Encog C# RBF网络，如何开始？

Question

我浏览了整个文档，但没有找到如何设置RBF网络的方法。在ConsoleExamples/Examples/Radial中找到了一些RBF示例，但是看起来它不再起作用了，因为Encog中的一些方法已经更改。

目前我被卡住了：

    public static double[][] XORInput = {
        new[] {0.0, 0.0},
        new[] {1.0, 0.0},
        new[] {0.0, 1.0},
        new[] {1.0, 1.0}
    };

    public static double[][] XORIdeal = {
        new[] {0.0},
        new[] {1.0},
        new[] {1.0},
        new[] {0.0}
    };

        int dimension = 8;
        int numNeuronsPerDimension = 64;
        double volumeNeuronWidth = 2.0 / numNeuronsPerDimension;
        bool includeEdgeRBFs = true;

        RBFNetwork n = new RBFNetwork(dimension, numNeuronsPerDimension, 1, RBFEnum.Gaussian);
        n.SetRBFCentersAndWidthsEqualSpacing(0, 1, RBFEnum.Gaussian, volumeNeuronWidth, includeEdgeRBFs);
        //n.RandomizeRBFCentersAndWidths(0, 1, RBFEnum.Gaussian);

        INeuralDataSet trainingSet = new BasicNeuralDataSet(XORInput, XORIdeal);
        SVDTraining train = new SVDTraining(n, trainingSet);

        int epoch = 1;
        do
        {
            train.Iteration();
            Console.WriteLine("Epoch #" + epoch + " Error:" + train.Error);
            epoch++;
        } while ((epoch < 1) && (train.Error > 0.001));

当我运行此代码时，SetRBFCentersAndWidthsEqualSpacing 方法会报错提示 "总的RBF神经元数量必须是某个整数的 'dimensions' 次幂."。如果我将此方法更改为 RandomizeRBFCentersAndWidths，直到达到 train.iteration()，则代码可以正常工作，但在那一步之后，会出现 "数组索引超出范围" 的错误提示。

我了解 RBF 网络的工作原理，但是对于 SetRBFCentersAndWidthsEqualSpacing 方法中的所有参数感到困惑，是否有人能够更详细地解释一下？

- EdWood

Answer 1

非常好的问题。

1. SetRBFCentersAndWidthsEqualSpacing and here is relatively new method of training neural networks and Jeff Heaton decided to implement it.

2. Looks like there is a difference between Java version and C# version at lines 230 - 240 and IMHO bug sits in Java version.

3. I've modified your code in order for it to be workable with additional comments:

   using System;
   using System.Collections.Generic;
   using System.Linq;
   using System.Text;
   using System.Threading.Tasks;
   using Encog.MathUtil.RBF;
   using Encog.Neural.Data.Basic;
   using Encog.Neural.NeuralData;
   using Encog.Neural.Rbf.Training;
   using Encog.Neural.RBF;
   
   namespace TestRBF
   {
       class Program
       {
           public static double[][] XORInput = {
           new[] {0.0, 0.0},
           new[] {1.0, 0.0},
           new[] {0.0, 1.0},
           new[] {1.0, 1.0}
       };
   
           public static double[][] XORIdeal = {
           new[] {0.0},
           new[] {1.0},
           new[] {1.0},
           new[] {0.0}
       };
   
           static void Main(string[] args)
           {
               int dimension = 2; // XORInput provides two-dimensional inputs. Not 8. 
               /*
               If XORInput is  8 dimensional  it should be like this:
   
               public static double[][] XORInput = {
               new[] {0.0, 0.0,0.0, 0.0,0.0, 0.0,0.0, 0.0}, 
               .
               .   
               .*/
               int numNeuronsPerDimension = 4; // could be also 16, 64, 256. I suppose it should accept 8, 32 but it needs additional investigation
               double volumeNeuronWidth = 2.0 / numNeuronsPerDimension;
               bool includeEdgeRBFs = true;
   
               RBFNetwork n = new RBFNetwork(dimension, numNeuronsPerDimension, 1, RBFEnum.Gaussian);
               n.SetRBFCentersAndWidthsEqualSpacing(0, 1, RBFEnum.Gaussian, volumeNeuronWidth, includeEdgeRBFs);
               //n.RandomizeRBFCentersAndWidths(0, 1, RBFEnum.Gaussian);
   
               INeuralDataSet trainingSet = new BasicNeuralDataSet(XORInput, XORIdeal);
               SVDTraining train = new SVDTraining(n, trainingSet);
   
               int epoch = 1;
               do
               {
                   train.Iteration();
                   Console.WriteLine("Epoch #" + epoch + " Error:" + train.Error);
                   epoch++;
               } while ((epoch < 1) && (train.Error > 0.001));
   
           }
       }
   }
   

- Yuriy Zaletskyy

---

我忘记改变我的维度，2是正确的。感谢您指出numNeuronsPerDimension，现在它可以工作了！我尝试了8、32，但都不行，所以只有16、64、256。 - EdWood

关于RBF中心和等宽间距算法的要求，与维度的幂次有关。 - Yuriy Zaletskyy

我认为.NET版本的第232行存在一个bug：var expectedSideLength = (int) Math.Pow(totalNumHiddenNeurons, 1.0d/dimensions); double cmp = Math.Pow(totalNumHiddenNeurons, 1.0d/dimensions); 如果expectedSideLength和cmp这两个变量不相等，那是因为"(int)"会对数字进行四舍五入。XOR示例可能偶然能够工作，但如果维度不同，例如19，则无法正常工作。 - EdWood

我建议为那个问题创建另一个SO线程。希望Jeff Heaton能加入我们的分析。 - Yuriy Zaletskyy

我已经创建了一个新的线程，但我不确定Jeff Heaton是否仍在这个项目上工作。http://stackoverflow.com/questions/40072675/encog-rbf-c-total-number-of-rbf-neurons-must-be-some-integer-to-the-power-of - EdWood