610842817282 618.9313498167,177.955550192835 25.7778882802361,27.6549569366756 140.847984766051,714.618547504125 438.618761728806,533.48764902702 481.347431274758,214.381256273194 21.6406916848573,393.559209519792 135.30397563209,158.419851317732 334.314685154853,814.275162949821 764.614904770914,50.1435267264692 42.8179292282173,47.8631582287434 237.216836650491,370.488416981179 388.849658539449,134.961087643151 305.903013161804,441.926902444068 10.6625048679591,369.567569480076 36.9316453891488,24.8947204607049 2.10067253471383,491.941975629861 7.94887068492774,573.037801189831 341.738006353722,653.497146697015 98.8424873439793,475.215988045193 272.248712629196,36.1088809138671 122.336823399801,169.158256422336 9.32281673202422,631.076001565473 201.118425176068,803.724831627554 415.514343714115,64.248651454341 227.791637123,230.512133914284 25.3438658925443,396.854282886188 596.238994411304,72.543763144195 230.239735877253,933.983901697669 796.060099040186,689.952468971234 9.30882684202344,269.22063744125 16.5005430148451,8.96549091859045 536.324005148524,358.829873788557 519.694526420764,17.3212184707267 552.628357889423,12.5541588051962 210.516099897454,388.57537739937 141.341571405689,268.082028986924 503.880356335491,753.447006912645 515.494990213539,444.451280259737 973.8670776076,168.922799013985 85.7111146094795,36.3784999169309 37.2147129193017,108.040356312432 504.590177939548,50.3934166889607 482.821039277511,888.984586256083 5.52549206350255,156.717087003271 405.833169031345,394.099059180868 459.249365587835,11.68776424494 429.421127440604,314.216759666901 126.908422469584,331.907062556551 62.1416232716952,3.19765723645578 4.16058817699579,604.04046284223 484.262182311277,220.177370167886 58.6774453314382,339.09660232677 463.482149892246,199.181594849183 344.128297473829,268.531428258182 0.883430369609702,209.346384477963 77.9462970131758,255.221325168955 583.629439312792,235.557751925922 358.409186083083,376.046612200349 81.2148325150902,10.7696774717279 53.7315618049966,274.171515094196 111.284646992239,130.174321939319 317.280491961763,338.077288461885 177.454564264722,7.53587801919127 69.2239431670047,233.693477620228 823.419546454875,0.111916855029723 23.7174749401014,200.989081544331 44.9598299125022,102.633862571155 74.1602278468945,292.485449988155 130.11182449251,23.4682153367755 243.088760058903,335.807090202722 13.3974915991526,436.983231269281 73.3900805168739,252.352352472186 592.144630201228,92.3395205570103 57.7306153447044,47.1416798900541 522.649018382024,584.427794722108 15.3662010204821,60.1693953262499 16.8335716728277,851.401980430541 33.9869734449251,0.930781653584345 116.66608504982,146.126050951949 92.8896130355492,711.765618208687 317.91980889529,322.186540377413 44.8574470732629,209.275617858058 751.201537871362,37.935519233316 161.817758424588,2.83156183493862 531.64078452142,79.1750782491523 114.803219681048,283.106988439852 123.472725123853,154.125248027558 89.9276725453919,63.4626924192825 105.623296753328,111.234188702067 435.72981759707,23.7058234576629 259.324810619152,69.3535200857341 719.885234421531,381.086239833891 24.2674900099018,198.408173349876 57.7761600361095,146.52277489124 77.4594609157459,710.746080866431 636.671781979814,538.894185951396 56.6035279932448,58.2563265684323 485.16099039333,427.849954283261 91.9552873247095,576.92944263617