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。
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。