C# Works like ksdensity in mathlab. KDE performs kernel density estimation (KDE)on one - dimensional data. Probability density function (PDF) signal analysis.

kernel density estimation C#

public static double[,] KernelDensityEstimation(double[] data, double sigma, int nsteps)
        {
            // probability density function (PDF) signal analysis
            // Works like ksdensity in mathlab. 
            // KDE performs kernel density estimation (KDE)on one - dimensional data
            // http://en.wikipedia.org/wiki/Kernel_density_estimation

            // Input:	-data: input data, one-dimensional
            //          -sigma: bandwidth(sometimes called "h")
            //          -nsteps: optional number of abscis points.If nsteps is an
            //          array, the abscis points will be taken directly from it. (default 100)
            // Output:	-x: equispaced abscis points
            //          -y: estimates of p(x)

            // This function is part of the Kernel Methods Toolbox(KMBOX) for MATLAB. 
            // http://sourceforge.net/p/kmbox
            // Converted to C# code by ksandric

            double[,] result = new double[nsteps, 2];
            double[] x = new double[nsteps], y = new double[nsteps];

            double MAX = Double.MinValue, MIN = Double.MaxValue;
            int N = data.Length; // number of data points

            // Find MIN MAX values in data
            for (int i = 0; i < N; i++)
            {
                if (MAX < data[i])
                {
                    MAX = data[i];
                }
                if (MIN > data[i])
                {
                    MIN = data[i];
                }
            }

            // Like MATLAB linspace(MIN, MAX, nsteps);
            x[0] = MIN;
            for (int i = 1; i < nsteps; i++)
            {
                x[i] = x[i - 1] + ((MAX - MIN) / nsteps);
            }

            // kernel density estimation
            double c = 1.0 / (Math.Sqrt(2 * Math.PI * sigma * sigma));
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < nsteps; j++)
                {
                    y[j] = y[j] + 1.0 / N * c * Math.Exp(-(data[i] - x[j]) * (data[i] - x[j]) / (2 * sigma * sigma));
                }
            }

            // compilation of the X,Y to result. Good for creating plot(x, y)
            for (int i = 0; i < nsteps; i++)
            {
                result[i, 0] = x[i];
                result[i, 1] = y[i];
            }
            return result;
        }

This function does not have such functionality. But it can be added by working with the result of the function double[,] result

To do this, you need to refine the function. Add an input parameter indicating the interval. And implement the logic, for example, the one you use "by padding or removing some range". Or take this functionality out into a separate function. This seems like a simple action.

Thanks. I just tried your KernelDensityEstimation and compared it with the matlab ksdensity, I used same input data but the result seems to be very different:

The above picture is plot from KernelDensityEstimation result

The above picture is plot from matlab result

I used same data for both of the two, and the code is as follows:

static void Main()
{
    // Sample data
    double[] x = new double[60] {0.5377,1.8339,-2.2588,0.8622,0.3188,-1.3077,-0.4336,0.3426,3.5784,2.7694,
                                -1.3499,3.0349,0.7254,-0.0631,0.7147,-0.205,-0.1241,1.4897,1.409,1.4172,
                                0.6715,-1.2075,0.7172,1.6302,0.4889,1.0347,0.7269,-0.3034,0.2939,-0.7873,
                                5.8884,3.8529,3.9311,4.1905,2.0557,6.4384,5.3252,4.2451,6.3703,3.2885,
                                4.8978,4.7586,5.3192,5.3129,4.1351,4.9699,4.8351,5.6277,6.0933,6.1093,4.1363,
                                5.0774,3.7859,3.8865,4.9932,6.5326,4.2303,5.3714,4.7744,6.1174};
    double[,] doubles = KernelDensityEstimation(x, 0.9, 128);  \\I firstly use 0.09 but it seems that 0.09 is too sensitive

    using (StreamWriter sw = new StreamWriter(@"D:\\Downloads\\data1.txt"))
    {
        int num = doubles.GetLength(0);
        for (int i = 0; i < num; i++)
        {
            sw.WriteLine(doubles[i, 0].ToString() + "," + doubles[i, 1].ToString());  \\write out and plot it using excel
        }
}
}

x = [0.5377;1.8339;-2.2588;0.8622;0.3188;-1.3077;-0.4336;0.3426;3.5784;2.7694;
-1.3499;3.0349;0.7254;-0.0631;0.7147;-0.205;-0.1241;1.4897;1.409;1.4172;
0.6715;-1.2075;0.7172;1.6302;0.4889;1.0347;0.7269;-0.3034;0.2939;-0.7873;
5.8884;3.8529;3.9311;4.1905;2.0557;6.4384;5.3252;4.2451;6.3703;3.2885;
4.8978;4.7586;5.3192;5.3129;4.1351;4.9699;4.8351;5.6277;6.0933;6.1093;4.1363;
5.0774;3.7859;3.8865;4.9932;6.5326;4.2303;5.3714;4.7744;6.1174];
num_pts = 128;
pts = 0:(6-0)/(num_pts-1):6;
[f,xi] = ksdensity(x, pts); 
figure
plot(xi,f);

I dont know what makes the result so different. Is it because sigma ?