为什么这些干净的数据提供了奇怪的SVM分类结果

本文关键字:SVM 结果 分类 数据 为什么 | 更新日期: 2023-09-27 17:59:10

我的问题在下面用粗体显示。

我已经成功地使用了Accord.NET的支持向量机,在它们的文档页面上举了这样的例子。但是,当使用带有OneclassSupportVectorLearning的KernelSupportVectorMachine进行训练时,训练过程会导致较大的错误值和不正确的分类

下面的例子说明了我的意思。它生成一个密集的训练点聚类,然后训练SVM将点分类为聚类的内点或外点。训练簇只是以原点为中心的0.6乘0.6的正方形,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。对于Accord.NET中的SVM(以及一般情况下),负分是一类,正分是另一类。在这里,一切都有一个积极的分数。Inlier被正确分类,但异常值(甚至非常遥远的值)也被分类为Inlier。

请注意,在我使用Accord.NET训练模型的其他任何时候,训练错误都非常接近于零,但这里的错误超过了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)

再次,非常高的训练失误,都是积极的分数。

模型肯定从训练中得到了的东西——内侧和外侧的分数不同。但是为什么这个简单的场景不能给出按正负号不同的结果


PS。这里有一个类似的程序,测试训练和模型参数的许多组合,下面是它的输出。同样,所有的结果都是正的分类分数、高错误值和错误分类的异常值。

为什么这些干净的数据提供了奇怪的SVM分类结果

问题中提出的问题已在Accord.NET的3.7.0版本中得到解决。commit be81aab中还添加了一个与您的示例类似的单元测试。