Question

我的问题和问题是加粗。

我通过在this one等文档页面上的示例成功使用了Accord.NET中的支持向量机。但是，当使用KernelSupportVectorMachine和OneclassSupportVectorLearning进行培训时，培训过程会导致较大的错误值和错误的分类。

下面的miminal示例显示了我的意思。它生成一个密集的训练点集群，然后训练SVM将点作为内点或异常值分类到集群。训练星团只有一个以原点为中心的0.6乘0.6平方，训练点的间隔为0.1：

static void Main(string[] args)
{
    // Model and training parameters
    double kernelSigma = 0.1;
    double teacherNu = 0.5;
    double teacherTolerance = 0.01;


    // Generate input point cloud, a 0.6 x 0.6 square centered at 0,0.
    double[][] trainingInputs = new double[49][];
    int inputIdx = 0;
    for (double x = -0.3; x <= 0.31; x += 0.1) {
        for (double y = -0.3; y <= 0.31; y += 0.1) {
            trainingInputs[inputIdx] = new double[] { x, y };
            inputIdx++;
        }
    }


    // Generate inlier and outlier test points.
    double[][] outliers =
    {
        new double[] { 1E6, 1E6 },  // Very far outlier
        new double[] { 0, 1E6 },    // Very far outlier
        new double[] { 100, -100 }, // Far outlier
        new double[] { 0, -100 },   // Far outlier
        new double[] { -10, -10 },  // Still far outlier
        new double[] { 0, -10 },    // Still far outlier
    };
    double[][] inliers =
    {
        new double[] { 0, 0 },      // Middle of cluster
        new double[] { .15, .15 },  // Halfway to corner of cluster
        new double[] { -0.1, 0 },   // Comfortably inside cluster
        new double[] { 0.25, 0 }    // Near inside edge of cluster
    };


    // Construct the kernel, model, and trainer, then train.
    Console.WriteLine($"Training model with parameters:");
    Console.WriteLine($"  kernelSigma = {kernelSigma.ToString("#.##")}");
    Console.WriteLine($"  teacherNu={teacherNu.ToString("#.##")}");
    Console.WriteLine($"  teacherTolerance={teacherTolerance}");
    Console.WriteLine();

    var kernel = new Gaussian(kernelSigma);
    var svm = new KernelSupportVectorMachine(kernel, inputs: 1);
    var teacher = new OneclassSupportVectorLearning(svm, trainingInputs)
    {
        Nu = teacherNu,
        Tolerance = teacherTolerance
    };
    double error = teacher.Run();

    Console.WriteLine($"Training complete - error is {error.ToString("#.##")}");
    Console.WriteLine();


    // Test trained classifier.
    Console.WriteLine("Testing outliers:");
    foreach (double[] outlier in outliers) {
        WriteResultDetail(svm, outlier);
    }
    Console.WriteLine();
    Console.WriteLine("Testing inliers:");
    foreach (double[] inlier in inliers) {
        WriteResultDetail(svm, inlier);
    }
}

private static void WriteResultDetail(KernelSupportVectorMachine svm, double[] coordinate)
{
    string prettyCoord = $"{{ {string.Join(", ", coordinate)} }}".PadRight(20);
    Console.Write($"Classifying: {prettyCoord} Result: ");

    // Classify coordinate, print results.
    double result = svm.Compute(coordinate);
    if (Math.Sign(result) == 1) {
        Console.Write("Inlier");
    }
    else {
        Console.Write("Outlier");
    }
    Console.Write($" ({result.ToString("#.##")})\n");
}

以下是合理参数集的输出：

Training model with parameters:
  kernelSigma = .1
  teacherNu=.5
  teacherTolerance=0.01

Training complete - error is 222.4

Testing outliers:
Classifying: { 1000000, 1000000 } Result: Inlier (2.28)
Classifying: { 0, 1000000 }       Result: Inlier (2.28)
Classifying: { 100, -100 }        Result: Inlier (2.28)
Classifying: { 0, -100 }          Result: Inlier (2.28)
Classifying: { -10, -10 }         Result: Inlier (2.28)
Classifying: { 0, -10 }           Result: Inlier (2.28)

Testing inliers:
Classifying: { 0, 0 }             Result: Inlier (4.58)
Classifying: { 0.15, 0.15 }       Result: Inlier (4.51)
Classifying: { -0.1, 0 }          Result: Inlier (4.55)
Classifying: { 0.25, 0 }          Result: Inlier (4.64)

括号中的数字是SVM为该坐标给出的分数。使用来自Accord.NET（以及一般）的SVM，负分数是一个类，正分数是另一个。在这里，一切都有积极的分数。内点被正确分类，但异常值（甚至非常远程的）也被归类为内点。

请注意，在我使用Accord.NET训练模型的任何其他时间，训练误差已经非常接近于零，但在这里它超过200.

这是另一个参数集的输出：

Training model with parameters:
  kernelSigma = .3
  teacherNu=.8
  teacherTolerance=0.01

Training complete - error is 1945.67

Testing outliers:
Classifying: { 1000000, 1000000 } Result: Inlier (20.96)
Classifying: { 0, 1000000 }       Result: Inlier (20.96)
Classifying: { 100, -100 }        Result: Inlier (20.96)
Classifying: { 0, -100 }          Result: Inlier (20.96)
Classifying: { -10, -10 }         Result: Inlier (20.96)
Classifying: { 0, -10 }           Result: Inlier (20.96)

Testing inliers:
Classifying: { 0, 0 }             Result: Inlier (44.52)
Classifying: { 0.15, 0.15 }       Result: Inlier (41.62)
Classifying: { -0.1, 0 }          Result: Inlier (43.85)
Classifying: { 0.25, 0 }          Result: Inlier (40.53)

同样，非常高的训练误差，所有正分数。

这些模型肯定会从培训中获得某些东西 - 内部和异常值之间的分数不同。但是为什么这个简单的场景不会给出正负符号的结果呢？

PS。 Here is a similar program测试许多培训和模型参数的组合，以及here is its output。同样，一切都会导致正分类分数，高误差值和错误分类的异常值。

Answer 1

issue raised in the question已在Accord.NET 3.7.0版中得到解决。提交unit test with an example similar to yours中也添加了be81aab。

为什么这个干净的数据提供了奇怪的SVM分类结果？

1 个答案: