散点图"最佳拟合"线的算法

Question

我正在使用MSChart控件在C#中编写一个小应用程序来执行X和Y数据点集的Scatter Plots.其中一些可能相当大(数百个数据点).

想要询问是否有一个"标准"算法来绘制点上最合适的线.我想将X数据点分成预定数量的集合,比如10或20,并且对于每个集合,取相应Y值和中间X值的平均值,依此类推以创建该行.这是正确的方法吗？

我搜索了现有的线程,但它们似乎都是使用像Matlab这样的现有应用程序实现相同的.

谢谢,

Answer 1

使用线性最小二乘算法

public class XYPoint
{
    public int X;
    public double Y;
}

class Program
{
    public static List<XYPoint> GenerateLinearBestFit(List<XYPoint> points, out double a, out double b)
    {
        int numPoints = points.Count;
        double meanX = points.Average(point => point.X);
        double meanY = points.Average(point => point.Y);

        double sumXSquared = points.Sum(point => point.X * point.X);
        double sumXY = points.Sum(point => point.X * point.Y);

        a = (sumXY / numPoints - meanX * meanY) / (sumXSquared / numPoints - meanX * meanX);
        b = (a * meanX - meanY);

        double a1 = a;
        double b1 = b;

        return points.Select(point => new XYPoint() { X = point.X, Y = a1 * point.X - b1 }).ToList();
    }

    static void Main(string[] args)
    {
        List<XYPoint> points = new List<XYPoint>()
                                   {
                                       new XYPoint() {X = 1, Y = 12},
                                       new XYPoint() {X = 2, Y = 16},
                                       new XYPoint() {X = 3, Y = 34},
                                       new XYPoint() {X = 4, Y = 45},
                                       new XYPoint() {X = 5, Y = 47}
                                   };

        double a, b;

        List<XYPoint> bestFit = GenerateLinearBestFit(points, out a, out b);

        Console.WriteLine("y = {0:#.####}x {1:+#.####;-#.####}", a, -b);

        for(int index = 0; index < points.Count; index++)
        {
            Console.WriteLine("X = {0}, Y = {1}, Fit = {2:#.###}", points[index].X, points[index].Y, bestFit[index].Y);
        }
    }
}