/// <summary>
/// Estimate appropriate values for sigma given a data set.
/// </summary>
///
/// <remarks>
/// This method uses a simple heuristic to obtain appropriate values
/// for sigma in a radial basis function kernel. The heuristic is shown
/// by Caputo, Sim, Furesjo and Smola, "Appearance-based object
/// recognition using SVMs: which kernel should I use?", 2002.
/// </remarks>
///
/// <param name="inputs">The data set.</param>
/// <param name="samples">The number of random samples to analyze.</param>
/// <param name="range">The range of suitable values for sigma.</param>
///
/// <returns>A Laplacian kernel initialized with an appropriate sigma value.</returns>
///
public static SparseLaplacian Estimate(double[][] inputs, int samples, out DoubleRange range)
{
if (samples > inputs.Length)
{
throw new ArgumentOutOfRangeException("samples");
}
double[] distances = Gaussian.Distances(inputs, samples);
double q1 = distances[(int)Math.Ceiling(0.15 * distances.Length)];
double q9 = distances[(int)Math.Ceiling(0.85 * distances.Length)];
double qm = distances.Median(alreadySorted: true);
range = new DoubleRange(q1, q9);
return(new SparseLaplacian(sigma: qm));
}
public void estimate_gaussian_distances()
{
Accord.Math.Random.Generator.Seed = 0;
double[][] data =
{
new double[] { 5.1, 3.5, 1.4, 0.2 },
new double[] { 5.0, 3.6, 1.4, 0.2 },
new double[] { 4.9, 3.0, 1.4, 0.2 },
new double[] { 5.8, 4.0, 1.2, 0.2 },
new double[] { 4.7, 3.2, 1.3, 0.2 },
};
var actual = Gaussian.Distances(data, 2);
Assert.IsTrue(actual.IsSorted());
Assert.AreEqual(0.95, actual.Mean(), 1e-5);
actual = Gaussian.Distances(data, data.Length);
Assert.IsTrue(actual.IsSorted());
Assert.AreEqual(0.5296, actual.Mean(), 1e-5);
Assert.Throws <ArgumentOutOfRangeException>(() => Gaussian.Distances(data, 10));
}
