55 lines
2.3 KiB
C#
55 lines
2.3 KiB
C#
|
using System;
|
|||
|
|
using System.Collections.Generic;
|
|||
|
|
using System.Linq;
|
|||
|
|
using System.Text;
|
|||
|
|
|
|||
|
|
namespace BotSharp.Algorithm.HiddenMarkovModel.MathUtils.Statistics
|
|||
|
|
{
|
|||
|
|
/// <summary>
|
|||
|
|
/// Correlation: strength of a linear relationship.
|
|||
|
|
///
|
|||
|
|
/// Correleation, which always taks values between -1 and 1, describse the strength of the lienar relationship between two variables.
|
|||
|
|
/// We denote the correlation by R.
|
|||
|
|
///
|
|||
|
|
/// Only when the relationship is perfectly linear is the correlation either -1 or +1.
|
|||
|
|
/// If the relationship is strong and positive, the correlation will be near +1
|
|||
|
|
/// If the relationship is strong and negative, the correlation will be near -1
|
|||
|
|
/// If there is no apparent linear relationship between the variables, then the correlation will be near zero.
|
|||
|
|
/// </summary>
|
|||
|
|
public class Correlation
|
|||
|
|
{
|
|||
|
|
/// <summary>
|
|||
|
|
/// Return the correlation for observations (x_1, y_1), (x_2, y_2), ... (x_n, y_n), where n is the sample size
|
|||
|
|
/// The correlation is computed as correlation(x, y) = sum_i((x_i - mu_x) * (y_i - mu_y)) / (sum_i((x_i - mu_x)^2) * sum_i((y_i - mu_y)^2))
|
|||
|
|
/// which can also be written as n * sum_i((x_i - mu_x) * (y_i - mu_y) / (sigma_x * sigma_y))
|
|||
|
|
/// where mu_x = sum_i(x_i) / n and sigma_x = sqrt(sum_i((x_i - mu_x)^2) / n)
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="observations">The observations (x_1, y_1), (x_2, y_2), ... (x_n, y_n), where n is the sample size</param>
|
|||
|
|
/// <returns>The correlation value for variable x and y</returns>
|
|||
|
|
public double GetCorrelation(Tuple<double, double>[] observations)
|
|||
|
|
{
|
|||
|
|
int n = observations.Length;
|
|||
|
|
double[] x = new double[n];
|
|||
|
|
double[] y = new double[n];
|
|||
|
|
for (int i = 0; i < n; ++i)
|
|||
|
|
{
|
|||
|
|
x[i] = observations[i].Item1;
|
|||
|
|
y[i] = observations[i].Item2;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
double mu_x = Mean.GetMean(x);
|
|||
|
|
double mu_y = Mean.GetMean(y);
|
|||
|
|
|
|||
|
|
double sigma_x = StdDev.GetStdDev(x, mu_x);
|
|||
|
|
double sigma_y = StdDev.GetStdDev(y, mu_y);
|
|||
|
|
|
|||
|
|
double sum = 0;
|
|||
|
|
for (int i = 0; i < n; ++i)
|
|||
|
|
{
|
|||
|
|
sum += ((x[i] - mu_x) / sigma_x) * ((y[i] - mu_y) / sigma_y);
|
|||
|
|
}
|
|||
|
|
return sum / n;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|